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[Octave-cvsupdate] SF.net SVN: octave:[9822] trunk/octave-forge/main/miscellaneous/inst/ publish.m

From: <car...@us...> - 2012-03-12 15:16:33

Revision: 9822
          http://octave.svn.sourceforge.net/octave/?rev=9822&view=rev
Author:   carandraug
Date:     2012-03-12 15:16:22 +0000 (Mon, 12 Mar 2012)
Log Message:
-----------
publish: fix bug due to incorrectly named variables

Modified Paths:
--------------
    trunk/octave-forge/main/miscellaneous/inst/publish.m

Modified: trunk/octave-forge/main/miscellaneous/inst/publish.m
===================================================================
--- trunk/octave-forge/main/miscellaneous/inst/publish.m	2012-03-12 15:06:46 UTC (rev 9821)
+++ trunk/octave-forge/main/miscellaneous/inst/publish.m	2012-03-12 15:16:22 UTC (rev 9822)
@@ -311,7 +311,7 @@
   if (!isempty (figures))
     for nfig = 1:length (figures)
       figure (figures(nfig));
-      print (sprintf ("%s%d.%s", iFile(1:end-2), nfig, options.imageFormat), 
+      print (sprintf ("%s%d.%s", ifile(1:end-2), nfig, options.imageFormat),
              sprintf ("-d%s", options.imageFormat), "-color");
       if (strcmpi (options.format, "html"));
         section3_title = "<h2>Generated graphics</h2>\n";
@@ -320,10 +320,10 @@
       elseif (strcmpi (options.format, "latex"))
         section3_title = "\\section*{Generated graphics}\n";
         disp_fig = strcat (disp_fig, "\\includegraphics[scale=0.6]{", ifile(1:end-2), 
-                           sprintf("%d",nFig), "}\n");
+                           sprintf("%d",nfig), "}\n");
       endif
-    endfor  
-  endif      
+    endfor
+  endif
 endfunction
 
 % TO DO

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[Octave-cvsupdate] SF.net SVN: octave:[9821] trunk/octave-forge/main/miscellaneous

From: <car...@us...> - 2012-03-12 15:06:57

Revision: 9821
          http://octave.svn.sourceforge.net/octave/?rev=9821&view=rev
Author:   carandraug
Date:     2012-03-12 15:06:46 +0000 (Mon, 12 Mar 2012)
Log Message:
-----------
map: deprecating function in favour of cellfun or arrayfun

Modified Paths:
--------------
    trunk/octave-forge/main/miscellaneous/NEWS
    trunk/octave-forge/main/miscellaneous/inst/apply.m
    trunk/octave-forge/main/miscellaneous/inst/map.m

Modified: trunk/octave-forge/main/miscellaneous/NEWS
===================================================================
--- trunk/octave-forge/main/miscellaneous/NEWS	2012-03-12 14:39:15 UTC (rev 9820)
+++ trunk/octave-forge/main/miscellaneous/NEWS	2012-03-12 15:06:46 UTC (rev 9821)
@@ -19,8 +19,8 @@
 
  ** The function clip was imported from the audio package.
 
- ** The function `apply' has been deprecated. `cellfun' and `arrayfun' from
-    octave core should be used instead.
+ ** The functions `apply' and `map' have been deprecated. `cellfun' and
+    `arrayfun' from octave core should be used instead.
 
  ** The function `partarray' has been removed. `mat2cell' from octave core
     should be used instead.

Modified: trunk/octave-forge/main/miscellaneous/inst/apply.m
===================================================================
--- trunk/octave-forge/main/miscellaneous/inst/apply.m	2012-03-12 14:39:15 UTC (rev 9820)
+++ trunk/octave-forge/main/miscellaneous/inst/apply.m	2012-03-12 15:06:46 UTC (rev 9821)
@@ -59,9 +59,7 @@
   if (! warned)
     warned = true;
     warning ("Octave:deprecated-function",
-             "apply.m has been deprecated, and will be removed in the future.")
-    warning ("Octave:deprecated-function",
-             "Use `arrayfun' or `cellfun' instead.");
+             "apply has been deprecated, and will be removed in the future. Use `arrayfun' or `cellfun' instead.");
   endif
 
   if (nargin == 0)
@@ -70,7 +68,7 @@
   elseif( nargin < 2)
     if iscell(fun_handle)
       for idx=1:length(fun_handle)
-	rval(idx)=feval(@feval,fun_handle{idx});
+        rval(idx)=feval(@feval,fun_handle{idx});
       end
     else
       rval=feval(@feval,fun_handle);

Modified: trunk/octave-forge/main/miscellaneous/inst/map.m
===================================================================
--- trunk/octave-forge/main/miscellaneous/inst/map.m	2012-03-12 14:39:15 UTC (rev 9820)
+++ trunk/octave-forge/main/miscellaneous/inst/map.m	2012-03-12 15:06:46 UTC (rev 9821)
@@ -62,6 +62,13 @@
 
 function return_type = map (fun_handle, data_struct, varargin)
 
+  persistent warned = false;
+  if (! warned)
+    warned = true;
+    warning ("Octave:deprecated-function",
+             "map has been deprecated, and will be removed in the future. Use `arrayfun' or `cellfun' instead.");
+  endif
+
   if (nargin < 2)
     print_usage;
   elseif (!(isnumeric (data_struct) || iscell (data_struct)))

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[Octave-cvsupdate] SF.net SVN: octave:[9820] trunk/octave-forge/main/queueing

From: <mma...@us...> - 2012-03-12 14:39:24

Revision: 9820
          http://octave.svn.sourceforge.net/octave/?rev=9820&view=rev
Author:   mmarzolla
Date:     2012-03-12 14:39:15 +0000 (Mon, 12 Mar 2012)
Log Message:
-----------
Enhancements to dtmc_mtta()

Modified Paths:
--------------
    trunk/octave-forge/main/queueing/doc/queueing.html
    trunk/octave-forge/main/queueing/doc/queueing.pdf
    trunk/octave-forge/main/queueing/doc/summary.txi
    trunk/octave-forge/main/queueing/inst/dtmc_mtta.m

Modified: trunk/octave-forge/main/queueing/doc/queueing.html
===================================================================
--- trunk/octave-forge/main/queueing/doc/queueing.html	2012-03-12 12:10:43 UTC (rev 9819)
+++ trunk/octave-forge/main/queueing/doc/queueing.html	2012-03-12 14:39:15 UTC (rev 9820)
@@ -218,11 +218,11 @@
 chains (DTMC) or continuous-time chains (CTMC):
 
      <ul>
-<li>Birth-death process (DTMC and CTMC);
-<li>Transient and steady-state occupancy probabilities (DTMC and CTMC);
-<li>Mean time to absorption (CTMC);
-<li>Time-averaged sojourn times (CTMC);
-<li>First passage times (DTMC and CTMC).
+<li>Birth-death process;
+<li>Transient and steady-state occupancy probabilities;
+<li>Mean times to absorption;
+<li>Expected sojourn times and time-averaged sojourn times (CTMC only);
+<li>Mean first passage times;
 
    </ul>
 
@@ -1007,28 +1007,39 @@
 
 <div class="defun">
 &mdash; Function File: [<var>t</var> <var>B</var>] = <b>dtmc_mtta</b> (<var>P</var>)<var><a name="index-dtmc_005fmtta-16"></a></var><br>
+&mdash; Function File: [<var>t</var> <var>B</var>] = <b>dtmc_mtta</b> (<var>P, p0</var>)<var><a name="index-dtmc_005fmtta-17"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-disctete-time-17"></a><a name="index-Mean-time-to-absorption-18"></a>
-Compute the expected number of steps before absorption for the DTMC
-described by the transition probability matrix <var>P</var>,
+        <p><a name="index-Markov-chain_002c-disctete-time-18"></a><a name="index-Mean-time-to-absorption-19"></a>
+Compute the expected number of steps before absorption for the
+DTMC with N \times N transition probability matrix <var>P</var>.
 
         <p><strong>INPUTS</strong>
 
           <dl>
-<dt><var>P</var><dd>Transition probability matrix .
+<dt><var>P</var><dd>Transition probability matrix.
 
+          <br><dt><var>p0</var><dd>Initial state occupancy probabilities.
+
         </dl>
 
         <p><strong>OUTPUTS</strong>
 
           <dl>
-<dt><var>t</var><dd><var>t</var><code>(i)</code> is the expected number of steps before being absorbed,
-starting from state i.
+<dt><var>t</var><dd>When called with a single argument, <var>t</var> is a vector such that
+<var>t</var><code>(i)</code> is the expected number of steps before being
+absorbed, starting from state i. When called with two
+arguments, <var>t</var> is a scalar and represents the average number of
+steps before absorption, given initial state occupancy probabilities
+<var>p0</var>.
 
-          <br><dt><var>B</var><dd><var>B</var><code>(i,j)</code> is the probability of being absorbed in state
-j, starting from state i. If j is not absorbing,
-<var>B</var><code>(i,j) = 0</code>; if i is absorbing, then
-<var>B</var><code>(i,i) = 1</code>..
+          <br><dt><var>B</var><dd>When called with a single argument, <var>B</var> is a N \times N
+matrix where <var>B</var><code>(i,j)</code> is the probability of being absorbed
+in state j, starting from state i; if j is not
+absorbing, <var>B</var><code>(i,j) = 0</code>; if i is absorbing, then
+<var>B</var><code>(i,i) = 1</code>. When called with two arguments, <var>B</var> is a
+vector with N elements where <var>B</var><code>(j)</code> is the
+probability of being absorbed in state <var>j</var>, given initial state
+occupancy probabilities <var>p0</var>.
 
         </dl>
 
@@ -1062,9 +1073,9 @@
    <p><a name="doc_002dctmc_005fcheck_005fQ"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>result</var> <var>err</var>] = <b>ctmc_check_Q</b> (<var>Q</var>)<var><a name="index-ctmc_005fcheck_005fQ-19"></a></var><br>
+&mdash; Function File: [<var>result</var> <var>err</var>] = <b>ctmc_check_Q</b> (<var>Q</var>)<var><a name="index-ctmc_005fcheck_005fQ-20"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-20"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-21"></a>
 If <var>Q</var> is a valid infinitesimal generator matrix, return
 the size (number of rows or columns) of <var>Q</var>. If <var>Q</var> is not
 an infinitesimal generator matrix, set <var>result</var> to zero, and
@@ -1114,10 +1125,10 @@
    <p><a name="doc_002dctmc"></a>
 
 <div class="defun">
-&mdash; Function File: <var>p</var> = <b>ctmc</b> (<var>Q</var>)<var><a name="index-ctmc-21"></a></var><br>
-&mdash; Function File: <var>p</var> = <b>ctmc</b> (<var>Q, t. p0</var>)<var><a name="index-ctmc-22"></a></var><br>
+&mdash; Function File: <var>p</var> = <b>ctmc</b> (<var>Q</var>)<var><a name="index-ctmc-22"></a></var><br>
+&mdash; Function File: <var>p</var> = <b>ctmc</b> (<var>Q, t. p0</var>)<var><a name="index-ctmc-23"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-23"></a><a name="index-Continuous-time-Markov-chain-24"></a><a name="index-Markov-chain_002c-state-occupancy-probabilities-25"></a><a name="index-Stationary-probabilities-26"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-24"></a><a name="index-Continuous-time-Markov-chain-25"></a><a name="index-Markov-chain_002c-state-occupancy-probabilities-26"></a><a name="index-Stationary-probabilities-27"></a>
 With a single argument, compute the stationary state occupancy
 probability vector <var>p</var>(1), <small class="dots">...</small>, <var>p</var>(N) for a
 Continuous-Time Markov Chain with infinitesimal generator matrix
@@ -1180,9 +1191,9 @@
 <p><a name="doc_002dctmc_005fbd"></a>
 
 <div class="defun">
-&mdash; Function File: <var>Q</var> = <b>ctmc_bd</b> (<var>birth, death</var>)<var><a name="index-ctmc_005fbd-27"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>ctmc_bd</b> (<var>birth, death</var>)<var><a name="index-ctmc_005fbd-28"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-28"></a><a name="index-Birth_002ddeath-process-29"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-29"></a><a name="index-Birth_002ddeath-process-30"></a>
 Returns the N \times N infinitesimal generator matrix Q
 for a birth-death process with given rates.
 
@@ -1242,10 +1253,10 @@
    <p><a name="doc_002dctmc_005fexps"></a>
 
 <div class="defun">
-&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, t, p </var>)<var><a name="index-ctmc_005fexps-30"></a></var><br>
-&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fexps-31"></a></var><br>
+&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, t, p </var>)<var><a name="index-ctmc_005fexps-31"></a></var><br>
+&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fexps-32"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-32"></a><a name="index-Expected-sojourn-time-33"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-33"></a><a name="index-Expected-sojourn-time-34"></a>
 With three arguments, compute the expected times <var>L</var><code>(i)</code>
 spent in each state i during the time interval
 [0,t], assuming that the state occupancy probabilities
@@ -1325,9 +1336,9 @@
 <p><a name="doc_002dctmc_005ftaexps"></a>
 
 <div class="defun">
-&mdash; Function File: <var>M</var> = <b>ctmc_taexps</b> (<var>Q, t, p</var>)<var><a name="index-ctmc_005ftaexps-34"></a></var><br>
+&mdash; Function File: <var>M</var> = <b>ctmc_taexps</b> (<var>Q, t, p</var>)<var><a name="index-ctmc_005ftaexps-35"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-35"></a><a name="index-Time_002dalveraged-sojourn-time-36"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-36"></a><a name="index-Time_002dalveraged-sojourn-time-37"></a>
 Compute the <em>time-averaged sojourn time</em> <var>M</var><code>(i)</code>,
 defined as the fraction of the time interval [0,t] spent in
 state i, assuming that the state occupancy probabilities at
@@ -1410,9 +1421,9 @@
    <p><a name="doc_002dctmc_005fmtta"></a>
 
 <div class="defun">
-&mdash; Function File: <var>t</var> = <b>ctmc_mtta</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fmtta-37"></a></var><br>
+&mdash; Function File: <var>t</var> = <b>ctmc_mtta</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fmtta-38"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-38"></a><a name="index-Mean-time-to-absorption-39"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-39"></a><a name="index-Mean-time-to-absorption-40"></a>
 Compute the Mean-Time to Absorption (MTTA) of the CTMC described by
 the infinitesimal generator matrix <var>Q</var>, starting from initial
 occupancy probabilities <var>p</var>. If there are no absorbing states, this
@@ -1473,7 +1484,7 @@
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998.
 
-   <p><a name="index-Bolch_002c-G_002e-40"></a><a name="index-Greiner_002c-S_002e-41"></a><a name="index-de-Meer_002c-H_002e-42"></a><a name="index-Trivedi_002c-K_002e-43"></a>
+   <p><a name="index-Bolch_002c-G_002e-41"></a><a name="index-Greiner_002c-S_002e-42"></a><a name="index-de-Meer_002c-H_002e-43"></a><a name="index-Trivedi_002c-K_002e-44"></a>
 <div class="node">
 <a name="First-Passage-Times"></a>
 <p><hr>
@@ -1487,10 +1498,10 @@
 <p><a name="doc_002dctmc_005ffpt"></a>
 
 <div class="defun">
-&mdash; Function File: <var>M</var> = <b>ctmc_fpt</b> (<var>Q</var>)<var><a name="index-ctmc_005ffpt-44"></a></var><br>
-&mdash; Function File: <var>m</var> = <b>ctmc_fpt</b> (<var>Q, i, j</var>)<var><a name="index-ctmc_005ffpt-45"></a></var><br>
+&mdash; Function File: <var>M</var> = <b>ctmc_fpt</b> (<var>Q</var>)<var><a name="index-ctmc_005ffpt-45"></a></var><br>
+&mdash; Function File: <var>m</var> = <b>ctmc_fpt</b> (<var>Q, i, j</var>)<var><a name="index-ctmc_005ffpt-46"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-46"></a><a name="index-First-passage-times-47"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-47"></a><a name="index-First-passage-times-48"></a>
 If called with a single argument, computes the mean first passage
 times <var>M</var><code>(i,j)</code>, the average times before state <var>j</var> is
 reached, starting from state <var>i</var>, for all 1 \leq i, j \leq
@@ -1596,9 +1607,9 @@
    <p><a name="doc_002dqnmm1"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmm1</b> (<var>lambda, mu</var>)<var><a name="index-qnmm1-48"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmm1</b> (<var>lambda, mu</var>)<var><a name="index-qnmm1-49"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002f1_007d-system-49"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002f1_007d-system-50"></a>
 Compute utilization, response time, average number of requests
 and throughput for a M/M/1 queue.
 
@@ -1643,7 +1654,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.3.
 
-   <p><a name="index-Bolch_002c-G_002e-50"></a><a name="index-Greiner_002c-S_002e-51"></a><a name="index-de-Meer_002c-H_002e-52"></a><a name="index-Trivedi_002c-K_002e-53"></a>
+   <p><a name="index-Bolch_002c-G_002e-51"></a><a name="index-Greiner_002c-S_002e-52"></a><a name="index-de-Meer_002c-H_002e-53"></a><a name="index-Trivedi_002c-K_002e-54"></a>
 <!-- M/M/m -->
 <div class="node">
 <a name="The-M%2fM%2fm-System"></a>
@@ -1669,10 +1680,10 @@
    <p><a name="doc_002dqnmmm"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu</var>)<var><a name="index-qnmmm-54"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu, m</var>)<var><a name="index-qnmmm-55"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu</var>)<var><a name="index-qnmmm-55"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu, m</var>)<var><a name="index-qnmmm-56"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002fm_007d-system-56"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002fm_007d-system-57"></a>
 Compute utilization, response time, average number of requests in
 service and throughput for a M/M/m queue, a queueing
 system with m identical service centers connected to a single queue.
@@ -1724,7 +1735,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.5.
 
-   <p><a name="index-Bolch_002c-G_002e-57"></a><a name="index-Greiner_002c-S_002e-58"></a><a name="index-de-Meer_002c-H_002e-59"></a><a name="index-Trivedi_002c-K_002e-60"></a>
+   <p><a name="index-Bolch_002c-G_002e-58"></a><a name="index-Greiner_002c-S_002e-59"></a><a name="index-de-Meer_002c-H_002e-60"></a><a name="index-Trivedi_002c-K_002e-61"></a>
 <!-- M/M/inf -->
 <div class="node">
 <a name="The-M%2fM%2finf-System"></a>
@@ -1747,7 +1758,7 @@
    <p><a name="doc_002dqnmminf"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmminf</b> (<var>lambda, mu</var>)<var><a name="index-qnmminf-61"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmminf</b> (<var>lambda, mu</var>)<var><a name="index-qnmminf-62"></a></var><br>
 <blockquote>
         <p>Compute utilization, response time, average number of requests and
 throughput for a M/M/\infty queue. This is a system with an
@@ -1755,7 +1766,7 @@
 system is always stable, regardless the values of the arrival and
 service rates.
 
-        <p><a name="index-g_t_0040math_007bM_002fM_002f_007dinf-system-62"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002f_007dinf-system-63"></a>
 
         <p><strong>INPUTS</strong>
 
@@ -1773,7 +1784,7 @@
 different from the utilization, which in the case of M/M/\infty
 centers is always zero.
 
-          <p><a name="index-traffic-intensity-63"></a>
+          <p><a name="index-traffic-intensity-64"></a>
 <br><dt><var>R</var><dd>Service center response time.
 
           <br><dt><var>Q</var><dd>Average number of requests in the system (which is equal to the
@@ -1801,7 +1812,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.4.
 
-   <p><a name="index-Bolch_002c-G_002e-64"></a><a name="index-Greiner_002c-S_002e-65"></a><a name="index-de-Meer_002c-H_002e-66"></a><a name="index-Trivedi_002c-K_002e-67"></a>
+   <p><a name="index-Bolch_002c-G_002e-65"></a><a name="index-Greiner_002c-S_002e-66"></a><a name="index-de-Meer_002c-H_002e-67"></a><a name="index-Trivedi_002c-K_002e-68"></a>
 <!-- M/M/1/k -->
 <div class="node">
 <a name="The-M%2fM%2f1%2fK-System"></a>
@@ -1825,9 +1836,9 @@
    <p><a name="doc_002dqnmm1k"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmm1k</b> (<var>lambda, mu, K</var>)<var><a name="index-qnmm1k-68"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmm1k</b> (<var>lambda, mu, K</var>)<var><a name="index-qnmm1k-69"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002f1_002fK_007d-system-69"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002f1_002fK_007d-system-70"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/M/1/K finite capacity system. In a
 M/M/1/K queue there is a single server; the maximum number of
@@ -1894,9 +1905,9 @@
    <p><a name="doc_002dqnmmmk"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmmmk</b> (<var>lambda, mu, m, K</var>)<var><a name="index-qnmmmk-70"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmmmk</b> (<var>lambda, mu, m, K</var>)<var><a name="index-qnmmmk-71"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002fm_002fK_007d-system-71"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002fm_002fK_007d-system-72"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/M/m/K finite capacity system. In a
 M/M/m/K system there are m \geq 1 identical service
@@ -1954,7 +1965,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.6.
 
-   <p><a name="index-Bolch_002c-G_002e-72"></a><a name="index-Greiner_002c-S_002e-73"></a><a name="index-de-Meer_002c-H_002e-74"></a><a name="index-Trivedi_002c-K_002e-75"></a>
+   <p><a name="index-Bolch_002c-G_002e-73"></a><a name="index-Greiner_002c-S_002e-74"></a><a name="index-de-Meer_002c-H_002e-75"></a><a name="index-Trivedi_002c-K_002e-76"></a>
 
 <!-- Approximate M/M/m -->
 <div class="node">
@@ -1976,9 +1987,9 @@
    <p><a name="doc_002dqnammm"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnammm</b> (<var>lambda, mu</var>)<var><a name="index-qnammm-76"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnammm</b> (<var>lambda, mu</var>)<var><a name="index-qnammm-77"></a></var><br>
 <blockquote>
-        <p><a name="index-Asymmetric-_0040math_007bM_002fM_002fm_007d-system-77"></a>
+        <p><a name="index-Asymmetric-_0040math_007bM_002fM_002fm_007d-system-78"></a>
 Compute <em>approximate</em> utilization, response time, average number
 of requests in service and throughput for an asymmetric  M/M/m
 queue. In this system there are m different service centers
@@ -2025,7 +2036,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998
 
-   <p><a name="index-Bolch_002c-G_002e-78"></a><a name="index-Greiner_002c-S_002e-79"></a><a name="index-de-Meer_002c-H_002e-80"></a><a name="index-Trivedi_002c-K_002e-81"></a>
+   <p><a name="index-Bolch_002c-G_002e-79"></a><a name="index-Greiner_002c-S_002e-80"></a><a name="index-de-Meer_002c-H_002e-81"></a><a name="index-Trivedi_002c-K_002e-82"></a>
 <div class="node">
 <a name="The-M%2fG%2f1-System"></a>
 <a name="The-M_002fG_002f1-System"></a>
@@ -2041,9 +2052,9 @@
 <p><a name="doc_002dqnmg1"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmg1</b> (<var>lambda, xavg, x2nd</var>)<var><a name="index-qnmg1-82"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmg1</b> (<var>lambda, xavg, x2nd</var>)<var><a name="index-qnmg1-83"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fG_002f1_007d-system-83"></a>
+        <p><a name="index-g_t_0040math_007bM_002fG_002f1_007d-system-84"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/G/1 system. The service time distribution
 is described by its mean <var>xavg</var>, and by its second moment
@@ -2100,9 +2111,9 @@
 <p><a name="doc_002dqnmh1"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmh1</b> (<var>lambda, mu, alpha</var>)<var><a name="index-qnmh1-84"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmh1</b> (<var>lambda, mu, alpha</var>)<var><a name="index-qnmh1-85"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fH_005fm_002f1_007d-system-85"></a>
+        <p><a name="index-g_t_0040math_007bM_002fH_005fm_002f1_007d-system-86"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/H_m/1 system. In this system, the customer
 service times have hyper-exponential distribution:
@@ -2184,7 +2195,7 @@
 <li><a accesskey="6" href="#Utility-functions">Utility functions</a>:                    Utility functions to compute miscellaneous quantities
 </ul>
 
-<p><a name="index-queueing-networks-86"></a>
+<p><a name="index-queueing-networks-87"></a>
 <!-- INTRODUCTION -->
 <div class="node">
 <a name="Introduction-to-QNs"></a>
@@ -2445,13 +2456,13 @@
    <p><a name="doc_002dqnmknode"></a>
 
 <div class="defun">
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S</var>)<var><a name="index-qnmknode-87"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S, m</var>)<var><a name="index-qnmknode-88"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/1-lcfs-pr", S</var>)<var><a name="index-qnmknode-89"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S</var>)<var><a name="index-qnmknode-90"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S, s2</var>)<var><a name="index-qnmknode-91"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S</var>)<var><a name="index-qnmknode-92"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S, s2</var>)<var><a name="index-qnmknode-93"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S</var>)<var><a name="index-qnmknode-88"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S, m</var>)<var><a name="index-qnmknode-89"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/1-lcfs-pr", S</var>)<var><a name="index-qnmknode-90"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S</var>)<var><a name="index-qnmknode-91"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S, s2</var>)<var><a name="index-qnmknode-92"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S</var>)<var><a name="index-qnmknode-93"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S, s2</var>)<var><a name="index-qnmknode-94"></a></var><br>
 <blockquote>
         <p>Creates a node; this function can be used together with
 <code>qnsolve</code>. It is possible to create either single-class nodes
@@ -2520,10 +2531,10 @@
    <p><a name="doc_002dqnsolve"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V</var>)<var><a name="index-qnsolve-94"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V, Z</var>)<var><a name="index-qnsolve-95"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"open", lambda, QQ, V</var>)<var><a name="index-qnsolve-96"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"mixed", lambda, N, QQ, V</var>)<var><a name="index-qnsolve-97"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V</var>)<var><a name="index-qnsolve-95"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V, Z</var>)<var><a name="index-qnsolve-96"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"open", lambda, QQ, V</var>)<var><a name="index-qnsolve-97"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"mixed", lambda, N, QQ, V</var>)<var><a name="index-qnsolve-98"></a></var><br>
 <blockquote>
         <p>General evaluator of QN models. Networks can be open,
 closed or mixed; single as well as multiclass networks are supported.
@@ -2701,11 +2712,11 @@
    <p><a name="doc_002dqnjackson"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P </var>)<var><a name="index-qnjackson-98"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P, m </var>)<var><a name="index-qnjackson-99"></a></var><br>
-&mdash; Function File: <var>pr</var> = <b>qnjackson</b> (<var>lambda, S, P, m, k</var>)<var><a name="index-qnjackson-100"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P </var>)<var><a name="index-qnjackson-99"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P, m </var>)<var><a name="index-qnjackson-100"></a></var><br>
+&mdash; Function File: <var>pr</var> = <b>qnjackson</b> (<var>lambda, S, P, m, k</var>)<var><a name="index-qnjackson-101"></a></var><br>
 <blockquote>
-        <p><a name="index-open-network_002c-single-class-101"></a><a name="index-Jackson-network-102"></a>
+        <p><a name="index-open-network_002c-single-class-102"></a><a name="index-Jackson-network-103"></a>
 With three or four input parameters, this function computes the
 steady-state occupancy probabilities for a Jackson network. With five
 input parameters, this function computes the steady-state probability
@@ -2787,7 +2798,7 @@
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998, pp. 284&ndash;287.
 
-   <p><a name="index-Bolch_002c-G_002e-103"></a><a name="index-Greiner_002c-S_002e-104"></a><a name="index-de-Meer_002c-H_002e-105"></a><a name="index-Trivedi_002c-K_002e-106"></a>
+   <p><a name="index-Bolch_002c-G_002e-104"></a><a name="index-Greiner_002c-S_002e-105"></a><a name="index-de-Meer_002c-H_002e-106"></a><a name="index-Trivedi_002c-K_002e-107"></a>
 
 <h4 class="subsection">6.3.2 The Convolution Algorithm</h4>
 
@@ -2821,10 +2832,10 @@
    <p><a name="doc_002dqnconvolution"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V</var>)<var><a name="index-qnconvolution-107"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V, m</var>)<var><a name="index-qnconvolution-108"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V</var>)<var><a name="index-qnconvolution-108"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V, m</var>)<var><a name="index-qnconvolution-109"></a></var><br>
 <blockquote>
-        <p><a name="index-closed-network-109"></a><a name="index-normalization-constant-110"></a><a name="index-convolution-algorithm-111"></a>
+        <p><a name="index-closed-network-110"></a><a name="index-normalization-constant-111"></a><a name="index-convolution-algorithm-112"></a>
 This function implements the <em>convolution algorithm</em> for
 computing steady-state performance measures of product-form,
 single-class closed queueing networks. Load-independent service
@@ -2915,20 +2926,20 @@
 16, number 9, september 1973,
 pp. 527&ndash;531. <a href="http://doi.acm.org/10.1145/362342.362345">http://doi.acm.org/10.1145/362342.362345</a>
 
-   <p><a name="index-Buzen_002c-J_002e-P_002e-112"></a>
+   <p><a name="index-Buzen_002c-J_002e-P_002e-113"></a>
 This implementation is based on G. Bolch, S. Greiner, H. de Meer and
 K. Trivedi, <cite>Queueing Networks and Markov Chains: Modeling and
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998, pp. 313&ndash;317.
 
-   <p><a name="index-Bolch_002c-G_002e-113"></a><a name="index-Greiner_002c-S_002e-114"></a><a name="index-de-Meer_002c-H_002e-115"></a><a name="index-Trivedi_002c-K_002e-116"></a>
+   <p><a name="index-Bolch_002c-G_002e-114"></a><a name="index-Greiner_002c-S_002e-115"></a><a name="index-de-Meer_002c-H_002e-116"></a><a name="index-Trivedi_002c-K_002e-117"></a>
 <!-- Convolution for load-dependent service centers -->
 <a name="doc_002dqnconvolutionld"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolutionld</b> (<var>N, S, V</var>)<var><a name="index-qnconvolutionld-117"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolutionld</b> (<var>N, S, V</var>)<var><a name="index-qnconvolutionld-118"></a></var><br>
 <blockquote>
-        <p><a name="index-closed-network-118"></a><a name="index-normalization-constant-119"></a><a name="index-convolution-algorithm-120"></a><a name="index-load_002ddependent-service-center-121"></a>
+        <p><a name="index-closed-network-119"></a><a name="index-normalization-constant-120"></a><a name="index-convolution-algorithm-121"></a><a name="index-load_002ddependent-service-center-122"></a>
 This function implements the <em>convolution algorithm</em> for
 product-form, single-class closed queueing networks with general
 load-dependent service centers.
@@ -2988,7 +2999,7 @@
 Purdue University, feb, 1981 (revised). 
 <a href="http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-354.pdf">http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-354.pdf</a>
 
-   <p><a name="index-Schwetman_002c-H_002e-122"></a>
+   <p><a name="index-Schwetman_002c-H_002e-123"></a>
 M. Reiser, H. Kobayashi, <cite>On The Convolution Algorithm for
 Separable Queueing Networks</cite>, In Proceedings of the 1976 ACM
 SIGMETRICS Conference on Computer Performance Modeling Measurement and
@@ -2996,7 +3007,7 @@
 1976). SIGMETRICS '76. ACM, New York, NY,
 pp. 109&ndash;117. <a href="http://doi.acm.org/10.1145/800200.806187">http://doi.acm.org/10.1145/800200.806187</a>
 
-   <p><a name="index-Reiser_002c-M_002e-123"></a><a name="index-Kobayashi_002c-H_002e-124"></a>
+   <p><a name="index-Reiser_002c-M_002e-124"></a><a name="index-Kobayashi_002c-H_002e-125"></a>
 This implementation is based on G. Bolch, S. Greiner, H. de Meer and
 K. Trivedi, <cite>Queueing Networks and Markov Chains: Modeling and
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
@@ -3008,7 +3019,7 @@
 function f_i defined in Schwetman, <code>Some Computational
 Aspects of Queueing Network Models</code>.
 
-   <p><a name="index-Bolch_002c-G_002e-125"></a><a name="index-Greiner_002c-S_002e-126"></a><a name="index-de-Meer_002c-H_002e-127"></a><a name="index-Trivedi_002c-K_002e-128"></a>
+   <p><a name="index-Bolch_002c-G_002e-126"></a><a name="index-Greiner_002c-S_002e-127"></a><a name="index-de-Meer_002c-H_002e-128"></a><a name="index-Trivedi_002c-K_002e-129"></a>
 
 <h4 class="subsection">6.3.3 Open networks</h4>
 
@@ -3016,10 +3027,10 @@
 <p><a name="doc_002dqnopensingle"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V</var>)<var><a name="index-qnopensingle-129"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopensingle-130"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V</var>)<var><a name="index-qnopensingle-130"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopensingle-131"></a></var><br>
 <blockquote>
-        <p><a name="index-open-network_002c-single-class-131"></a><a name="index-BCMP-network-132"></a>
+        <p><a name="index-open-network_002c-single-class-132"></a><a name="index-BCMP-network-133"></a>
 Analyze open, single class BCMP queueing networks.
 
         <p>This function works for a subset of BCMP single-class open networks
@@ -3112,16 +3123,16 @@
 Networks and Markov Chains: Modeling and Performance Evaluation with
 Computer Science Applications</cite>, Wiley, 1998.
 
-   <p><a name="index-Bolch_002c-G_002e-133"></a><a name="index-Greiner_002c-S_002e-134"></a><a name="index-de-Meer_002c-H_002e-135"></a><a name="index-Trivedi_002c-K_002e-136"></a>
+   <p><a name="index-Bolch_002c-G_002e-134"></a><a name="index-Greiner_002c-S_002e-135"></a><a name="index-de-Meer_002c-H_002e-136"></a><a name="index-Trivedi_002c-K_002e-137"></a>
 
 <!-- Open network with multiple classes -->
    <p><a name="doc_002dqnopenmulti"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V</var>)<var><a name="index-qnopenmulti-137"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopenmulti-138"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V</var>)<var><a name="index-qnopenmulti-138"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopenmulti-139"></a></var><br>
 <blockquote>
-        <p><a name="index-open-network_002c-multiple-classes-139"></a>
+        <p><a name="index-open-network_002c-multiple-classes-140"></a>
 Exact analysis of open, multiple-class BCMP networks. The network can
 be made of <em>single-server</em> queueing centers (FCFS, LCFS-PR or
 PS) or delay centers (IS). This function assumes a network with
@@ -3186,7 +3197,7 @@
 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In
 particular, see section 7.4.1 ("Open Model Solution Techniques").
 
-   <p><a name="index-Lazowska_002c-E_002e-D_002e-140"></a><a name="index-Zahorjan_002c-J_002e-141"></a><a name="index-Graham_002c-G_002e-S_002e-142"></a><a name="index-Sevcik_002c-K_002e-C_002e-143"></a>
+   <p><a name="index-Lazowska_002c-E_002e-D_002e-141"></a><a name="index-Zahorjan_002c-J_002e-142"></a><a name="index-Graham_002c-G_002e-S_002e-143"></a><a name="index-Sevcik_002c-K_002e-C_002e-144"></a>
 
 <h4 class="subsection">6.3.4 Closed Networks</h4>
 
@@ -3194,11 +3205,11 @@
 <p><a name="doc_002dqnclosedsinglemva"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemva-144"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemva-145"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemva-146"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemva-145"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemva-146"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemva-147"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-147"></a><a name="index-closed-network_002c-single-class-148"></a><a name="index-normalization-constant-149"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-148"></a><a name="index-closed-network_002c-single-class-149"></a><a name="index-normalization-constant-150"></a>
 Analyze closed, single class queueing networks using the exact Mean
 Value Analysis (MVA) algorithm. The following queueing disciplines
 are supported: FCFS, LCFS-PR, PS and IS (Infinite Server). This
@@ -3299,7 +3310,7 @@
 Multichain Queuing Networks</cite>, Journal of the ACM, vol. 27, n. 2, April
 1980, pp. 313&ndash;322. <a href="http://doi.acm.org/10.1145/322186.322195">http://doi.acm.org/10.1145/322186.322195</a>
 
-   <p><a name="index-Reiser_002c-M_002e-150"></a><a name="index-Lavenberg_002c-S_002e-S_002e-151"></a>
+   <p><a name="index-Reiser_002c-M_002e-151"></a><a name="index-Lavenberg_002c-S_002e-S_002e-152"></a>
 This implementation is described in R. Jain , <cite>The Art of Computer
 Systems Performance Analysis</cite>, Wiley, 1991, p. 577.  Multi-server nodes
 <!-- and the computation of @math{G(N)}, -->
@@ -3308,15 +3319,15 @@
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998, Section 8.2.1, "Single Class Queueing Networks".
 
-   <p><a name="index-Jain_002c-R_002e-152"></a><a name="index-Bolch_002c-G_002e-153"></a><a name="index-Greiner_002c-S_002e-154"></a><a name="index-de-Meer_002c-H_002e-155"></a><a name="index-Trivedi_002c-K_002e-156"></a>
+   <p><a name="index-Jain_002c-R_002e-153"></a><a name="index-Bolch_002c-G_002e-154"></a><a name="index-Greiner_002c-S_002e-155"></a><a name="index-de-Meer_002c-H_002e-156"></a><a name="index-Trivedi_002c-K_002e-157"></a>
 <!-- MVA for single class, closed networks with load dependent servers -->
 <a name="doc_002dqnclosedsinglemvald"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvald-157"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V, Z</var>)<var><a name="index-qnclosedsinglemvald-158"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvald-158"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V, Z</var>)<var><a name="index-qnclosedsinglemvald-159"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-159"></a><a name="index-closed-network_002c-single-class-160"></a><a name="index-load_002ddependent-service-center-161"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-160"></a><a name="index-closed-network_002c-single-class-161"></a><a name="index-load_002ddependent-service-center-162"></a>
 Exact MVA algorithm for closed, single class queueing networks
 with load-dependent service centers. This function supports
 FCFS, LCFS-PR, PS and IS nodes. For networks with only fixed-rate
@@ -3374,15 +3385,15 @@
 1998, Section 8.2.4.1, &ldquo;Networks with Load-Deèpendent Service: Closed
 Networks&rdquo;.
 
-   <p><a name="index-Bolch_002c-G_002e-162"></a><a name="index-Greiner_002c-S_002e-163"></a><a name="index-de-Meer_002c-H_002e-164"></a><a name="index-Trivedi_002c-K_002e-165"></a>
+   <p><a name="index-Bolch_002c-G_002e-163"></a><a name="index-Greiner_002c-S_002e-164"></a><a name="index-de-Meer_002c-H_002e-165"></a><a name="index-Trivedi_002c-K_002e-166"></a>
 <!-- CMVA for single class, closed networks with a single load dependent servers -->
 <a name="doc_002dqncmva"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V</var>)<var><a name="index-qncmva-166"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V, Z</var>)<var><a name="index-qncmva-167"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V</var>)<var><a name="index-qncmva-167"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V, Z</var>)<var><a name="index-qncmva-168"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-168"></a><a name="index-CMVA-169"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-169"></a><a name="index-CMVA-170"></a>
 Implementation of the Conditional MVA (CMVA) algorithm, a numerically
 stable variant of MVA for load-dependent servers. CMVA is described
 in G. Casale, <cite>A Note on Stable Flow-Equivalent Aggregation in
@@ -3436,19 +3447,19 @@
 closed networks</cite>. Queueing Syst. Theory Appl., 60:193–202, December
 2008.
 
-   <p><a name="index-Casale_002c-G_002e-170"></a>
+   <p><a name="index-Casale_002c-G_002e-171"></a>
 <!-- Approximate MVA for single class, closed networks -->
 
    <p><a name="doc_002dqnclosedsinglemvaapprox"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvaapprox-171"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemvaapprox-172"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemvaapprox-173"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedsinglemvaapprox-174"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedsinglemvaapprox-175"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvaapprox-172"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemvaapprox-173"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemvaapprox-174"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedsinglemvaapprox-175"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedsinglemvaapprox-176"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-176"></a><a name="index-Approximate-MVA-177"></a><a name="index-Closed-network_002c-single-class-178"></a><a name="index-Closed-network_002c-approximate-analysis-179"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-177"></a><a name="index-Approximate-MVA-178"></a><a name="index-Closed-network_002c-single-class-179"></a><a name="index-Closed-network_002c-approximate-analysis-180"></a>
 Analyze closed, single class queueing networks using the Approximate
 Mean Value Analysis (MVA) algorithm. This function is based on
 approximating the number of customers seen at center k when a
@@ -3527,20 +3538,20 @@
 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In
 particular, see section 6.4.2.2 ("Approximate Solution Techniques").
 
-   <p><a name="index-Lazowska_002c-E_002e-D_002e-180"></a><a name="index-Zahorjan_002c-J_002e-181"></a><a name="index-Graham_002c-G_002e-S_002e-182"></a><a name="index-Sevcik_002c-K_002e-C_002e-183"></a>
+   <p><a name="index-Lazowska_002c-E_002e-D_002e-181"></a><a name="index-Zahorjan_002c-J_002e-182"></a><a name="index-Graham_002c-G_002e-S_002e-183"></a><a name="index-Sevcik_002c-K_002e-C_002e-184"></a>
 
 <!-- MVA for multiple class, closed networks -->
    <p><a name="doc_002dqnclosedmultimva"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S </var>)<var><a name="index-qnclosedmultimva-184"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimva-185"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimva-186"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimva-187"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P</var>)<var><a name="index-qnclosedmultimva-188"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P, m</var>)<var><a name="index-qnclosedmultimva-189"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S </var>)<var><a name="index-qnclosedmultimva-185"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimva-186"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimva-187"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimva-188"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P</var>)<var><a name="index-qnclosedmultimva-189"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P, m</var>)<var><a name="index-qnclosedmultimva-190"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-190"></a><a name="index-closed-network_002c-multiple-classes-191"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-191"></a><a name="index-closed-network_002c-multiple-classes-192"></a>
 Analyze closed, multiclass queueing networks with K service
 centers and C independent customer classes (chains) using the
 Mean Value Analysys (MVA) algorithm.
@@ -3670,7 +3681,7 @@
 Multichain Queuing Networks</cite>, Journal of the ACM, vol. 27, n. 2, April
 1980, pp. 313&ndash;322. <a href="http://doi.acm.org/10.1145/322186.322195">http://doi.acm.org/10.1145/322186.322195</a>
 
-   <p><a name="index-Reiser_002c-M_002e-192"></a><a name="index-Lavenberg_002c-S_002e-S_002e-193"></a>
+   <p><a name="index-Reiser_002c-M_002e-193"></a><a name="index-Lavenberg_002c-S_002e-S_002e-194"></a>
 This implementation is based on G. Bolch, S. Greiner, H. de Meer and
 K. Trivedi, <cite>Queueing Networks and Markov Chains: Modeling and
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
@@ -3680,18 +3691,18 @@
 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In
 particular, see section 7.4.2.1 ("Exact Solution Techniques").
 
-   <p><a name="index-Bolch_002c-G_002e-194"></a><a name="index-Greiner_002c-S_002e-195"></a><a name="index-de-Meer_002c-H_002e-196"></a><a name="index-Trivedi_002c-K_002e-197"></a><a name="index-Lazowska_002c-E_002e-D_002e-198"></a><a name="index-Zahorjan_002c-J_002e-199"></a><a name="index-Graham_002c-G_002e-S_002e-200"></a><a name="index-Sevcik_002c-K_002e-C_002e-201"></a>
+   <p><a name="index-Bolch_002c-G_002e-195"></a><a name="index-Greiner_002c-S_002e-196"></a><a name="index-de-Meer_002c-H_002e-197"></a><a name="index-Trivedi_002c-K_002e-198"></a><a name="index-Lazowska_002c-E_002e-D_002e-199"></a><a name="index-Zahorjan_002c-J_002e-200"></a><a name="index-Graham_002c-G_002e-S_002e-201"></a><a name="index-Sevcik_002c-K_002e-C_002e-202"></a>
 <!-- Approximate MVA, with Bard-Schweitzer approximation -->
 <a name="doc_002dqnclosedmultimvaapprox"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimvaapprox-202"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimvaapprox-203"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimvaapprox-204"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedmultimvaapprox-205"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedmultimvaapprox-206"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimvaapprox-203"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimvaapprox-204"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimvaapprox-205"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedmultimvaapprox-206"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedmultimvaapprox-207"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-207"></a><a name="index-Approximate-MVA-208"></a><a name="index-Closed-network_002c-multiple-classes-209"></a><a name="index-Closed-network_002c-approximate-analysis-210"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-208"></a><a name="index-Approximate-MVA-209"></a><a name="index-Closed-network_002c-multiple-classes-210"></a><a name="index-Closed-network_002c-approximate-analysis-211"></a>
 Analyze closed, multiclass queueing networks with K service
 centers and C customer classes using the approximate Mean
 Value Analysys (MVA) algorithm.
@@ -3776,12 +3787,12 @@
 proc. 4th Int. Symp. on Modelling and Performance Evaluation of
 Computer Systems, feb. 1979, pp. 51&ndash;62.
 
-   <p><a name="index-Bard_002c-Y_002e-211"></a>
+   <p><a name="index-Bard_002c-Y_002e-212"></a>
 P. Schweitzer, <cite>Approximate Analysis of Multiclass Closed
 Networks of Queues</cite>, Proc. Int. Conf. on Stochastic Control and
 Optimization, jun 1979, pp. 25&ndash;29.
 
-   <p><a name="index-Schweitzer_002c-P_002e-212"></a>
+   <p><a name="index-Schweitzer_002c-P_002e-213"></a>
 This implementation is based on Edward D. Lazowska, John Zahorjan, G. 
 Scott Graham, and Kenneth C. Sevcik, <cite>Quantitative System
 Performance: Computer System Analysis Using Queueing Network Models</cite>,
@@ -3792,7 +3803,7 @@
 described above, as it computes the average response times R
 instead of the residence times.
 
-   <p><a name="index-Lazowska_002c-E_002e-D_002e-213"></a><a name="index-Zahorjan_002c-J_002e-214"></a><a name="index-Graham_002c-G_002e-S_002e-215"></a><a name="index-Sevcik_002c-K_002e-C_002e-216"></a>
+   <p><a name="index-Lazowska_002c-E_002e-D_002e-214"></a><a name="index-Zahorjan_002c-J_002e-215"></a><a name="index-Graham_002c-G_002e-S_002e-216"></a><a name="index-Sevcik_002c-K_002e-C_002e-217"></a>
 
 <h4 class="subsection">6.3.5 Mixed Networks</h4>
 
@@ -3800,9 +3811,9 @@
 <p><a name="doc_002dqnmix"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmix</b> (<var>lambda, N, S, V, m</var>)<var><a name="index-qnmix-217"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmix</b> (<var>lambda, N, S, V, m</var>)<var><a name="index-qnmix-218"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-218"></a><a name="index-mixed-network-219"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-219"></a><a name="index-mixed-network-220"></a>
 Solution of mixed queueing networks through MVA. The network consists
 of K service centers (single-server or delay centers) and
 C independent customer chains. Both open and closed chains
@@ -3893,14 +3904,14 @@
 Note that in this function we compute the mean response time R
 instead of the mean residence time as in the reference.
 
-   <p><a name="index-Lazowska_002c-E_002e-D_002e-220"></a><a name="index-Zahorjan_002c-J_002e-221"></a><a name="index-Graham_002c-G_002e-S_002e-222"></a><a name="index-Sevcik_002c-K_002e-C_002e-223"></a>
+   <p><a name="index-Lazowska_002c-E_002e-D_002e-221"></a><a name="index-Zahorjan_002c-J_002e-222"></a><a name="index-Graham_002c-G_002e-S_002e-223"></a><a name="index-Sevcik_002c-K_002e-C_002e-224"></a>
 Herb Schwetman, <cite>Implementing the Mean Value Algorithm for the
 Solution of Queueing Network Models</cite>, Technical Report CSD-TR-355,
 Department of Computer Sciences, Purdue University, feb 15, 1982,
 available at
 <a href="http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-355.pdf">http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-355.pdf</a>
 
-   <p><a name="index-Schwetman_002c-H_002e-224"></a>
+   <p><a name="index-Schwetman_002c-H_002e-225"></a>
 
 <div class="node">
 <a name="Algorithms-for-non-Product-form-QNs"></a>
@@ -3919,9 +3930,9 @@
 <p><a name="doc_002dqnmvablo"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmvablo</b> (<var>N, S, M, P</var>)<var><a name="index-qnmvablo-225"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmvablo</b> (<var>N, S, M, P</var>)<var><a name="index-qnmvablo-226"></a></var><br>
 <blockquote>
-        <p><a name="index-queueing-network-with-blocking-226"></a><a name="index-blocking-queueing-network-227"></a><a name="index-closed-network_002c-finite-capacity-228"></a>
+        <p><a name="index-queueing-network-with-blocking-227"></a><a name="index-blocking-queueing-network-228"></a><a name="index-closed-network_002c-finite-capacity-229"></a>
 MVA algorithm for closed queueing networks with blocking. <samp><span class="command">qnmvablo</span></samp>
 computes approximate utilization, response time and mean queue length
 for closed, single class queueing networks with blocking.
@@ -3976,16 +3987,16 @@
 Networks</cite>, IEEE Transactions on Software Engineering, vol. 14, n. 2,
 april 1988, pp. 418&ndash;428.  <a href="http://dx.doi.org/10.1109/32.4663">http://dx.doi.org/10.1109/32.4663</a>
 
-   <p><a name="index-Akyildiz_002c-I_002e-F_002e-229"></a>
+   <p><a name="index-Akyildiz_002c-I_002e-F_002e-230"></a>
 <a name="doc_002dqnmarkov"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>lambda, S, C, P</var>)<var><a name="index-qnmarkov-230"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>lambda, S, C, P, m</var>)<var><a name="index-qnmarkov-231"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>N, S, C, P</var>)<var><a name="index-qnmarkov-232"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>N, S, C, P, m</var>)<var><a name="index-qnmarkov-233"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>lambda, S, C, P</var>)<var><a name="index-qnmarkov-231"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>lambda, S, C, P, m</var>)<var><a name="index-qnmarkov-232"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>N, S, C, P</var>)<var><a name="index-qnmarkov-233"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>N, S, C, P, m</var>)<var><a name="index-qnmarkov-234"></a></var><br>
 <blockquote>
-        <p><a name="index-closed-network_002c-multiple-classes-234"></a><a name="index-closed-network_002c-finite-capacity-235"></a><a name="index-blocking-queueing-network-236"></a><a name="index-RS-blocking-237"></a>
+        <p><a name="index-closed-network_002c-multiple-classes-235"></a><a name="index-closed-network_002c-finite-capacity-236"></a><a name="index-blocking-queueing-network-237"></a><a name="index-RS-blocking-238"></a>
 Compute utilization, response time, average queue length and
 throughput for open or closed queueing networks with finite capacity. 
 Blocking type is Repetitive-Service (RS). This function explicitly
@@ -4095,9 +4106,9 @@
 <p><a name="doc_002dqnopenab"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>Xu</var>, <var>Rl</var>] = <b>qnopenab</b> (<var>lambda, D</var>)<var><a name="index-qnopenab-238"></a></var><br>
+&mdash; Function File: [<var>Xu</var>, <var>Rl</var>] = <b>qnopenab</b> (<var>lambda, D</var>)<var><a name="index-qnopenab-239"></a></var><br>
 <blockquote>
-        <p><a name="index-bounds_002c-asymptotic-239"></a><a name="index-open-network-240"></a>
+        <p><a name="index-bounds_002c-asymptotic-240"></a><a name="index-open-network-241"></a>
 Compute Asymptotic Bounds for single-class, open Queueing Networks
 with K service centers.
 
@@ -4137,14 +4148,14 @@
 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In
 parti...
 
[truncated message content]

[Octave-cvsupdate] SF.net SVN: octave:[9819] trunk/octave-forge/main/queueing/inst/dtmc_mtta.m

From: <mma...@us...> - 2012-03-12 12:10:50

Revision: 9819
          http://octave.svn.sourceforge.net/octave/?rev=9819&view=rev
Author:   mmarzolla
Date:     2012-03-12 12:10:43 +0000 (Mon, 12 Mar 2012)
Log Message:
-----------
modifications

Modified Paths:
--------------
    trunk/octave-forge/main/queueing/inst/dtmc_mtta.m

Modified: trunk/octave-forge/main/queueing/inst/dtmc_mtta.m
===================================================================
--- trunk/octave-forge/main/queueing/inst/dtmc_mtta.m	2012-03-12 10:58:39 UTC (rev 9818)
+++ trunk/octave-forge/main/queueing/inst/dtmc_mtta.m	2012-03-12 12:10:43 UTC (rev 9819)
@@ -100,4 +100,73 @@
 %! assert( t, [0 3 4 3 0], 10*eps );
 %! assert( B([2 3 4],[1 5]), [3/4 1/4; 1/2 1/2; 1/4 3/4], 10*eps );
 %! assert( B(1,1), 1 );
-%! assert( B(5,5), 1 );
\ No newline at end of file
+%! assert( B(5,5), 1 );
+
+## Compute the probability of completing the "snakes and ladders"
+## game in n steps, for various values of n. Also, computes the expected
+## number of steps which are necessary to complete the game.
+## Source: 
+## http://mapleta.emich.edu/aross15/coursepack3419/419/ch-04/chutes-and-ladders.pdf
+%!demo
+%! n = 6;
+%! P = zeros(101,101);
+%! ## setup transitions through the spinner
+%! for j=0:(100-n)
+%!   for i=1:n
+%!     P(1+j,1+j+i) = 1/n;
+%!   endfor
+%! endfor  
+%! for j=(101-n):100 
+%!   P(1+j,1+j) = (n-100+j)/n;
+%! endfor
+%! for j=(101-n):100
+%!   for i=1:(100-j)
+%!     P(1+j,1+j+i) = 1/n;
+%!   endfor
+%! endfor
+%! Pstar = P;
+%! ## setup snakes and ladders
+%! SL = [1 38; \
+%!       4 14; \
+%!       9 31; \
+%!       16 6; \
+%!       21 42; \
+%!       28 84; \
+%!       36 44; \
+%!       47 26; \
+%!       49 11; \
+%!       51 67; \
+%!       56 53; \
+%!       62 19; \
+%!       64 60; \
+%!       71 91; \
+%!       80 100; \
+%!       87 24; \
+%!       93 73; \
+%!       95 75; \
+%!       98 78 ];
+%! for ii=SL;
+%!   i = ii(1);
+%!   j = ii(2);
+%!   Pstar(1+i,:) = 0;
+%!   for k=0:100
+%!     if ( k != j )
+%!       Pstar(1+k,1+j) = P(1+k,1+j) + P(1+k,1+i);
+%!     endif
+%!   endfor
+%!   Pstar(:,1+i) = 0;
+%! endfor
+%! Pstar += diag( 1-sum(Pstar,2) );
+%!
+%! nsteps = 50; # number of steps
+%! Pfinish = zeros(1,nsteps); # Pfinish(i) = probability of finishing after step i
+%! start = zeros(1,101); start(1) = 1;
+%! for i=1:nsteps
+%!   pn = dtmc(Pstar,i,start);
+%!   Pfinish(i) = pn(101); # state 101 is the ending (absorbing) state
+%! endfor
+%! f = dtmc_mtta(Pstar);
+%! ## f(1) is the mean time to absorption starting from state 1
+%! printf("Average number of steps to complete the game: %f\n", f(1) );
+%! plot(Pfinish, ";Probability of finishing the game;");
+%! xlabel("Step number");

This was sent by the SourceForge.net collaborative development platform, the world's largest Open Source development site.

[Octave-cvsupdate] SF.net SVN: octave:[9818] trunk/octave-forge/main/queueing

From: <mma...@us...> - 2012-03-12 10:58:53

Revision: 9818
          http://octave.svn.sourceforge.net/octave/?rev=9818&view=rev
Author:   mmarzolla
Date:     2012-03-12 10:58:39 +0000 (Mon, 12 Mar 2012)
Log Message:
-----------
New function dtmc_mtta() added; removed deprecated functions

Modified Paths:
--------------
    trunk/octave-forge/main/queueing/ChangeLog
    trunk/octave-forge/main/queueing/NEWS
    trunk/octave-forge/main/queueing/doc/markovchains.txi
    trunk/octave-forge/main/queueing/doc/queueing.html
    trunk/octave-forge/main/queueing/doc/queueing.pdf

Added Paths:
-----------
    trunk/octave-forge/main/queueing/inst/dtmc_mtta.m

Removed Paths:
-------------
    trunk/octave-forge/main/queueing/inst/ctmc_solve.m
    trunk/octave-forge/main/queueing/inst/dtmc_solve.m

Modified: trunk/octave-forge/main/queueing/ChangeLog
===================================================================
--- trunk/octave-forge/main/queueing/ChangeLog	2012-03-11 20:53:31 UTC (rev 9817)
+++ trunk/octave-forge/main/queueing/ChangeLog	2012-03-12 10:58:39 UTC (rev 9818)
@@ -11,9 +11,12 @@
 	  in future releases.
 	* ctmc_bd() now returns the infinitesimal generator matrix
 	  of the birth-death process, not the steady-state solution.
-	* ctmc_bd_solve() has been removed
-	* dtmc_bd() has been added
-	* ctmc_check_Q() has been added
+	* ctmc_bd_solve() (which was deprecated) has been removed
+	* ctmc_solve() (which was deprecated) has been removed
+	* dtmc_solve() (which was deprecated) has been removed
+	* dtmc_bd() added
+	* ctmc_check_Q() added
+	* dtmc_mtta() added
 	* Miscellaneous fixes/improvements to the documentation
 
 2012-02-04 Moreno Marzolla <mar...@cs...>

Modified: trunk/octave-forge/main/queueing/NEWS
===================================================================
--- trunk/octave-forge/main/queueing/NEWS	2012-03-11 20:53:31 UTC (rev 9817)
+++ trunk/octave-forge/main/queueing/NEWS	2012-03-12 10:58:39 UTC (rev 9818)
@@ -11,11 +11,12 @@
    of the birth-death process with given rates, not the steady-state
    solution.
 
-** New function dtmc_bd() added
+** The following new functions have been added: dtmc_bd(), dtmc_mtta(), 
+   ctmc_check_Q()
 
-** Function ctmc_bd_solve() has been removed
+** The following deprecated functions have been removed: ctmc_bd_solve(),
+   ctmc_solve(), dtmc_solve()
 
-** New function ctmc_check_Q() added
 
 Summary of important user-visible changes for queueing-1.0.0
 ------------------------------------------------------------------------------

Modified: trunk/octave-forge/main/queueing/doc/markovchains.txi
===================================================================
--- trunk/octave-forge/main/queueing/doc/markovchains.txi	2012-03-11 20:53:31 UTC (rev 9817)
+++ trunk/octave-forge/main/queueing/doc/markovchains.txi	2012-03-12 10:58:39 UTC (rev 9818)
@@ -145,8 +145,13 @@
 @DOCSTRING(dtmc_fpt)
 
 @c
+@subsection Mean Time to Absorption
+
+@DOCSTRING(dtmc_mtta)
+
 @c
 @c
+@c
 @node Continuous-Time Markov Chains
 @section Continuous-Time Markov Chains
 
@@ -178,7 +183,7 @@
 * Birth-Death process::
 * Expected Sojourn Time::
 * Time-Averaged Expected Sojourn Time::
-* Expected Time to Absorption::
+* Mean Time to Absorption::
 * First Passage Times::
 @end menu
 
@@ -323,8 +328,8 @@
 @c
 @c
 @c
-@node Expected Time to Absorption
-@subsection Expected Time to Absorption
+@node Mean Time to Absorption
+@subsection Mean Time to Absorption
 
 If we consider a Markov Chain with absorbing states, it is possible to
 define the @emph{expected time to absorption} as the expected time

Modified: trunk/octave-forge/main/queueing/doc/queueing.html
===================================================================
--- trunk/octave-forge/main/queueing/doc/queueing.html	2012-03-11 20:53:31 UTC (rev 9817)
+++ trunk/octave-forge/main/queueing/doc/queueing.html	2012-03-12 10:58:39 UTC (rev 9818)
@@ -59,6 +59,7 @@
 <li><a href="#Discrete_002dTime-Markov-Chains">4.1.1 State occupancy probabilities</a>
 <li><a href="#Discrete_002dTime-Markov-Chains">4.1.2 Birth-Death process</a>
 <li><a href="#Discrete_002dTime-Markov-Chains">4.1.3 First passage times</a>
+<li><a href="#Discrete_002dTime-Markov-Chains">4.1.4 Mean Time to Absorption</a>
 </li></ul>
 <li><a href="#Continuous_002dTime-Markov-Chains">4.2 Continuous-Time Markov Chains</a>
 <ul>
@@ -66,7 +67,7 @@
 <li><a href="#Birth_002dDeath-process">4.2.2 Birth-Death process</a>
 <li><a href="#Expected-Sojourn-Time">4.2.3 Expected Sojourn Time</a>
 <li><a href="#Time_002dAveraged-Expected-Sojourn-Time">4.2.4 Time-Averaged Expected Sojourn Time</a>
-<li><a href="#Expected-Time-to-Absorption">4.2.5 Expected Time to Absorption</a>
+<li><a href="#Mean-Time-to-Absorption">4.2.5 Mean Time to Absorption</a>
 <li><a href="#First-Passage-Times">4.2.6 First Passage Times</a>
 </li></ul>
 </li></ul>
@@ -1000,6 +1001,39 @@
 
         </blockquote></div>
 
+<h4 class="subsection">4.1.4 Mean Time to Absorption</h4>
+
+<p><a name="doc_002ddtmc_005fmtta"></a>
+
+<div class="defun">
+&mdash; Function File: [<var>t</var> <var>B</var>] = <b>dtmc_mtta</b> (<var>P</var>)<var><a name="index-dtmc_005fmtta-16"></a></var><br>
+<blockquote>
+        <p><a name="index-Markov-chain_002c-disctete-time-17"></a><a name="index-Mean-time-to-absorption-18"></a>
+Compute the expected number of steps before absorption for the DTMC
+described by the transition probability matrix <var>P</var>,
+
+        <p><strong>INPUTS</strong>
+
+          <dl>
+<dt><var>P</var><dd>Transition probability matrix .
+
+        </dl>
+
+        <p><strong>OUTPUTS</strong>
+
+          <dl>
+<dt><var>t</var><dd><var>t</var><code>(i)</code> is the expected number of steps before being absorbed,
+starting from state i.
+
+          <br><dt><var>B</var><dd><var>B</var><code>(i,j)</code> is the probability of being absorbed in state
+j, starting from state i. If j is not absorbing,
+<var>B</var><code>(i,j) = 0</code>; if i is absorbing, then
+<var>B</var><code>(i,i) = 1</code>..
+
+        </dl>
+
+        </blockquote></div>
+
 <div class="node">
 <a name="Continuous-Time-Markov-Chains"></a>
 <a name="Continuous_002dTime-Markov-Chains"></a>
@@ -1028,9 +1062,9 @@
    <p><a name="doc_002dctmc_005fcheck_005fQ"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>result</var> <var>err</var>] = <b>ctmc_check_Q</b> (<var>Q</var>)<var><a name="index-ctmc_005fcheck_005fQ-16"></a></var><br>
+&mdash; Function File: [<var>result</var> <var>err</var>] = <b>ctmc_check_Q</b> (<var>Q</var>)<var><a name="index-ctmc_005fcheck_005fQ-19"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-17"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-20"></a>
 If <var>Q</var> is a valid infinitesimal generator matrix, return
 the size (number of rows or columns) of <var>Q</var>. If <var>Q</var> is not
 an infinitesimal generator matrix, set <var>result</var> to zero, and
@@ -1043,7 +1077,7 @@
 <li><a accesskey="2" href="#Birth_002dDeath-process">Birth-Death process</a>
 <li><a accesskey="3" href="#Expected-Sojourn-Time">Expected Sojourn Time</a>
 <li><a accesskey="4" href="#Time_002dAveraged-Expected-Sojourn-Time">Time-Averaged Expected Sojourn Time</a>
-<li><a accesskey="5" href="#Expected-Time-to-Absorption">Expected Time to Absorption</a>
+<li><a accesskey="5" href="#Mean-Time-to-Absorption">Mean Time to Absorption</a>
 <li><a accesskey="6" href="#First-Passage-Times">First Passage Times</a>
 </ul>
 
@@ -1080,10 +1114,10 @@
    <p><a name="doc_002dctmc"></a>
 
 <div class="defun">
-&mdash; Function File: <var>p</var> = <b>ctmc</b> (<var>Q</var>)<var><a name="index-ctmc-18"></a></var><br>
-&mdash; Function File: <var>p</var> = <b>ctmc</b> (<var>Q, t. p0</var>)<var><a name="index-ctmc-19"></a></var><br>
+&mdash; Function File: <var>p</var> = <b>ctmc</b> (<var>Q</var>)<var><a name="index-ctmc-21"></a></var><br>
+&mdash; Function File: <var>p</var> = <b>ctmc</b> (<var>Q, t. p0</var>)<var><a name="index-ctmc-22"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-20"></a><a name="index-Continuous-time-Markov-chain-21"></a><a name="index-Markov-chain_002c-state-occupancy-probabilities-22"></a><a name="index-Stationary-probabilities-23"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-23"></a><a name="index-Continuous-time-Markov-chain-24"></a><a name="index-Markov-chain_002c-state-occupancy-probabilities-25"></a><a name="index-Stationary-probabilities-26"></a>
 With a single argument, compute the stationary state occupancy
 probability vector <var>p</var>(1), <small class="dots">...</small>, <var>p</var>(N) for a
 Continuous-Time Markov Chain with infinitesimal generator matrix
@@ -1146,9 +1180,9 @@
 <p><a name="doc_002dctmc_005fbd"></a>
 
 <div class="defun">
-&mdash; Function File: <var>Q</var> = <b>ctmc_bd</b> (<var>birth, death</var>)<var><a name="index-ctmc_005fbd-24"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>ctmc_bd</b> (<var>birth, death</var>)<var><a name="index-ctmc_005fbd-27"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-25"></a><a name="index-Birth_002ddeath-process-26"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-28"></a><a name="index-Birth_002ddeath-process-29"></a>
 Returns the N \times N infinitesimal generator matrix Q
 for a birth-death process with given rates.
 
@@ -1208,10 +1242,10 @@
    <p><a name="doc_002dctmc_005fexps"></a>
 
 <div class="defun">
-&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, t, p </var>)<var><a name="index-ctmc_005fexps-27"></a></var><br>
-&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fexps-28"></a></var><br>
+&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, t, p </var>)<var><a name="index-ctmc_005fexps-30"></a></var><br>
+&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fexps-31"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-29"></a><a name="index-Expected-sojourn-time-30"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-32"></a><a name="index-Expected-sojourn-time-33"></a>
 With three arguments, compute the expected times <var>L</var><code>(i)</code>
 spent in each state i during the time interval
 [0,t], assuming that the state occupancy probabilities
@@ -1280,7 +1314,7 @@
 <a name="Time-Averaged-Expected-Sojourn-Time"></a>
 <a name="Time_002dAveraged-Expected-Sojourn-Time"></a>
 <p><hr>
-Next:&nbsp;<a rel="next" accesskey="n" href="#Expected-Time-to-Absorption">Expected Time to Absorption</a>,
+Next:&nbsp;<a rel="next" accesskey="n" href="#Mean-Time-to-Absorption">Mean Time to Absorption</a>,
 Previous:&nbsp;<a rel="previous" accesskey="p" href="#Expected-Sojourn-Time">Expected Sojourn Time</a>,
 Up:&nbsp;<a rel="up" accesskey="u" href="#Continuous_002dTime-Markov-Chains">Continuous-Time Markov Chains</a>
 
@@ -1291,9 +1325,9 @@
 <p><a name="doc_002dctmc_005ftaexps"></a>
 
 <div class="defun">
-&mdash; Function File: <var>M</var> = <b>ctmc_taexps</b> (<var>Q, t, p</var>)<var><a name="index-ctmc_005ftaexps-31"></a></var><br>
+&mdash; Function File: <var>M</var> = <b>ctmc_taexps</b> (<var>Q, t, p</var>)<var><a name="index-ctmc_005ftaexps-34"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-32"></a><a name="index-Time_002dalveraged-sojourn-time-33"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-35"></a><a name="index-Time_002dalveraged-sojourn-time-36"></a>
 Compute the <em>time-averaged sojourn time</em> <var>M</var><code>(i)</code>,
 defined as the fraction of the time interval [0,t] spent in
 state i, assuming that the state occupancy probabilities at
@@ -1348,7 +1382,7 @@
       ylabel("Time-averaged Expected sojourn time");</pre>
 </pre>
    <div class="node">
-<a name="Expected-Time-to-Absorption"></a>
+<a name="Mean-Time-to-Absorption"></a>
 <p><hr>
 Next:&nbsp;<a rel="next" accesskey="n" href="#First-Passage-Times">First Passage Times</a>,
 Previous:&nbsp;<a rel="previous" accesskey="p" href="#Time_002dAveraged-Expected-Sojourn-Time">Time-Averaged Expected Sojourn Time</a>,
@@ -1356,7 +1390,7 @@
 
 </div>
 
-<h4 class="subsection">4.2.5 Expected Time to Absorption</h4>
+<h4 class="subsection">4.2.5 Mean Time to Absorption</h4>
 
 <p>If we consider a Markov Chain with absorbing states, it is possible to
 define the <em>expected time to absorption</em> as the expected time
@@ -1376,9 +1410,9 @@
    <p><a name="doc_002dctmc_005fmtta"></a>
 
 <div class="defun">
-&mdash; Function File: <var>t</var> = <b>ctmc_mtta</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fmtta-34"></a></var><br>
+&mdash; Function File: <var>t</var> = <b>ctmc_mtta</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fmtta-37"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-35"></a><a name="index-Mean-time-to-absorption-36"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-38"></a><a name="index-Mean-time-to-absorption-39"></a>
 Compute the Mean-Time to Absorption (MTTA) of the CTMC described by
 the infinitesimal generator matrix <var>Q</var>, starting from initial
 occupancy probabilities <var>p</var>. If there are no absorbing states, this
@@ -1439,11 +1473,11 @@
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998.
 
-   <p><a name="index-Bolch_002c-G_002e-37"></a><a name="index-Greiner_002c-S_002e-38"></a><a name="index-de-Meer_002c-H_002e-39"></a><a name="index-Trivedi_002c-K_002e-40"></a>
+   <p><a name="index-Bolch_002c-G_002e-40"></a><a name="index-Greiner_002c-S_002e-41"></a><a name="index-de-Meer_002c-H_002e-42"></a><a name="index-Trivedi_002c-K_002e-43"></a>
 <div class="node">
 <a name="First-Passage-Times"></a>
 <p><hr>
-Previous:&nbsp;<a rel="previous" accesskey="p" href="#Expected-Time-to-Absorption">Expected Time to Absorption</a>,
+Previous:&nbsp;<a rel="previous" accesskey="p" href="#Mean-Time-to-Absorption">Mean Time to Absorption</a>,
 Up:&nbsp;<a rel="up" accesskey="u" href="#Continuous_002dTime-Markov-Chains">Continuous-Time Markov Chains</a>
 
 </div>
@@ -1453,10 +1487,10 @@
 <p><a name="doc_002dctmc_005ffpt"></a>
 
 <div class="defun">
-&mdash; Function File: <var>M</var> = <b>ctmc_fpt</b> (<var>Q</var>)<var><a name="index-ctmc_005ffpt-41"></a></var><br>
-&mdash; Function File: <var>m</var> = <b>ctmc_fpt</b> (<var>Q, i, j</var>)<var><a name="index-ctmc_005ffpt-42"></a></var><br>
+&mdash; Function File: <var>M</var> = <b>ctmc_fpt</b> (<var>Q</var>)<var><a name="index-ctmc_005ffpt-44"></a></var><br>
+&mdash; Function File: <var>m</var> = <b>ctmc_fpt</b> (<var>Q, i, j</var>)<var><a name="index-ctmc_005ffpt-45"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-43"></a><a name="index-First-passage-times-44"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-46"></a><a name="index-First-passage-times-47"></a>
 If called with a single argument, computes the mean first passage
 times <var>M</var><code>(i,j)</code>, the average times before state <var>j</var> is
 reached, starting from state <var>i</var>, for all 1 \leq i, j \leq
@@ -1562,9 +1596,9 @@
    <p><a name="doc_002dqnmm1"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmm1</b> (<var>lambda, mu</var>)<var><a name="index-qnmm1-45"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmm1</b> (<var>lambda, mu</var>)<var><a name="index-qnmm1-48"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002f1_007d-system-46"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002f1_007d-system-49"></a>
 Compute utilization, response time, average number of requests
 and throughput for a M/M/1 queue.
 
@@ -1609,7 +1643,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.3.
 
-   <p><a name="index-Bolch_002c-G_002e-47"></a><a name="index-Greiner_002c-S_002e-48"></a><a name="index-de-Meer_002c-H_002e-49"></a><a name="index-Trivedi_002c-K_002e-50"></a>
+   <p><a name="index-Bolch_002c-G_002e-50"></a><a name="index-Greiner_002c-S_002e-51"></a><a name="index-de-Meer_002c-H_002e-52"></a><a name="index-Trivedi_002c-K_002e-53"></a>
 <!-- M/M/m -->
 <div class="node">
 <a name="The-M%2fM%2fm-System"></a>
@@ -1635,10 +1669,10 @@
    <p><a name="doc_002dqnmmm"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu</var>)<var><a name="index-qnmmm-51"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu, m</var>)<var><a name="index-qnmmm-52"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu</var>)<var><a name="index-qnmmm-54"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu, m</var>)<var><a name="index-qnmmm-55"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002fm_007d-system-53"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002fm_007d-system-56"></a>
 Compute utilization, response time, average number of requests in
 service and throughput for a M/M/m queue, a queueing
 system with m identical service centers connected to a single queue.
@@ -1690,7 +1724,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.5.
 
-   <p><a name="index-Bolch_002c-G_002e-54"></a><a name="index-Greiner_002c-S_002e-55"></a><a name="index-de-Meer_002c-H_002e-56"></a><a name="index-Trivedi_002c-K_002e-57"></a>
+   <p><a name="index-Bolch_002c-G_002e-57"></a><a name="index-Greiner_002c-S_002e-58"></a><a name="index-de-Meer_002c-H_002e-59"></a><a name="index-Trivedi_002c-K_002e-60"></a>
 <!-- M/M/inf -->
 <div class="node">
 <a name="The-M%2fM%2finf-System"></a>
@@ -1713,7 +1747,7 @@
    <p><a name="doc_002dqnmminf"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmminf</b> (<var>lambda, mu</var>)<var><a name="index-qnmminf-58"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmminf</b> (<var>lambda, mu</var>)<var><a name="index-qnmminf-61"></a></var><br>
 <blockquote>
         <p>Compute utilization, response time, average number of requests and
 throughput for a M/M/\infty queue. This is a system with an
@@ -1721,7 +1755,7 @@
 system is always stable, regardless the values of the arrival and
 service rates.
 
-        <p><a name="index-g_t_0040math_007bM_002fM_002f_007dinf-system-59"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002f_007dinf-system-62"></a>
 
         <p><strong>INPUTS</strong>
 
@@ -1739,7 +1773,7 @@
 different from the utilization, which in the case of M/M/\infty
 centers is always zero.
 
-          <p><a name="index-traffic-intensity-60"></a>
+          <p><a name="index-traffic-intensity-63"></a>
 <br><dt><var>R</var><dd>Service center response time.
 
           <br><dt><var>Q</var><dd>Average number of requests in the system (which is equal to the
@@ -1767,7 +1801,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.4.
 
-   <p><a name="index-Bolch_002c-G_002e-61"></a><a name="index-Greiner_002c-S_002e-62"></a><a name="index-de-Meer_002c-H_002e-63"></a><a name="index-Trivedi_002c-K_002e-64"></a>
+   <p><a name="index-Bolch_002c-G_002e-64"></a><a name="index-Greiner_002c-S_002e-65"></a><a name="index-de-Meer_002c-H_002e-66"></a><a name="index-Trivedi_002c-K_002e-67"></a>
 <!-- M/M/1/k -->
 <div class="node">
 <a name="The-M%2fM%2f1%2fK-System"></a>
@@ -1791,9 +1825,9 @@
    <p><a name="doc_002dqnmm1k"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmm1k</b> (<var>lambda, mu, K</var>)<var><a name="index-qnmm1k-65"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmm1k</b> (<var>lambda, mu, K</var>)<var><a name="index-qnmm1k-68"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002f1_002fK_007d-system-66"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002f1_002fK_007d-system-69"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/M/1/K finite capacity system. In a
 M/M/1/K queue there is a single server; the maximum number of
@@ -1860,9 +1894,9 @@
    <p><a name="doc_002dqnmmmk"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmmmk</b> (<var>lambda, mu, m, K</var>)<var><a name="index-qnmmmk-67"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmmmk</b> (<var>lambda, mu, m, K</var>)<var><a name="index-qnmmmk-70"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002fm_002fK_007d-system-68"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002fm_002fK_007d-system-71"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/M/m/K finite capacity system. In a
 M/M/m/K system there are m \geq 1 identical service
@@ -1920,7 +1954,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.6.
 
-   <p><a name="index-Bolch_002c-G_002e-69"></a><a name="index-Greiner_002c-S_002e-70"></a><a name="index-de-Meer_002c-H_002e-71"></a><a name="index-Trivedi_002c-K_002e-72"></a>
+   <p><a name="index-Bolch_002c-G_002e-72"></a><a name="index-Greiner_002c-S_002e-73"></a><a name="index-de-Meer_002c-H_002e-74"></a><a name="index-Trivedi_002c-K_002e-75"></a>
 
 <!-- Approximate M/M/m -->
 <div class="node">
@@ -1942,9 +1976,9 @@
    <p><a name="doc_002dqnammm"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnammm</b> (<var>lambda, mu</var>)<var><a name="index-qnammm-73"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnammm</b> (<var>lambda, mu</var>)<var><a name="index-qnammm-76"></a></var><br>
 <blockquote>
-        <p><a name="index-Asymmetric-_0040math_007bM_002fM_002fm_007d-system-74"></a>
+        <p><a name="index-Asymmetric-_0040math_007bM_002fM_002fm_007d-system-77"></a>
 Compute <em>approximate</em> utilization, response time, average number
 of requests in service and throughput for an asymmetric  M/M/m
 queue. In this system there are m different service centers
@@ -1991,7 +2025,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998
 
-   <p><a name="index-Bolch_002c-G_002e-75"></a><a name="index-Greiner_002c-S_002e-76"></a><a name="index-de-Meer_002c-H_002e-77"></a><a name="index-Trivedi_002c-K_002e-78"></a>
+   <p><a name="index-Bolch_002c-G_002e-78"></a><a name="index-Greiner_002c-S_002e-79"></a><a name="index-de-Meer_002c-H_002e-80"></a><a name="index-Trivedi_002c-K_002e-81"></a>
 <div class="node">
 <a name="The-M%2fG%2f1-System"></a>
 <a name="The-M_002fG_002f1-System"></a>
@@ -2007,9 +2041,9 @@
 <p><a name="doc_002dqnmg1"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmg1</b> (<var>lambda, xavg, x2nd</var>)<var><a name="index-qnmg1-79"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmg1</b> (<var>lambda, xavg, x2nd</var>)<var><a name="index-qnmg1-82"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fG_002f1_007d-system-80"></a>
+        <p><a name="index-g_t_0040math_007bM_002fG_002f1_007d-system-83"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/G/1 system. The service time distribution
 is described by its mean <var>xavg</var>, and by its second moment
@@ -2066,9 +2100,9 @@
 <p><a name="doc_002dqnmh1"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmh1</b> (<var>lambda, mu, alpha</var>)<var><a name="index-qnmh1-81"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmh1</b> (<var>lambda, mu, alpha</var>)<var><a name="index-qnmh1-84"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fH_005fm_002f1_007d-system-82"></a>
+        <p><a name="index-g_t_0040math_007bM_002fH_005fm_002f1_007d-system-85"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/H_m/1 system. In this system, the customer
 service times have hyper-exponential distribution:
@@ -2150,7 +2184,7 @@
 <li><a accesskey="6" href="#Utility-functions">Utility functions</a>:                    Utility functions to compute miscellaneous quantities
 </ul>
 
-<p><a name="index-queueing-networks-83"></a>
+<p><a name="index-queueing-networks-86"></a>
 <!-- INTRODUCTION -->
 <div class="node">
 <a name="Introduction-to-QNs"></a>
@@ -2411,13 +2445,13 @@
    <p><a name="doc_002dqnmknode"></a>
 
 <div class="defun">
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S</var>)<var><a name="index-qnmknode-84"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S, m</var>)<var><a name="index-qnmknode-85"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/1-lcfs-pr", S</var>)<var><a name="index-qnmknode-86"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S</var>)<var><a name="index-qnmknode-87"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S, s2</var>)<var><a name="index-qnmknode-88"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S</var>)<var><a name="index-qnmknode-89"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S, s2</var>)<var><a name="index-qnmknode-90"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S</var>)<var><a name="index-qnmknode-87"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S, m</var>)<var><a name="index-qnmknode-88"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/1-lcfs-pr", S</var>)<var><a name="index-qnmknode-89"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S</var>)<var><a name="index-qnmknode-90"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S, s2</var>)<var><a name="index-qnmknode-91"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S</var>)<var><a name="index-qnmknode-92"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S, s2</var>)<var><a name="index-qnmknode-93"></a></var><br>
 <blockquote>
         <p>Creates a node; this function can be used together with
 <code>qnsolve</code>. It is possible to create either single-class nodes
@@ -2486,10 +2520,10 @@
    <p><a name="doc_002dqnsolve"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V</var>)<var><a name="index-qnsolve-91"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V, Z</var>)<var><a name="index-qnsolve-92"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"open", lambda, QQ, V</var>)<var><a name="index-qnsolve-93"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"mixed", lambda, N, QQ, V</var>)<var><a name="index-qnsolve-94"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V</var>)<var><a name="index-qnsolve-94"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V, Z</var>)<var><a name="index-qnsolve-95"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"open", lambda, QQ, V</var>)<var><a name="index-qnsolve-96"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"mixed", lambda, N, QQ, V</var>)<var><a name="index-qnsolve-97"></a></var><br>
 <blockquote>
         <p>General evaluator of QN models. Networks can be open,
 closed or mixed; single as well as multiclass networks are supported.
@@ -2667,11 +2701,11 @@
    <p><a name="doc_002dqnjackson"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P </var>)<var><a name="index-qnjackson-95"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P, m </var>)<var><a name="index-qnjackson-96"></a></var><br>
-&mdash; Function File: <var>pr</var> = <b>qnjackson</b> (<var>lambda, S, P, m, k</var>)<var><a name="index-qnjackson-97"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P </var>)<var><a name="index-qnjackson-98"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P, m </var>)<var><a name="index-qnjackson-99"></a></var><br>
+&mdash; Function File: <var>pr</var> = <b>qnjackson</b> (<var>lambda, S, P, m, k</var>)<var><a name="index-qnjackson-100"></a></var><br>
 <blockquote>
-        <p><a name="index-open-network_002c-single-class-98"></a><a name="index-Jackson-network-99"></a>
+        <p><a name="index-open-network_002c-single-class-101"></a><a name="index-Jackson-network-102"></a>
 With three or four input parameters, this function computes the
 steady-state occupancy probabilities for a Jackson network. With five
 input parameters, this function computes the steady-state probability
@@ -2753,7 +2787,7 @@
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998, pp. 284&ndash;287.
 
-   <p><a name="index-Bolch_002c-G_002e-100"></a><a name="index-Greiner_002c-S_002e-101"></a><a name="index-de-Meer_002c-H_002e-102"></a><a name="index-Trivedi_002c-K_002e-103"></a>
+   <p><a name="index-Bolch_002c-G_002e-103"></a><a name="index-Greiner_002c-S_002e-104"></a><a name="index-de-Meer_002c-H_002e-105"></a><a name="index-Trivedi_002c-K_002e-106"></a>
 
 <h4 class="subsection">6.3.2 The Convolution Algorithm</h4>
 
@@ -2787,10 +2821,10 @@
    <p><a name="doc_002dqnconvolution"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V</var>)<var><a name="index-qnconvolution-104"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V, m</var>)<var><a name="index-qnconvolution-105"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V</var>)<var><a name="index-qnconvolution-107"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V, m</var>)<var><a name="index-qnconvolution-108"></a></var><br>
 <blockquote>
-        <p><a name="index-closed-network-106"></a><a name="index-normalization-constant-107"></a><a name="index-convolution-algorithm-108"></a>
+        <p><a name="index-closed-network-109"></a><a name="index-normalization-constant-110"></a><a name="index-convolution-algorithm-111"></a>
 This function implements the <em>convolution algorithm</em> for
 computing steady-state performance measures of product-form,
 single-class closed queueing networks. Load-independent service
@@ -2881,20 +2915,20 @@
 16, number 9, september 1973,
 pp. 527&ndash;531. <a href="http://doi.acm.org/10.1145/362342.362345">http://doi.acm.org/10.1145/362342.362345</a>
 
-   <p><a name="index-Buzen_002c-J_002e-P_002e-109"></a>
+   <p><a name="index-Buzen_002c-J_002e-P_002e-112"></a>
 This implementation is based on G. Bolch, S. Greiner, H. de Meer and
 K. Trivedi, <cite>Queueing Networks and Markov Chains: Modeling and
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998, pp. 313&ndash;317.
 
-   <p><a name="index-Bolch_002c-G_002e-110"></a><a name="index-Greiner_002c-S_002e-111"></a><a name="index-de-Meer_002c-H_002e-112"></a><a name="index-Trivedi_002c-K_002e-113"></a>
+   <p><a name="index-Bolch_002c-G_002e-113"></a><a name="index-Greiner_002c-S_002e-114"></a><a name="index-de-Meer_002c-H_002e-115"></a><a name="index-Trivedi_002c-K_002e-116"></a>
 <!-- Convolution for load-dependent service centers -->
 <a name="doc_002dqnconvolutionld"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolutionld</b> (<var>N, S, V</var>)<var><a name="index-qnconvolutionld-114"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolutionld</b> (<var>N, S, V</var>)<var><a name="index-qnconvolutionld-117"></a></var><br>
 <blockquote>
-        <p><a name="index-closed-network-115"></a><a name="index-normalization-constant-116"></a><a name="index-convolution-algorithm-117"></a><a name="index-load_002ddependent-service-center-118"></a>
+        <p><a name="index-closed-network-118"></a><a name="index-normalization-constant-119"></a><a name="index-convolution-algorithm-120"></a><a name="index-load_002ddependent-service-center-121"></a>
 This function implements the <em>convolution algorithm</em> for
 product-form, single-class closed queueing networks with general
 load-dependent service centers.
@@ -2954,7 +2988,7 @@
 Purdue University, feb, 1981 (revised). 
 <a href="http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-354.pdf">http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-354.pdf</a>
 
-   <p><a name="index-Schwetman_002c-H_002e-119"></a>
+   <p><a name="index-Schwetman_002c-H_002e-122"></a>
 M. Reiser, H. Kobayashi, <cite>On The Convolution Algorithm for
 Separable Queueing Networks</cite>, In Proceedings of the 1976 ACM
 SIGMETRICS Conference on Computer Performance Modeling Measurement and
@@ -2962,7 +2996,7 @@
 1976). SIGMETRICS '76. ACM, New York, NY,
 pp. 109&ndash;117. <a href="http://doi.acm.org/10.1145/800200.806187">http://doi.acm.org/10.1145/800200.806187</a>
 
-   <p><a name="index-Reiser_002c-M_002e-120"></a><a name="index-Kobayashi_002c-H_002e-121"></a>
+   <p><a name="index-Reiser_002c-M_002e-123"></a><a name="index-Kobayashi_002c-H_002e-124"></a>
 This implementation is based on G. Bolch, S. Greiner, H. de Meer and
 K. Trivedi, <cite>Queueing Networks and Markov Chains: Modeling and
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
@@ -2974,7 +3008,7 @@
 function f_i defined in Schwetman, <code>Some Computational
 Aspects of Queueing Network Models</code>.
 
-   <p><a name="index-Bolch_002c-G_002e-122"></a><a name="index-Greiner_002c-S_002e-123"></a><a name="index-de-Meer_002c-H_002e-124"></a><a name="index-Trivedi_002c-K_002e-125"></a>
+   <p><a name="index-Bolch_002c-G_002e-125"></a><a name="index-Greiner_002c-S_002e-126"></a><a name="index-de-Meer_002c-H_002e-127"></a><a name="index-Trivedi_002c-K_002e-128"></a>
 
 <h4 class="subsection">6.3.3 Open networks</h4>
 
@@ -2982,10 +3016,10 @@
 <p><a name="doc_002dqnopensingle"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V</var>)<var><a name="index-qnopensingle-126"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopensingle-127"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V</var>)<var><a name="index-qnopensingle-129"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopensingle-130"></a></var><br>
 <blockquote>
-        <p><a name="index-open-network_002c-single-class-128"></a><a name="index-BCMP-network-129"></a>
+        <p><a name="index-open-network_002c-single-class-131"></a><a name="index-BCMP-network-132"></a>
 Analyze open, single class BCMP queueing networks.
 
         <p>This function works for a subset of BCMP single-class open networks
@@ -3078,16 +3112,16 @@
 Networks and Markov Chains: Modeling and Performance Evaluation with
 Computer Science Applications</cite>, Wiley, 1998.
 
-   <p><a name="index-Bolch_002c-G_002e-130"></a><a name="index-Greiner_002c-S_002e-131"></a><a name="index-de-Meer_002c-H_002e-132"></a><a name="index-Trivedi_002c-K_002e-133"></a>
+   <p><a name="index-Bolch_002c-G_002e-133"></a><a name="index-Greiner_002c-S_002e-134"></a><a name="index-de-Meer_002c-H_002e-135"></a><a name="index-Trivedi_002c-K_002e-136"></a>
 
 <!-- Open network with multiple classes -->
    <p><a name="doc_002dqnopenmulti"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V</var>)<var><a name="index-qnopenmulti-134"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopenmulti-135"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V</var>)<var><a name="index-qnopenmulti-137"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopenmulti-138"></a></var><br>
 <blockquote>
-        <p><a name="index-open-network_002c-multiple-classes-136"></a>
+        <p><a name="index-open-network_002c-multiple-classes-139"></a>
 Exact analysis of open, multiple-class BCMP networks. The network can
 be made of <em>single-server</em> queueing centers (FCFS, LCFS-PR or
 PS) or delay centers (IS). This function assumes a network with
@@ -3152,7 +3186,7 @@
 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In
 particular, see section 7.4.1 ("Open Model Solution Techniques").
 
-   <p><a name="index-Lazowska_002c-E_002e-D_002e-137"></a><a name="index-Zahorjan_002c-J_002e-138"></a><a name="index-Graham_002c-G_002e-S_002e-139"></a><a name="index-Sevcik_002c-K_002e-C_002e-140"></a>
+   <p><a name="index-Lazowska_002c-E_002e-D_002e-140"></a><a name="index-Zahorjan_002c-J_002e-141"></a><a name="index-Graham_002c-G_002e-S_002e-142"></a><a name="index-Sevcik_002c-K_002e-C_002e-143"></a>
 
 <h4 class="subsection">6.3.4 Closed Networks</h4>
 
@@ -3160,11 +3194,11 @@
 <p><a name="doc_002dqnclosedsinglemva"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemva-141"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemva-142"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemva-143"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemva-144"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemva-145"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemva-146"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-144"></a><a name="index-closed-network_002c-single-class-145"></a><a name="index-normalization-constant-146"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-147"></a><a name="index-closed-network_002c-single-class-148"></a><a name="index-normalization-constant-149"></a>
 Analyze closed, single class queueing networks using the exact Mean
 Value Analysis (MVA) algorithm. The following queueing disciplines
 are supported: FCFS, LCFS-PR, PS and IS (Infinite Server). This
@@ -3265,7 +3299,7 @@
 Multichain Queuing Networks</cite>, Journal of the ACM, vol. 27, n. 2, April
 1980, pp. 313&ndash;322. <a href="http://doi.acm.org/10.1145/322186.322195">http://doi.acm.org/10.1145/322186.322195</a>
 
-   <p><a name="index-Reiser_002c-M_002e-147"></a><a name="index-Lavenberg_002c-S_002e-S_002e-148"></a>
+   <p><a name="index-Reiser_002c-M_002e-150"></a><a name="index-Lavenberg_002c-S_002e-S_002e-151"></a>
 This implementation is described in R. Jain , <cite>The Art of Computer
 Systems Performance Analysis</cite>, Wiley, 1991, p. 577.  Multi-server nodes
 <!-- and the computation of @math{G(N)}, -->
@@ -3274,15 +3308,15 @@
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998, Section 8.2.1, "Single Class Queueing Networks".
 
-   <p><a name="index-Jain_002c-R_002e-149"></a><a name="index-Bolch_002c-G_002e-150"></a><a name="index-Greiner_002c-S_002e-151"></a><a name="index-de-Meer_002c-H_002e-152"></a><a name="index-Trivedi_002c-K_002e-153"></a>
+   <p><a name="index-Jain_002c-R_002e-152"></a><a name="index-Bolch_002c-G_002e-153"></a><a name="index-Greiner_002c-S_002e-154"></a><a name="index-de-Meer_002c-H_002e-155"></a><a name="index-Trivedi_002c-K_002e-156"></a>
 <!-- MVA for single class, closed networks with load dependent servers -->
 <a name="doc_002dqnclosedsinglemvald"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvald-154"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V, Z</var>)<var><a name="index-qnclosedsinglemvald-155"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvald-157"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V, Z</var>)<var><a name="index-qnclosedsinglemvald-158"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-156"></a><a name="index-closed-network_002c-single-class-157"></a><a name="index-load_002ddependent-service-center-158"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-159"></a><a name="index-closed-network_002c-single-class-160"></a><a name="index-load_002ddependent-service-center-161"></a>
 Exact MVA algorithm for closed, single class queueing networks
 with load-dependent service centers. This function supports
 FCFS, LCFS-PR, PS and IS nodes. For networks with only fixed-rate
@@ -3340,15 +3374,15 @@
 1998, Section 8.2.4.1, &ldquo;Networks with Load-Deèpendent Service: Closed
 Networks&rdquo;.
 
-   <p><a name="index-Bolch_002c-G_002e-159"></a><a name="index-Greiner_002c-S_002e-160"></a><a name="index-de-Meer_002c-H_002e-161"></a><a name="index-Trivedi_002c-K_002e-162"></a>
+   <p><a name="index-Bolch_002c-G_002e-162"></a><a name="index-Greiner_002c-S_002e-163"></a><a name="index-de-Meer_002c-H_002e-164"></a><a name="index-Trivedi_002c-K_002e-165"></a>
 <!-- CMVA for single class, closed networks with a single load dependent servers -->
 <a name="doc_002dqncmva"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V</var>)<var><a name="index-qncmva-163"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V, Z</var>)<var><a name="index-qncmva-164"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V</var>)<var><a name="index-qncmva-166"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V, Z</var>)<var><a name="index-qncmva-167"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-165"></a><a name="index-CMVA-166"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-168"></a><a name="index-CMVA-169"></a>
 Implementation of the Conditional MVA (CMVA) algorithm, a numerically
 stable variant of MVA for load-dependent servers. CMVA is described
 in G. Casale, <cite>A Note on Stable Flow-Equivalent Aggregation in
@@ -3402,19 +3436,19 @@
 closed networks</cite>. Queueing Syst. Theory Appl., 60:193–202, December
 2008.
 
-   <p><a name="index-Casale_002c-G_002e-167"></a>
+   <p><a name="index-Casale_002c-G_002e-170"></a>
 <!-- Approximate MVA for single class, closed networks -->
 
    <p><a name="doc_002dqnclosedsinglemvaapprox"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvaapprox-168"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemvaapprox-169"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemvaapprox-170"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedsinglemvaapprox-171"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedsinglemvaapprox-172"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvaapprox-171"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemvaapprox-172"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemvaapprox-173"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedsinglemvaapprox-174"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedsinglemvaapprox-175"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-173"></a><a name="index-Approximate-MVA-174"></a><a name="index-Closed-network_002c-single-class-175"></a><a name="index-Closed-network_002c-approximate-analysis-176"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-176"></a><a name="index-Approximate-MVA-177"></a><a name="index-Closed-network_002c-single-class-178"></a><a name="index-Closed-network_002c-approximate-analysis-179"></a>
 Analyze closed, single class queueing networks using the Approximate
 Mean Value Analysis (MVA) algorithm. This function is based on
 approximating the number of customers seen at center k when a
@@ -3493,20 +3527,20 @@
 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In
 particular, see section 6.4.2.2 ("Approximate Solution Techniques").
 
-   <p><a name="index-Lazowska_002c-E_002e-D_002e-177"></a><a name="index-Zahorjan_002c-J_002e-178"></a><a name="index-Graham_002c-G_002e-S_002e-179"></a><a name="index-Sevcik_002c-K_002e-C_002e-180"></a>
+   <p><a name="index-Lazowska_002c-E_002e-D_002e-180"></a><a name="index-Zahorjan_002c-J_002e-181"></a><a name="index-Graham_002c-G_002e-S_002e-182"></a><a name="index-Sevcik_002c-K_002e-C_002e-183"></a>
 
 <!-- MVA for multiple class, closed networks -->
    <p><a name="doc_002dqnclosedmultimva"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S </var>)<var><a name="index-qnclosedmultimva-181"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimva-182"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimva-183"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimva-184"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P</var>)<var><a name="index-qnclosedmultimva-185"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P, m</var>)<var><a name="index-qnclosedmultimva-186"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S </var>)<var><a name="index-qnclosedmultimva-184"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimva-185"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimva-186"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimva-187"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P</var>)<var><a name="index-qnclosedmultimva-188"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P, m</var>)<var><a name="index-qnclosedmultimva-189"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-187"></a><a name="index-closed-network_002c-multiple-classes-188"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-190"></a><a name="index-closed-network_002c-multiple-classes-191"></a>
 Analyze closed, multiclass queueing networks with K service
 centers and C independent customer classes (chains) using the
 Mean Value Analysys (MVA) algorithm.
@@ -3636,7 +3670,7 @@
 Multichain Queuing Networks</cite>, Journal of the ACM, vol. 27, n. 2, April
 1980, pp. 313&ndash;322. <a href="http://doi.acm.org/10.1145/322186.322195">http://doi.acm.org/10.1145/322186.322195</a>
 
-   <p><a name="index-Reiser_002c-M_002e-189"></a><a name="index-Lavenberg_002c-S_002e-S_002e-190"></a>
+   <p><a name="index-Reiser_002c-M_002e-192"></a><a name="index-Lavenberg_002c-S_002e-S_002e-193"></a>
 This implementation is based on G. Bolch, S. Greiner, H. de Meer and
 K. Trivedi, <cite>Queueing Networks and Markov Chains: Modeling and
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
@@ -3646,18 +3680,18 @@
 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In
 particular, see section 7.4.2.1 ("Exact Solution Techniques").
 
-   <p><a name="index-Bolch_002c-G_002e-191"></a><a name="index-Greiner_002c-S_002e-192"></a><a name="index-de-Meer_002c-H_002e-193"></a><a name="index-Trivedi_002c-K_002e-194"></a><a name="index-Lazowska_002c-E_002e-D_002e-195"></a><a name="index-Zahorjan_002c-J_002e-196"></a><a name="index-Graham_002c-G_002e-S_002e-197"></a><a name="index-Sevcik_002c-K_002e-C_002e-198"></a>
+   <p><a name="index-Bolch_002c-G_002e-194"></a><a name="index-Greiner_002c-S_002e-195"></a><a name="index-de-Meer_002c-H_002e-196"></a><a name="index-Trivedi_002c-K_002e-197"></a><a name="index-Lazowska_002c-E_002e-D_002e-198"></a><a name="index-Zahorjan_002c-J_002e-199"></a><a name="index-Graham_002c-G_002e-S_002e-200"></a><a name="index-Sevcik_002c-K_002e-C_002e-201"></a>
 <!-- Approximate MVA, with Bard-Schweitzer approximation -->
 <a name="doc_002dqnclosedmultimvaapprox"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimvaapprox-199"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimvaapprox-200"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimvaapprox-201"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedmultimvaapprox-202"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedmultimvaapprox-203"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimvaapprox-202"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimvaapprox-203"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimvaapprox-204"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedmultimvaapprox-205"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedmultimvaapprox-206"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-204"></a><a name="index-Approximate-MVA-205"></a><a name="index-Closed-network_002c-multiple-classes-206"></a><a name="index-Closed-network_002c-approximate-analysis-207"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-207"></a><a name="index-Approximate-MVA-208"></a><a name="index-Closed-network_002c-multiple-classes-209"></a><a name="index-Closed-network_002c-approximate-analysis-210"></a>
 Analyze closed, multiclass queueing networks with K service
 centers and C customer classes using the approximate Mean
 Value Analysys (MVA) algorithm.
@@ -3742,12 +3776,12 @@
 proc. 4th Int. Symp. on Modelling and Performance Evaluation of
 Computer Systems, feb. 1979, pp. 51&ndash;62.
 
-   <p><a name="index-Bard_002c-Y_002e-208"></a>
+   <p><a name="index-Bard_002c-Y_002e-211"></a>
 P. Schweitzer, <cite>Approximate Analysis of Multiclass Closed
 Networks of Queues</cite>, Proc. Int. Conf. on Stochastic Control and
 Optimization, jun 1979, pp. 25&ndash;29.
 
-   <p><a name="index-Schweitzer_002c-P_002e-209"></a>
+   <p><a name="index-Schweitzer_002c-P_002e-212"></a>
 This implementation is based on Edward D. Lazowska, John Zahorjan, G. 
 Scott Graham, and Kenneth C. Sevcik, <cite>Quantitative System
 Performance: Computer System Analysis Using Queueing Network Models</cite>,
@@ -3758,7 +3792,7 @@
 described above, as it computes the average response times R
 instead of the residence times.
 
-   <p><a name="index-Lazowska_002c-E_002e-D_002e-210"></a><a name="index-Zahorjan_002c-J_002e-211"></a><a name="index-Graham_002c-G_002e-S_002e-212"></a><a name="index-Sevcik_002c-K_002e-C_002e-213"></a>
+   <p><a name="index-Lazowska_002c-E_002e-D_002e-213"></a><a name="index-Zahorjan_002c-J_002e-214"></a><a name="index-Graham_002c-G_002e-S_002e-215"></a><a name="index-Sevcik_002c-K_002e-C_002e-216"></a>
 
 <h4 class="subsection">6.3.5 Mixed Networks</h4>
 
@@ -3766,9 +3800,9 @@
 <p><a name="doc_002dqnmix"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmix</b> (<var>lambda, N, S, V, m</var>)<var><a name="index-qnmix-214"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmix</b> (<var>lambda, N, S, V, m</var>)<var><a name="index-qnmix-217"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-215"></a><a name="index-mixed-network-216"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-218"></a><a name="index-mixed-network-219"></a>
 Solution of mixed queueing networks through MVA. The network consists
 of K service centers (single-server or delay centers) and
 C independent customer chains. Both open and closed chains
@@ -3859,14 +3893,14 @@
 Note that in this function we compute the mean response time R
 instead of the mean residence time as in the reference.
 
-   <p><a name="index-Lazowska_002c-E_002e-D_002e-217"></a><a name="index-Zahorjan_002c-J_002e-218"></a><a name="index-Graham_002c-G_002e-S_002e-219"></a><a name="index-Sevcik_002c-K_002e-C_002e-220"></a>
+   <p><a name="index-Lazowska_002c-E_002e-D_002e-220"></a><a name="index-Zahorjan_002c-J_002e-221"></a><a name="index-Graham_002c-G_002e-S_002e-222"></a><a name="index-Sevcik_002c-K_002e-C_002e-223"></a>
 Herb Schwetman, <cite>Implementing the Mean Value Algorithm for the
 Solution of Queueing Network Models</cite>, Technical Report CSD-TR-355,
 Department of Computer Sciences, Purdue University, feb 15, 1982,
 available at
 <a href="http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-355.pdf">http://www.cs.purdue.edu/research/technical_reports/1980/TR%...
 
[truncated message content]

[Octave-cvsupdate] SF.net SVN: octave:[9817] trunk/octave-forge/extra/dataframe/inst/@ dataframe

From: <cde...@us...> - 2012-03-11 20:53:40

Revision: 9817
          http://octave.svn.sourceforge.net/octave/?rev=9817&view=rev
Author:   cdemills
Date:     2012-03-11 20:53:31 +0000 (Sun, 11 Mar 2012)
Log Message:
-----------
apply the emptiness test in dataframe.m only if more than one row

Modified Paths:
--------------
    trunk/octave-forge/extra/dataframe/inst/@dataframe/cat.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/dataframe.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/display.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/find.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/fold.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/horzcat.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/inv.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/isfield.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/isscalar.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/isvector.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/ne.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/permute.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_allmeta.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_basecomp.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_check_char_array.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_colmeta.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_cow.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_func.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_mapper2.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_matassign.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_name2idx.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_pad.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_strjust.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_strset.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_thirddim.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_whole.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/prod.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/repmat.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/reshape.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/size.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/sort.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/subsasgn.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/subsref.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/sum.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/summary.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/sumsq.m
    trunk/octave-forge/extra/dataframe/inst/@dataframe/vertcat.m

Modified: trunk/octave-forge/extra/dataframe/inst/@dataframe/cat.m
===================================================================
--- trunk/octave-forge/extra/dataframe/inst/@dataframe/cat.m	2012-03-11 20:34:47 UTC (rev 9816)
+++ trunk/octave-forge/extra/dataframe/inst/@dataframe/cat.m	2012-03-11 20:53:31 UTC (rev 9817)
@@ -29,172 +29,172 @@
   %# $Id$
   %#
 
-  if (!isa(A, 'dataframe')),
-    A = dataframe(A);
+  if (~isa (A, 'dataframe')),
+    A = dataframe (A);
   endif
 
   switch dim
     case 1
       resu = A;
           
-      for indi = 1:length(varargin),
-	B = varargin{indi};
-	if !isa(B, 'dataframe'),
-	  if iscell(B) && 2 == length(B),
-	    B = dataframe(B{2}, 'rownames', B{1});
-	  else
-	    B = dataframe(B, 'colnames', inputname(2+indi));
-	  endif
-	endif
-	if resu._cnt(2) != B._cnt(2),
-	  error('Different number of columns in dataframes');
-	endif
-	%# do not duplicate empty names
-	if !isempty(resu._name{1}) || !isempty(B._name{1}),
-	  if length(resu._name{1}) < resu._cnt(1),
-	    resu._name{1}(end+1:resu._cnt(1), 1) = {''};
-	  endif
-	  if length(B._name{1}) < B._cnt(1),
-	    B._name{1}(end+1:B._cnt(1), 1) = {''};
-	  endif
-	  resu._name{1} = vertcat(resu._name{1}(:),  B._name{1}(:));
-	  resu._over{1} = [resu._over{1} B._over{1}];
-	endif
-	resu._cnt(1) = resu._cnt(1) + B._cnt(1);
-	if size(resu._ridx, 2) < size(B._ridx, 2),
-	  resu._ridx(:, end+1:size(B._ridx, 2)) = NA;
-	elseif size(resu._ridx, 2) > size(B._ridx, 2),
-	  B._ridx(:, end+1:size(resu._ridx, 2)) = NA;
-	endif
-	resu._ridx = [resu._ridx; B._ridx];
-	%# find data with same column names
-	dummy = A._over{2} & B._over{2}; 
-	indA = true(1, resu._cnt(2));
-	indB = true(1, resu._cnt(2));
-	for indj = 1:resu._cnt(2),
-	  if (dummy(indj)),
-	    indk = strmatch(resu._name{2}(indj), B._name{2}, 'exact');
-	    if (~isempty(indk)),
-	      indk = indk(1);
-	      if ~strcmp(resu._type{indj}, B._type{indk}),
-		error("Trying to mix columns of different types");
-	      endif
-	    endif
-	  else
-	    indk = indj;
-	  endif
-	  resu._data{indj} = [resu._data{indj}; B._data{indk}];
-	  indA(indj) = false; indB(indk) = false;
-	endfor
-	if any(indA) || any(indB)
-	  error('Different number/names of columns in dataframe');
-	endif
-	
+      for indi = (1:length (varargin))
+        B = varargin{indi};
+        if (~isa (B, 'dataframe'))
+          if (iscell (B) && 2 == length (B))
+            B = dataframe (B{2}, 'rownames', B{1});
+          else
+            B = dataframe (B, 'colnames', inputname(2+indi));
+          endif
+        endif
+        if (resu._cnt(2) ~= B._cnt(2))
+          error ('Different number of columns in dataframes');
+        endif
+        %# do not duplicate empty names
+        if (~isempty (resu._name{1}) || ~isempty (B._name{1}))
+          if (length (resu._name{1}) < resu._cnt(1))
+            resu._name{1}(end+1:resu._cnt(1), 1) = {''};
+          endif
+          if (length (B._name{1}) < B._cnt(1))
+            B._name{1}(end+1:B._cnt(1), 1) = {''};
+          endif
+          resu._name{1} = vertcat (resu._name{1}(:),  B._name{1}(:));
+          resu._over{1} = [resu._over{1} B._over{1}];
+        endif
+        resu._cnt(1) = resu._cnt(1) + B._cnt(1);
+        if (size (resu._ridx, 2) < size (B._ridx, 2))
+          resu._ridx(:, end+1:size(B._ridx, 2)) = NA;
+        elseif (size (resu._ridx, 2) > size (B._ridx, 2))
+          B._ridx(:, end+1:size(resu._ridx, 2)) = NA;
+        endif
+        resu._ridx = [resu._ridx; B._ridx];
+        %# find data with same column names
+        dummy = A._over{2} & B._over{2}; 
+        indA = true (1, resu._cnt(2));
+        indB = true (1, resu._cnt(2));
+        for indj = (1:resu._cnt(2))
+          if (dummy(indj))
+            indk = strmatch (resu._name{2}(indj), B._name{2}, 'exact');
+            if (~isempty (indk))
+              indk = indk(1);
+              if (~strcmp (resu._type{indj}, B._type{indk}))
+                error ("Trying to mix columns of different types");
+              endif
+            endif
+          else
+            indk = indj;
+          endif
+          resu._data{indj} = [resu._data{indj}; B._data{indk}];
+          indA(indj) = false; indB(indk) = false;
+        endfor
+        if (any (indA) || any (indB))
+          error ('Different number/names of columns in dataframe');
+        endif
+        
       endfor
       
     case 2
       resu = A;
 
-      for indi = 1:length(varargin),
-	B = varargin{indi};
-	if !isa(B, 'dataframe'),
-	  if iscell(B) && 2 == length(B),
-	    B = dataframe(B{2}, 'colnames', B{1});
-	  else
-	    B = dataframe(B, 'colnames', inputname(2+indi));
-	  endif
-	  B._ridx = resu._ridx; %# make them compatibles
-	endif
-	if resu._cnt(1) != B._cnt(1),
-	  error('Different number of rows in dataframes');
-	endif
-	if any(resu._ridx(:) - B._ridx(:))
-	  error('dataframes row indexes not matched');
-	endif
-	resu._name{2} = vertcat(resu._name{2}, B._name{2});
-	resu._over{2} = [resu._over{2} B._over{2}];
-	resu._data(resu._cnt(2)+(1:B._cnt(2))) = B._data;
-	resu._type(resu._cnt(2)+(1:B._cnt(2))) = B._type;
-	resu._cnt(2) = resu._cnt(2) + B._cnt(2);	
+      for indi = (1:length (varargin))
+        B = varargin{indi};
+        if (~isa (B, 'dataframe'))
+          if (iscell (B) && 2 == length (B))
+            B = dataframe (B{2}, 'colnames', B{1});
+          else
+            B = dataframe (B, 'colnames', inputname(2+indi));
+          endif
+          B._ridx = resu._ridx; %# make them compatibles
+        endif
+        if (resu._cnt(1) ~= B._cnt(1))
+          error ('Different number of rows in dataframes');
+        endif
+        if (any(resu._ridx(:) - B._ridx(:)))
+          error ('dataframes row indexes not matched');
+        endif
+        resu._name{2} = vertcat (resu._name{2}, B._name{2});
+        resu._over{2} = [resu._over{2} B._over{2}];
+        resu._data(resu._cnt(2)+(1:B._cnt(2))) = B._data;
+        resu._type(resu._cnt(2)+(1:B._cnt(2))) = B._type;
+        resu._cnt(2) = resu._cnt(2) + B._cnt(2);        
       endfor
       
     case 3
       resu = A;
       
-      for indi = 1:length(varargin),
-	B = varargin{indi};
-	if (!isa(B, 'dataframe')),
-	  if (iscell(B) && 2 == length(B)),
-	    B = dataframe(B{2}, 'rownames', B{1});
-	  else
-	    B = dataframe(B, 'colnames', inputname(indi+2)); 
-	  endif
-	endif
-	if (resu._cnt(1) != B._cnt(1)),
-	  error('Different number of rows in dataframes');
-	endif
-	if (resu._cnt(2) != B._cnt(2)),
-	  error('Different number of columns in dataframes');
-	endif
-	%# to be merged against 3rd dim, rownames must be equals, if
-	%# non-empty. Columns are merged based upon their name; columns
-	%# with identic content are kept.
+      for indi = (1:length (varargin))
+        B = varargin{indi};
+        if (~isa (B, 'dataframe'))
+          if (iscell (B) && 2 == length (B)),
+            B = dataframe (B{2}, 'rownames', B{1});
+          else
+            B = dataframe (B, 'colnames', inputname(indi+2)); 
+          endif
+        endif
+        if (resu._cnt(1) ~= B._cnt(1))
+          error ('Different number of rows in dataframes');
+        endif
+        if (resu._cnt(2) ~= B._cnt(2)),
+          error ('Different number of columns in dataframes');
+        endif
+        %# to be merged against 3rd dim, rownames must be equals, if
+        %# non-empty. Columns are merged based upon their name; columns
+        %# with identic content are kept.
 
-	if size(resu._ridx, 2) < size(B._ridx, 2),
-	  resu._ridx(:, end+1:size(B._ridx, 2)) = NA;
-	elseif size(resu._ridx, 2) > size(B._ridx, 2),
-	  B._ridx(:, end+1:size(resu._ridx, 2)) = NA;
-	endif
-	resu._ridx = cat(3, resu._ridx, B._ridx);
-	%# find data with same column names
-	indA = true(1, resu._cnt(2));
-	indB = true(1, resu._cnt(2));
-	dummy = A._over{2} & B._over{2}; 
-	for indj = 1:resu._cnt(2),
-	  if (dummy(indj)),
-	    indk = strmatch(resu._name{2}(indj), B._name{2}, 'exact');
-	    if (~isempty(indk)),
-	      indk = indk(1);
-	      if (~strcmp(resu._type{indj}, B._type{indk})),
-		error("Trying to mix columns of different types");
-	      endif
-	    endif
-	  else
-	    indk = indj;
-	  endif
-	  if (all([isnumeric(resu._data{indj}) isnumeric(B._data{indk})])),
-	    %# iterate over the columns of resu and B
-	    op1 = resu._data{indj}; op2 = B._data{indk};
-	    for ind2=1:columns(op2),
-	      indr = false;
-	      for ind1=1:columns(op1),
-		if (all(abs(op1(:, ind1) - op2(:, ind2)) <= eps)),
-		  resu._rep{indj} = [resu._rep{indj} ind1];
-		  indr = true;
-		  break;
-		endif
-	      endfor
-	      if (!indr),
-		%# pad in the second dim
-		resu._data{indj} = [resu._data{indj}, B._data{indk}];
-		resu._rep{indj} = [resu._rep{indj} 1+length(resu._rep{indj})];
-	      endif
-	    endfor
-	  else
-	    resu._data{indj} = [resu._data{indj} B._data{indk}];
-	    resu._rep{indj} = [resu._rep{indj} 1+length(resu._rep({indj}))];
-	  endif
-	  indA(indj) = false; indB(indk) = false;
-	endfor
-	if (any(indA) || any(indB)),
-	  error('Different number/names of columns in dataframe');
-	endif
+        if (size(resu._ridx, 2) < size(B._ridx, 2))
+          resu._ridx(:, end+1:size(B._ridx, 2)) = NA;
+        elseif (size(resu._ridx, 2) > size(B._ridx, 2))
+          B._ridx(:, end+1:size(resu._ridx, 2)) = NA;
+        endif
+        resu._ridx = cat (3, resu._ridx, B._ridx);
+        %# find data with same column names
+        indA = true (1, resu._cnt(2));
+        indB = true (1, resu._cnt(2));
+        dummy = A._over{2} & B._over{2}; 
+        for indj = (1:resu._cnt(2))
+          if (dummy(indj))
+            indk = strmatch (resu._name{2}(indj), B._name{2}, 'exact');
+            if (~isempty (indk)),
+              indk = indk(1);
+              if (~strcmp (resu._type{indj}, B._type{indk})),
+                error("Trying to mix columns of different types");
+              endif
+            endif
+          else
+            indk = indj;
+          endif
+          if (all ([isnumeric(resu._data{indj}) isnumeric(B._data{indk})])),
+            %# iterate over the columns of resu and B
+            op1 = resu._data{indj}; op2 = B._data{indk};
+            for ind2 = (1:columns (op2))
+              indr = false;
+              for ind1 = (1:columns (op1))
+                if (all (abs (op1(:, ind1) - op2(:, ind2)) <= eps)),
+                  resu._rep{indj} = [resu._rep{indj} ind1];
+                  indr = true;
+                  break;
+                endif
+              endfor
+              if (~indr),
+                %# pad in the second dim
+                resu._data{indj} = [resu._data{indj}, B._data{indk}];
+                resu._rep{indj} = [resu._rep{indj} 1+length(resu._rep{indj})];
+              endif
+            endfor
+          else
+            resu._data{indj} = [resu._data{indj} B._data{indk}];
+            resu._rep{indj} = [resu._rep{indj} 1+length(resu._rep({indj}))];
+          endif
+          indA(indj) = false; indB(indk) = false;
+        endfor
+        if (any (indA) || any (indB))
+          error ('Different number/names of columns in dataframe');
+        endif
       endfor
      
-      resu = df_thirddim(resu);
+      resu = df_thirddim (resu);
       
     otherwise
-      error('Incorrect call to cat');
+      error ('Incorrect call to cat');
   endswitch
   
   %#  disp('End of cat'); keyboard

Modified: trunk/octave-forge/extra/dataframe/inst/@dataframe/dataframe.m
===================================================================
--- trunk/octave-forge/extra/dataframe/inst/@dataframe/dataframe.m	2012-03-11 20:34:47 UTC (rev 9816)
+++ trunk/octave-forge/extra/dataframe/inst/@dataframe/dataframe.m	2012-03-11 20:53:31 UTC (rev 9817)
@@ -92,7 +92,7 @@
 seeked = []; trigger =[]; unquot = true; sep = "\t,"; cmt_lines = [];
 locales = "C";
 
-if (length(varargin) > 0)
+if (length (varargin) > 0)
   indi = 1;
   %# loop over possible arguments
   while (indi <= size (varargin, 2))
@@ -155,7 +155,7 @@
   endwhile
 endif
 
-if (!isempty (seeked) && !isempty (trigger))
+if (~isempty (seeked) && ~isempty (trigger))
   error ('seeked and trigger are mutuallly incompatible arguments');
 endif
 
@@ -175,10 +175,10 @@
         unwind_protect
           dummy = tilde_expand (x);
           fid = fopen (dummy);
-          if (fid != -1)
+          if (fid ~= -1)
             df._src{end+1, 1} = dummy;
             dummy = fgetl (fid);
-            if (!strcmp (dummy, UTF8_BOM))
+            if (~strcmp (dummy, UTF8_BOM))
               frewind (fid);
             endif
             %# slurp everything and convert doubles to char, avoiding
@@ -188,10 +188,10 @@
             in = [];
           endif
         unwind_protect_cleanup
-          if (fid != -1) fclose (fid); endif
+          if (fid ~= -1) fclose (fid); endif
         end_unwind_protect
 
-        if (!isempty (in))
+        if (~isempty (in))
           %# explicit list taken from 'man pcrepattern' -- we enclose all
           %# vertical separators in case the underlying regexp engine
           %# doesn't have them all.
@@ -212,7 +212,7 @@
           %# lines, 'UniformOutput', false); %# extract fields
           content = cellfun (@(x) strsplit (x, sep), lines, \
                              'UniformOutput', false); %# extract fields  
-          indl = 1; indj = 1; %# disp('line 151 '); keyboard
+          indl = 1; indj = 1;  %#disp('line 151 '); keyboard
           if (~isempty (seeked))
             while (indl <= length (lines))
               dummy = content{indl};
@@ -246,7 +246,7 @@
           endif
           x = cell (1+length (lines)-indl, size(dummy, 2)); 
           empty_lines = []; cmt_lines = [];
-          while (indl <= length(lines))
+          while (indl <= length (lines))
             dummy = content{indl};
             if (all (cellfun ('size', dummy, 2) == 0))
               empty_lines = [empty_lines indj];
@@ -273,7 +273,7 @@
                   catch
                     %# if the previous test fails, try a simpler one
                     in = regexp (dummy{indk}, '[^'' ]+', 'match');
-                    if (!isempty(in))
+                    if (~isempty (in))
                       x(indj, indk) = in{1};
                       %# else
                       %#    x(indj, indk) = [];
@@ -284,7 +284,7 @@
                   x(indj, indk) = regexp (dummy{indk}, '[^ ].*', 'match');
                 endif
               else
-                if (!isempty (regexp (dummy{indk}, '[/:]')))
+                if (~isempty (regexp (dummy{indk}, '[/:]')))
                   %# try to convert to a date
                   [timeval, nfields] = strptime( dummy{indk}, 
                                                 [char(37) 'd/' char(37) 'm/' char(37) 'Y ' char(37) 'T']);
@@ -293,7 +293,7 @@
                                          timeval);
                     %# try to extract the usec field, if any
                     idx = regexp (dummy{indk}, timestr, 'end');
-                    if (!isempty (idx))
+                    if (~isempty (idx))
                       idx = idx + 1;
                       if (ispunct (dummy{indk}(idx)))
                         idx = idx + 1;
@@ -310,12 +310,12 @@
             endfor
             indl = indl + 1; indj = indj + 1;
           endwhile
-          if (!isempty(empty_lines))
+          if (~isempty (empty_lines))
             x(empty_lines, :) = [];
           endif
           %# detect empty columns
           empty_lines = find (0 == sum (cellfun ('size', x, 2)));
-          if (!isempty(empty_lines))
+          if (~isempty (empty_lines))
             x(:, empty_lines) = [];
           endif
           clear UTF8_BOM fid in lines indl the_line content empty_lines
@@ -326,7 +326,7 @@
   
     %# fallback, avoiding a recursive call
     idx.type = '()';
-    if (!isa (x, 'char'))
+    if (~isa (x, 'char'))
       indj = df._cnt(2)+(1:size (x, 2));
     else
       %# at this point, reading some filename failed
@@ -337,7 +337,7 @@
       if (2 == length (x))
         %# use the intermediate value as destination column
         [indc, ncol] = df_name2idx (df._name{2}, x{1}, df._cnt(2), "column");
-        if (ncol != 1)
+        if (ncol ~= 1)
           error (["With two-elements cell, the first should resolve " ...
                   "to a single column"]);
         endif
@@ -362,7 +362,7 @@
       %# allow overwriting of column names
       df._over{2}(1, indj) = true;
     else
-      if (!isempty(indj))        
+      if (~isempty (indj))        
         if (1 == length (df._name{2}) && length (df._name{2}) < \
             length (indj))
           [df._name{2}(indj, 1),  df._over{2}(1, indj)] ...
@@ -374,15 +374,15 @@
         df._name{2} = genvarname (df._name{2});
       endif
     endif
-    if (!isempty (indj))
+    if (~isempty (indj))
       %# the exact row size will be determined latter
       idx.subs = {'', indj};
       %# use direct assignement
       if (ndims (x) > 2), idx.subs{3} = 1:size (x, 3); endif
       %#      df = subsasgn(df, idx, x);        <= call directly lower level
-      df = df_matassign (df, idx, indj, length(indj), x);
-      if (!isempty (cmt_lines))
-        df._cmt = vertcat(df._cmt, cellstr(cmt_lines));
+      df = df_matassign (df, idx, indj, length (indj), x);
+      if (~isempty (cmt_lines))
+        df._cmt = vertcat (df._cmt, cellstr (cmt_lines));
         cmt_lines = [];
       endif
     else

Modified: trunk/octave-forge/extra/dataframe/inst/@dataframe/display.m
===================================================================
--- trunk/octave-forge/extra/dataframe/inst/@dataframe/display.m	2012-03-11 20:34:47 UTC (rev 9816)
+++ trunk/octave-forge/extra/dataframe/inst/@dataframe/display.m	2012-03-11 20:53:31 UTC (rev 9817)
@@ -29,7 +29,7 @@
 
   %# generate header name
   dummy = inputname (1);
-  if (isempty(dummy))
+  if (isempty (dummy))
     dummy = "ans";
   endif
 
@@ -41,7 +41,7 @@
                     dummy, df._cnt);
   endif
 
-  if (!isempty (df._src))
+  if (~isempty (df._src))
     for indi = (1:size (df._src, 1))
       head = strvcat\
           (head, [repmat("Src: ", size (df._src{indi, 1}, 1), 1)\
@@ -49,7 +49,7 @@
     endfor
   endif
 
-  if (!isempty (df._cmt))
+  if (~isempty (df._cmt))
     for indi = (1:size(df._cmt, 1))
       head = strvcat\
           (head, [repmat("Comment: ", size (df._cmt{indi, 1}, 1), 1)\
@@ -58,7 +58,7 @@
   endif
   
   if (all (df._cnt > 0))  %# stop for empty df
-    dummy=[]; vspace = repmat (' ', df._cnt(1), 1);
+    dummy = []; vspace = repmat (' ', df._cnt(1), 1);
     indi = 1; %# the real, unfolded index
     %# loop over columns where the corresponding _data really exists
     for indc = (1:min (df._cnt(2), size (df._data, 2))) 
@@ -85,7 +85,7 @@
             tmp_str = df._data{indc}(:, indk); %#get the whole column
             indj = cellfun ('isprint', tmp_str, 'UniformOutput', false); 
             indj = ~cellfun ('all', indj);
-            for indr = (1:length(indj))
+            for indr = (1:length (indj))
               if (indj(indr)),
                 if (isna (tmp_str{indr})),
                   tmp_str{indr} = "NA";
@@ -125,10 +125,10 @@
     vspace = [' '; ' '; vspace];
     %# second line content
     resu = []; 
-    if (!isempty (df._ridx))
+    if (~isempty (df._ridx))
       for (ind1 = 1:size (df._ridx, 2))
         if ((1 == size(df._ridx, 3)) && \
-              (any (!isna (df._ridx(1:df._cnt(1), ind1)))))
+              (any (~isna (df._ridx(1:df._cnt(1), ind1)))))
           dummy{2, 1} = [sprintf("_%d", ind1) ; "Nr"];
           dummy{3, 1} = disp (df._ridx(1:df._cnt(1), ind1)); 
           indi = regexp (dummy{3, 1}, '\b.*\b', 'match', 'dotexceptnewline');
@@ -140,7 +140,7 @@
           endif
         else 
           for ind2 = (1:size (df._ridx, 3))
-            if (any (!isna (df._ridx(1:df._cnt(1), ind1, ind2)))),
+            if (any (~isna (df._ridx(1:df._cnt(1), ind1, ind2)))),
               dummy{2, 1} = [sprintf("_%d.%d", ind1, ind2) ; "Nr"];
               dummy{3, 1} = disp (df._ridx(1:df._cnt(1), ind1, ind2)); 
               indi = regexp (dummy{3, 1}, '\b.*\b', 'match', 'dotexceptnewline');
@@ -165,7 +165,7 @@
     endif
     
     %# insert a vertical space
-    if (!isempty(dummy{3, 2}))
+    if (~isempty (dummy{3, 2}))
       indi = ~cellfun ('isempty', dummy{3, 2});
       if (any (indi))
         try

Modified: trunk/octave-forge/extra/dataframe/inst/@dataframe/find.m
===================================================================
--- trunk/octave-forge/extra/dataframe/inst/@dataframe/find.m	2012-03-11 20:34:47 UTC (rev 9816)
+++ trunk/octave-forge/extra/dataframe/inst/@dataframe/find.m	2012-03-11 20:53:31 UTC (rev 9817)
@@ -26,35 +26,35 @@
 
   switch nargout
     case {0, 1}
-      resu = []; mz = max(cellfun(@length, df._rep));
-      for indc = 1:df._cnt(2),
-	[indr, inds] = feval(@find, df._data{indc}(:, df._rep{indc}));
-	%# create a vector the same size as indr
-	dummy = indr; dummy(:) = indc;
-	resu = [resu; sub2ind([df._cnt(1:2) mz], indr, dummy, inds)];
+      resu = []; mz = max (cellfun (@length, df._rep));
+      for indc = (1:df._cnt(2))
+        [indr, inds] = feval (@find, df._data{indc}(:, df._rep{indc}));
+        %# create a vector the same size as indr
+        dummy = indr; dummy(:) = indc;
+        resu = [resu; sub2ind([df._cnt(1:2) mz], indr, dummy, inds)];
       endfor
-      varargout{1} = sort(resu);
+      varargout{1} = sort (resu);
     case 2
       nz = 0; idx_i = []; idx_j = [];
-      for indc = 1:df._cnt(2),
-	[dum1, dum2] = feval(@find, df._data{indc}(:, df._rep{indc}));
-	idx_i = [idx_i; dum1];
-	idx_j = [idx_j; nz + dum2];
-	nz = nz + df._cnt(1)*length(df._rep{indc});
+      for indc = (1:df._cnt(2))
+        [dum1, dum2] = feval (@find, df._data{indc}(:, df._rep{indc}));
+        idx_i = [idx_i; dum1];
+        idx_j = [idx_j; nz + dum2];
+        nz = nz + df._cnt(1)*length (df._rep{indc});
       endfor
       varargout{1} = idx_i; varargout{2} = idx_j;
     case 3
       nz = 0; idx_i = []; idx_j = []; val = [];
-      for indc = 1:df._cnt(2),
-	[dum1, dum2, dum3] = feval(@find, df._data{indc}(:, df._rep{indc}));
-	idx_i = [idx_i; dum1];
-	idx_j = [idx_j; nz + dum2];
-	val = [val; dum3];
-	nz = nz + df._cnt(1)*length(df._rep{indc});
+      for indc = (1:df._cnt(2))
+        [dum1, dum2, dum3] = feval (@find, df._data{indc}(:, df._rep{indc}));
+        idx_i = [idx_i; dum1];
+        idx_j = [idx_j; nz + dum2];
+        val = [val; dum3];
+        nz = nz + df._cnt(1)*length (df._rep{indc});
       endfor
       varargout{1} = idx_i; varargout{2} = idx_j; varargout{3} = val;
     otherwise
-      print_usage('find');
+      print_usage ('find');
   endswitch
 
 endfunction

Modified: trunk/octave-forge/extra/dataframe/inst/@dataframe/fold.m
===================================================================
--- trunk/octave-forge/extra/dataframe/inst/@dataframe/fold.m	2012-03-11 20:34:47 UTC (rev 9816)
+++ trunk/octave-forge/extra/dataframe/inst/@dataframe/fold.m	2012-03-11 20:53:31 UTC (rev 9817)
@@ -32,65 +32,63 @@
   %#
 switch dim
   case 1
-    [indr, nrow] = df_name2idx(df._name{1}, indr, df._cnt(1), 'row');
-    [indc, ncol] = df_name2idx(df._name{2}, indc, df._cnt(2), 'column');
+    [indr, nrow] = df_name2idx (df._name{1}, indr, df._cnt(1), 'row');
+    [indc, ncol] = df_name2idx (df._name{2}, indc, df._cnt(2), 'column');
     
-    if (indr(1) > 1),
+    if (indr(1) > 1)
       slice_size = indr(1) - 1;
       %# we can't use directly resu = df(1:slice_size, :, :)
       S.type = '()';
       S.subs = { 1:slice_size, ':', ':', 'dataframe'};
-      resu = subsref(df, S);
+      resu = subsref (df, S);
       
       %# how many columns for each slice
-      targets = cellfun(@length, df._rep);
+      targets = cellfun (@length, df._rep);
       %# a test function to determine if the location is free
-      for indj = 1:df._cnt(2),
-	if (any(indj == indc)),
-	  continue;
-	endif
-	switch df._type{indj}
-	  case { 'char' }
-	    testfunc{indj} = @(x, indr, indc) ...
-		!isna(x{indr, indc});
-	  otherwise
-	    testfunc{indj} = @(x, indr, indc) ...
-		!isna(x(indr, indc));
-	endswitch
+      for indj = (1:df._cnt(2))
+        if (any (indj == indc))
+          continue;
+        endif
+        switch (df._type{indj})
+          case { 'char' }
+            testfunc{indj} = @(x, indr, indc) ...
+                ~isna (x{indr, indc});
+          otherwise
+            testfunc{indj} = @(x, indr, indc) ...
+                ~isna (x(indr, indc));
+        endswitch
       endfor
 
-      for indi = indr,
-	%# where does this line go ?
-	where = find(df._data{indc}(1:slice_size, 1) ...
-		     == df._data{indc}(indi, 1));
-	if (!isempty(where)),
-	  %# transfering one line -- loop over columns
-	  for indj = 1:df._cnt(2),
-	    if any(indj == indc),
-	      continue;
-	    endif
-	   
-	    if (testfunc{indj}(resu._data{indj}, where, targets(indj))),
-	      %# add one more sheet
-	      resu = df_pad(resu, 3, 1, indj);
-	      targets(indj) = targets(indj) + 1;
-	    endif
-	    %# transfer field
-	    stop
-	    resu._data{indj}(where, targets(indj)) = ...
-		df._data{indj}(indi, 1);
-	  endfor
-	  %# update row index
-	  resu._ridx(where, max(targets)) = df._ridx(indi);
-	else
-	  disp('line 65: FIXME'); keyboard;
-	endif
+      for indi = (indr)
+        %# where does this line go ?
+        where = find (df._data{indc}(1:slice_size, 1) ...
+                      == df._data{indc}(indi, 1));
+        if (~isempty (where))
+          %# transfering one line -- loop over columns
+          for indj = (1:df._cnt(2))
+            if (any (indj == indc))
+              continue;
+            endif
+           
+            if (testfunc{indj}(resu._data{indj}, where, targets(indj)))
+              %# add one more sheet
+              resu = df_pad(resu, 3, 1, indj);
+              targets(indj) = targets(indj) + 1;
+            endif
+            %# transfer field
+            stop
+            resu._data{indj}(where, targets(indj)) = ...
+                df._data{indj}(indi, 1);
+          endfor
+          %# update row index
+          resu._ridx(where, max(targets)) = df._ridx(indi);
+        else
+          disp ('line 65: FIXME'); keyboard;
+        endif
       endfor
 
     else
-
-      disp('line 70: FIXME '); keyboard
+      disp ('line 70: FIXME '); keyboard
     endif
 
-
 endswitch

Modified: trunk/octave-forge/extra/dataframe/inst/@dataframe/horzcat.m
===================================================================
--- trunk/octave-forge/extra/dataframe/inst/@dataframe/horzcat.m	2012-03-11 20:34:47 UTC (rev 9816)
+++ trunk/octave-forge/extra/dataframe/inst/@dataframe/horzcat.m	2012-03-11 20:53:31 UTC (rev 9817)
@@ -24,10 +24,10 @@
   %# $Id$
   %#
 
- for indi = 1:length(varargin),
-    varargin{indi} = dataframe(varargin{indi}, 'colnames', inputname(1+indi));,
+ for indi = (1:length (varargin))
+    varargin{indi} = dataframe (varargin{indi}, 'colnames', inputname(1+indi));,
   endfor
   
-  resu = cat(2, df, varargin{:});
+  resu = cat (2, df, varargin{:});
 
 endfunction

Modified: trunk/octave-forge/extra/dataframe/inst/@dataframe/inv.m
===================================================================
--- trunk/octave-forge/extra/dataframe/inst/@dataframe/inv.m	2012-03-11 20:34:47 UTC (rev 9816)
+++ trunk/octave-forge/extra/dataframe/inst/@dataframe/inv.m	2012-03-11 20:53:31 UTC (rev 9817)
@@ -29,24 +29,24 @@
   %# $Id$
   %#
 
-  if (length(df._cnt) > 2 || (df._cnt(1) != df._cnt(2))),
-    error("Dataframe is not square");
+  if (length (df._cnt) > 2 || (df._cnt(1) ~= df._cnt(2)))
+    error ("Dataframe is not square");
   endif
 
   %# quick and dirty conversion
-  [dummy, rcond] = inv(horzcat(df._data{:}));
+  [dummy, rcond] = inv (horzcat (df._data{:}));
 
   resu = df_allmeta(df);
   
-  [resu._name{2}, resu._name{1}] = deal(resu._name{1}, resu._name{2});
-  [resu._over{2}, resu._over{1}] = deal(resu._over{1}, resu._over{2});
-  if (isempty(resu._name{2})),
-    resu._name{2} = cellstr(repmat('_', resu._cnt(2), 1));
-    resu._over{2} = ones(1, resu._cnt(2));
+  [resu._name{2}, resu._name{1}] = deal (resu._name{1}, resu._name{2});
+  [resu._over{2}, resu._over{1}] = deal (resu._over{1}, resu._over{2});
+  if (isempty (resu._name{2})),
+    resu._name{2} = cellstr (repmat('_', resu._cnt(2), 1));
+    resu._over{2} = ones (1, resu._cnt(2));
   endif
-  for indi = resu._cnt(1):-1:1,
+  for indi = (resu._cnt(1):-1:1)
     resu._data{indi} = dummy(:, indi);
   endfor
-  resu._type(:) = class(dummy);
+  resu._type(:) = class (dummy);
   
 endfunction

Modified: trunk/octave-forge/extra/dataframe/inst/@dataframe/isfield.m
===================================================================
--- trunk/octave-forge/extra/dataframe/inst/@dataframe/isfield.m	2012-03-11 20:34:47 UTC (rev 9816)
+++ trunk/octave-forge/extra/dataframe/inst/@dataframe/isfield.m	2012-03-11 20:53:31 UTC (rev 9817)
@@ -35,57 +35,57 @@
   %# $Id$
   %#
 
-  if !isa(df, 'dataframe'),
+  if (~isa (df, 'dataframe'))
     resu = false; return;
   endif
 
-  if nargin <2 || nargin > 3,
-    print_usage();
+  if (nargin < 2 || nargin > 3)
+    print_usage ();
     resu = false; return;
   endif
 
-  if 2 == nargin, strict = false; endif
+  if (2 == nargin) strict = false; endif
 
-  if isa(name, 'char'),
-    if strict, %# use strmatch to get indexes
-      for indi = size(name, 1):-1:1,
-	dummy = strmatch(name(indi, :), df._name{2}, "exact");
-	resu(indi, 1) = !isempty(dummy);
-	for indj = 1:length(dummy),
-	  idx(indi, indj) = dummy(indj);
-	endfor
+  if (isa (name, 'char'))
+    if (strict) %# use strmatch to get indexes
+      for indi = (size (name, 1):-1:1)
+        dummy = strmatch (name(indi, :), df._name{2}, "exact");
+        resu(indi, 1) = ~isempty (dummy);
+        for indj = (1:length (dummy))
+          idx(indi, indj) = dummy(indj);
+        endfor
       endfor
     else
-      for indi = size(name, 1):-1:1,
-	try
-	  dummy = df_name2idx(df._name{2}, name(indi, :), \
-			      df._cnt(2), 'column');
-	  resu(indi, 1) = !isempty(dummy);
-	  for indj = 1:length(dummy),
-	    idx(indi, indj) = dummy(indj);
-	  endfor
-	catch
-	  resu(indi, 1) = false; idx(indi, 1) = 0;
-	end_try_catch
+      for indi = (size (name, 1):-1:1)
+        try
+          dummy = df_name2idx (df._name{2}, name(indi, :), \
+                               df._cnt(2), 'column');
+          resu(indi, 1) = ~isempty (dummy);
+          for indj = (1:length (dummy))
+            idx(indi, indj) = dummy(indj);
+          endfor
+        catch
+          resu(indi, 1) = false; idx(indi, 1) = 0;
+        end_try_catch
       endfor
     endif
-  elseif isa(name, 'cell'),
-    if strict, %# use strmatch to get indexes
-      for indi = size(name, 1):-1:1,
-	dummy = strmatch(name{indi}, df._name{2}, "exact");
-	resu{indi, 1} = !isempty(dummy);
-	idx{indi, 1} = dummy;
+  elseif (isa (name, 'cell'))
+    if (strict) %# use strmatch to get indexes
+      for indi = (size (name, 1):-1:1)
+        dummy = strmatch (name{indi}, df._name{2}, "exact");
+        resu{indi, 1} = ~isempty (dummy);
+        idx{indi, 1} = dummy;
       endfor
     else
-      for indi = length(name):-1:1,
-	try
-	  dummy = df_name2idx(df._name{2}, name{indi}, \
-			      df._cnt(2), 'column');
-	  keyboard
-	  resu{indi, 1} = !isempty(dummy); idx{indi, 1} = dummy;
-	catch
-	  resu{indi, 1} = false; cnt{indi, 1} = 0;
-	end_try_catch
+      for indi = (length (name):-1:1)
+        try
+          dummy = df_name2idx (df._name{2}, name{indi}, \
+                               df._cnt(2), 'column');
+          keyboard
+          resu{indi, 1} = ~isempty (dummy); idx{indi, 1} = dummy;
+        catch
+          resu{indi, 1} = false; cnt{indi, 1} = 0;
+        end_try_catch
       endfor
     endif
   endif

Modified: trunk/octave-forge/extra/dataframe/inst/@dataframe/isscalar.m
===================================================================
--- trunk/octave-forge/extra/dataframe/inst/@dataframe/isscalar.m	2012-03-11 20:34:47 UTC (rev 9816)
+++ trunk/octave-forge/extra/dataframe/inst/@dataframe/isscalar.m	2012-03-11 20:53:31 UTC (rev 9817)
@@ -26,6 +26,6 @@
   %# $Id$
   %#
 
-  resu = ismatrix(df) & (length(find(df._cnt > 1)) < 1);  
+  resu = ismatrix (df) & (length (find (df._cnt > 1)) < 1);  
 
 endfunction

Modified: trunk/octave-forge/extra/dataframe/inst/@dataframe/isvector.m
===================================================================
--- trunk/octave-forge/extra/dataframe/inst/@dataframe/isvector.m	2012-03-11 20:34:47 UTC (rev 9816)
+++ trunk/octave-forge/extra/dataframe/inst/@dataframe/isvector.m	2012-03-11 20:53:31 UTC (rev 9817)
@@ -26,6 +26,6 @@
   %# $Id$
   %#
 
-  resu = ismatrix(df) & (length(find(df._cnt > 1)) <= 1);  
+  resu = ismatrix (df) & (length (find (df._cnt > 1)) <= 1);  
 
 endfunction

Modified: trunk/octave-forge/extra/dataframe/inst/@dataframe/ne.m
===================================================================
--- trunk/octave-forge/extra/dataframe/inst/@dataframe/ne.m	2012-03-11 20:34:47 UTC (rev 9816)
+++ trunk/octave-forge/extra/dataframe/inst/@dataframe/ne.m	2012-03-11 20:53:31 UTC (rev 9817)
@@ -1,7 +1,7 @@
 function resu = ne(A, B);
 
   %# function resu = ne(A, B)
-  %# Implements the '!=' operator when at least one argument is a dataframe.
+  %# Implements the '~=' operator when at least one argument is a dataframe.
 
   %% Copyright (C) 2009-2012 Pascal Dupuis <Pas...@uc...>
   %%
@@ -27,6 +27,6 @@
   %# $Id$
   %#
 
-  resu = df_func(@ne, A, B);
+  resu = df_func (@ne, A, B);
 
 endfunction

Modified: trunk/octave-forge/extra/dataframe/inst/@dataframe/permute.m
===================================================================
--- trunk/octave-forge/extra/dataframe/inst/@dataframe/permute.m	2012-03-11 20:34:47 UTC (rev 9816)
+++ trunk/octave-forge/extra/dataframe/inst/@dataframe/permute.m	2012-03-11 20:53:31 UTC (rev 9817)
@@ -24,21 +24,21 @@
   %# $Id$
   %#
 
-  resu = dataframe([]);
+  resu = dataframe ([]);
 
-  if (length(df._cnt) >= length(perm)),
+  if (length (df._cnt) >= length (perm))
     resu._cnt = df._cnt(perm);
   else
     resu._cnt = [df._cnt 1](perm);
   endif
   
-  if (ndims(df._ridx) < 3),
-    resu._ridx = permute(df._ridx, [min(perm(1), 2) min(perm(2:end))]);
+  if (ndims (df._ridx) < 3)
+    resu._ridx = permute (df._ridx, [min(perm(1), 2) min(perm(2:end))]);
   else
-    resu._ridx = permute(df._ridx, perm);
+    resu._ridx = permute (df._ridx, perm);
   endif
 
-  if (size(resu._ridx, 1) < resu._cnt(1)),
+  if (size (resu._ridx, 1) < resu._cnt(1))
     %# adjust index size, if required
     resu._ridx(end+1:resu._cnt(1), :, :) = NA;
   endif
@@ -46,13 +46,13 @@
   if (2 == perm(1)),
     resu._name{1} = df._name{2};
     resu._over{1} = df._over{2};
-    indc = length(resu._name{1});
+    indc = length (resu._name{1});
     indi = resu._cnt(1) - indc;
-    if (indi > 0),
+    if (indi > 0)
       %# generate a name for the new row(s)
-      dummy = cstrcat(repmat('_', indi, 1), ...
-		      strjust(num2str(indc + (1:indi).'), 'left'));
-      resu._name{1}(indc + (1:indi)) = cellstr(dummy);
+      dummy = cstrcat (repmat ('_', indi, 1), ...
+                       strjust (num2str (indc + (1:indi).'), 'left'));
+      resu._name{1}(indc + (1:indi)) = cellstr (dummy);
       resu._over{1}(1, indc + (1:indi)) = true;
     endif 
   else
@@ -61,7 +61,7 @@
   endif
 
   
-  if (2 == perm(2)),
+  if (2 == perm(2))
     resu._name{2} = df._name{2};
     resu._over{2} = df._over{2};
   else
@@ -69,41 +69,41 @@
     resu._over{2} = df._over{1};
   endif
   
-  if (isempty(resu._name{2})),
+  if (isempty (resu._name{2})),
     indc = 0;
   else
-    indc = length(resu._name{2});
+    indc = length (resu._name{2});
   endif
   indi = resu._cnt(2) - indc;
-  if (indi > 0),
+  if (indi > 0)
     %# generate a name for the new column(s)
-    dummy = cstrcat(repmat('_', indi, 1), ...
-		    strjust(num2str(indc + (1:indi).'), 'left'));
-    resu._name{2}(indc + (1:indi)) = cellstr(dummy);
+    dummy = cstrcat (repmat ('_', indi, 1), ...
+                     strjust (num2str (indc + (1:indi).'), 'left'));
+    resu._name{2}(indc + (1:indi)) = cellstr (dummy);
     resu._over{2}(1, indc + (1:indi)) = true;    
   endif 
   
-  if (2 != perm(2)),
+  if (2 ~= perm(2)),
     %# recompute the new type
-    dummy = zeros(0, class(sum(cellfun(@(x) zeros(1, class(x(1))),\
-				       df._data))));
-    resu._type(1:resu._cnt(2)) = class(dummy);
-    dummy = permute(df_whole(df), perm);
-    for indi = 1:resu._cnt(2),
-      resu._data{indi} = squeeze(dummy(:, indi, :));
-      resu._rep{indi} = 1:size(resu._data{indi}, 2);
+    dummy = zeros (0, class (sum (cellfun (@(x) zeros (1, class(x(1))),\
+                                           df._data))));
+    resu._type(1:resu._cnt(2)) = class (dummy);
+    dummy = permute (df_whole(df), perm);
+    for indi = (1:resu._cnt(2))
+      resu._data{indi} = squeeze (dummy(:, indi, :));
+      resu._rep{indi} = 1:size (resu._data{indi}, 2);
     endfor 
   else %# 2 == perm(2)
-    if (1 == perm(1)), %# blank operation
+    if (1 == perm(1)) %# blank operation
       resu._type = df._type;
       resu._data = df._data;
       resu._rep = df._rep;
     else
-      for indi = 1:resu._cnt(2),
-	unfolded = df._data{indi}(:, df._rep{indi});
-	resu._data{indi} = permute(unfolded, [2 1]);
-	resu._rep{indi} = 1:size(resu._data{indi}, 2);
-	resu._type{indi} = df._type{indi};
+      for indi = (1:resu._cnt(2))
+        unfolded = df._data{indi}(:, df._rep{indi});
+        resu._data{indi} = permute (unfolded, [2 1]);
+        resu._rep{indi} = 1:size (resu._data{indi}, 2);
+        resu._type{indi} = df._type{indi};
       endfor    
     endif
   endif

Modified: trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_allmeta.m
===================================================================
--- trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_allmeta.m	2012-03-11 20:34:47 UTC (rev 9816)
+++ trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_allmeta.m	2012-03-11 20:53:31 UTC (rev 9817)
@@ -28,33 +28,33 @@
   %# $Id$
   %#
 
-  resu = dataframe([]);
+  resu = dataframe ([]);
 
-  if (isempty(dim)), 
+  if (isempty (dim)), 
     dim = df._cnt(1:2); 
   else
     dim = dim(1:2); %# ignore third dim, if any
   endif
 
-  resu._cnt(1:2) = min(dim, df._cnt(1:2));
-  if (!isempty(df._name{1})),
+  resu._cnt(1:2) = min (dim, df._cnt(1:2));
+  if (~isempty(df._name{1}))
     resu._name{1} = df._name{1}(1:resu._cnt(1));
     resu._over{1} = df._over{1}(1:resu._cnt(1));
   endif
-  if (!isempty(df._name{2})),
+  if (~isempty(df._name{2}))
     resu._name{2} = df._name{2}(1:resu._cnt(2));
     resu._over{2} = df._over{2}(1:resu._cnt(2));
   endif
-  if (!isempty(df._ridx)),
-    if (size(df._ridx, 2) >= resu._cnt(2)),
+  if (~isempty(df._ridx))
+    if (size (df._ridx, 2) >= resu._cnt(2)),
       resu._ridx = df._ridx(1:resu._cnt(1), :, :);
     else
       resu._ridx = df._ridx(1:resu._cnt(1), 1, :);
     endif
   endif
   %# init it with the right orientation
-  resu._data = cell(size(df._data));
-  resu._rep = cell(size(df._rep));
+  resu._data = cell (size (df._data));
+  resu._rep = cell (size (df._rep));
   resu._type = df._type(1:resu._cnt(2));
   resu._src  = df._src;
   resu._cmt  = df._cmt;

Modified: trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_basecomp.m
===================================================================
--- trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_basecomp.m	2012-03-11 20:34:47 UTC (rev 9816)
+++ trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_basecomp.m	2012-03-11 20:53:31 UTC (rev 9817)
@@ -30,162 +30,162 @@
   %# $Id$
   %#
 
-  if 1 == length(itercol), 
+  if (1 == length (itercol)) 
     strict = false;
   else
     strict = itercol(2); itercol = itercol(1);
   endif
 
-  if (iscell(A)), A = dataframe(A); endif
-  if (iscell(B)), B = dataframe(B); endif  
+  if (iscell (A)), A = dataframe (A); endif
+  if (iscell (B)), B = dataframe (B); endif  
 
-  switch (func2str(func)),
+  switch (func2str (func)),
     case 'bsxfun'
       %# bsxfun compatibility rule: if there is at least one singleton
       %# dim, the smallest is repeated to reach the size of the
       %# greatest. Otherwise, all dims must be equal.
-      if (any(size(A)(1:2) != size(B)(1:2)))
-	if (!any (1 == [size(A) size(B)]))
-	  error('bsxfun: both arguments must have the same dim, of one of them must have at least one singleton dim');
-	else
-	  Csize = max([size(A)(1:2); size(B)(1:2)]);
-	endif
+      if (any (size (A)(1:2) ~= size (B)(1:2)))
+        if (~any (1 == [size(A) size(B)]))
+          error ('bsxfun: both arguments must have the same dim, of one of them must have at least one singleton dim');
+        else
+          Csize = max ([size(A)(1:2); size(B)(1:2)]);
+        endif
       else
-	Csize = size(A)(1:2);
+        Csize = size (A)(1:2);
       endif
     case 'mldivide'
-      if (isscalar(A)), 
-	Csize = size(B)(1:2);
+      if (isscalar (A)), 
+        Csize = size (B)(1:2);
       else
-        if (size(A, 1) != size(B, 1)),
-	  error("Non compatible row sizes (op1 is %dx%d, op2 is %dx%d)",\
-		size(A), size(B)(1:2));
-	endif
-	Csize = [size(A, 2) size(B, 2)];
+        if (size (A, 1) ~= size (B, 1))
+          error ("Non compatible row sizes (op1 is %dx%d, op2 is %dx%d)",\
+                 size (A), size (B)(1:2));
+        endif
+        Csize = [size(A, 2) size(B, 2)];
       endif
     otherwise
       %# if strict is set, B may not be non-scalar vs scalar
-      if ((!(isscalar(A) || isscalar(B)))||(strict && isscalar(A))),
-	if (itercol), %# requires full compatibility
-	  Csize = size(A)(1:2);
-	  if (any(Csize - size(B)(1:2))),
-	    %# disp([size(A) size(B)])
-	    error("Non compatible row and columns sizes (op1 is %dx%d, op2 is %dx%d)",\
-		  Csize, size(B));
-	  endif
-	else %# compatibility with matrix product
-	  if (size(A, 2) - size(B, 1)),
-	    error("Non compatible columns vs. rows size (op1 is %dx%d, op2 is %dx%d)",\
-		  size(A)(1:2), size(B)(1:2));
-	  endif
-	  Csize = [size(A, 1) size(B, 2)];
-	endif
+      if ((~(isscalar (A) || isscalar (B)))||(strict && isscalar (A)))
+        if (itercol), %# requires full compatibility
+          Csize = size (A)(1:2);
+          if (any (Csize - size (B)(1:2)))
+            %# disp([size(A) size(B)])
+            error ("Non compatible row and columns sizes (op1 is %dx%d, op2 is %dx%d)",\
+                   Csize, size (B));
+          endif
+        else %# compatibility with matrix product
+          if (size (A, 2) - size (B, 1)),
+            error ("Non compatible columns vs. rows size (op1 is %dx%d, op2 is %dx%d)",\
+                  size (A)(1:2), size (B)(1:2));
+          endif
+          Csize = [size(A, 1) size(B, 2)];
+        endif
       endif
   endswitch
 
-  if !(isscalar(A) || isscalar(B))
+  if (~(isscalar (A) || isscalar (B)))
     C = [];
-    if (isa(A, 'dataframe'))
-      if (nargout > 2 && all(Csize == size(A)(1:2))),
-	C = df_allmeta(A, Csize);
+    if (isa (A, 'dataframe'))
+      if (nargout > 2 && all (Csize == size (A)(1:2))),
+        C = df_allmeta (A, Csize);
       endif         
-      if (isa(B, 'dataframe'))
-	if (nargout > 2 && isempty(C) && all(Csize == size(B)(1:2))),
-	  C = df_allmeta(B, Csize);
-	endif
-	if (strict),
-	  %# compare indexes if both exist
-	  if (!isempty(A._ridx))
-	    if (!isempty(B._ridx) && itercol),
-	      if (any(A._ridx-B._ridx)),
-		error("Non compatible indexes");
-	      endif
-	    endif
-	  else
-	    if (nargout > 2 && itercol), C._ridx = B._ridx; endif
-	  endif
-	  
-	  if (itercol),
-	    idxB = 1; %# row-row comparison
-	  else
-	    idxB = 2; %# row-col comparsion
-	  endif
-	  
-	  if (!isempty(A._name{1})) 
-	    if (!isempty(B._name{idxB}))
-	      dummy = !(strcmp(cellstr(A._name{1}), cellstr(B._name{idxB}))\
-			| (A._over{1}(:)) | (B._over{idxB}(:)));
-	      if (any(dummy)),
-		if (itercol),
-		  error("Incompatible row names");
-		else
-		  error("Incompatible row vs. column names");
-		endif
-	      endif
-	      dummy = A._over{1} > B._over{idxB};
-	      if (any(dummy)),
-		C._name{1}(dummy) = B._name{idxB}(dummy);
-		C._over{1}(dummy) = B._over{idxB}(dummy);
-	      endif
-	    endif
-	  else
-	    if (nargout > 2), 
-	      C._name{1} = B._name{idxB}; C._over{1} = B._over{idxB};
-	    endif
-	  endif
-	  
-	  idxB = 3-idxB;
-	  
-	  if (!isempty(A._name{2}))
-	    if (!isempty(B._name{idxB}))
-	      dummy = !(strcmp(cellstr(A._name{2}), cellstr(B._name{2}))\
-			| (A._over{2}(:)) | (B._over{2}(:)));
-	      if (any(dummy)),
-		if (itercol),
-		  error("Incompatible column vs row names");
-		else
-		  error("Incompatible column names");
-		endif
-	      endif
-	      dummy = A._over{2} > B._over{idxB};
-	      if (any(dummy)),
-		C._name{2}(dummy) = B._name{idxB}(dummy);
-		C._over{2}(dummy) = B._over{idxB}(dummy);
-	      endif
-	    endif
-	  else
-	    if (nargout > 2 && !isempty(B._name{idxB})),
-	      C._name{2} = B._name{idxB}; C._over{2} = B._over{idxB}; 
-	    endif
-	  endif
-	endif
+      if (isa (B, 'dataframe'))
+        if (nargout > 2 && isempty (C) && all (Csize == size (B)(1:2))),
+          C = df_allmeta (B, Csize);
+        endif
+        if (strict)
+          %# compare indexes if both exist
+          if (~isempty (A._ridx))
+            if (~isempty(B._ridx) && itercol)
+              if (any (A._ridx-B._ridx)),
+                error ("Non compatible indexes");
+              endif
+            endif
+          else
+            if (nargout > 2 && itercol), C._ridx = B._ridx; endif
+          endif
+          
+          if (itercol),
+            idxB = 1; %# row-row comparison
+          else
+            idxB = 2; %# row-col comparsion
+          endif
+          
+          if (~isempty (A._name{1})) 
+            if (~isempty (B._name{idxB}))
+              dummy = ~(strcmp (cellstr (A._name{1}), cellstr (B._name{idxB}))\
+                        | (A._over{1}(:)) | (B._over{idxB}(:)));
+              if (any (dummy))
+                if (itercol),
+                  error ("Incompatible row names");
+                else
+                  error ("Incompatible row vs. column names");
+                endif
+              endif
+              dummy = A._over{1} > B._over{idxB};
+              if (any (dummy)),
+                C._name{1}(dummy) = B._name{idxB}(dummy);
+                C._over{1}(dummy) = B._over{idxB}(dummy);
+              endif
+            endif
+          else
+            if (nargout > 2), 
+              C._name{1} = B._name{idxB}; C._over{1} = B._over{idxB};
+            endif
+          endif
+          
+          idxB = 3-idxB;
+          
+          if (~isempty(A._name{2}))
+            if (~isempty(B._name{idxB}))
+              dummy = ~(strcmp (cellstr (A._name{2}), cellstr (B._name{2}))\
+                        | (A._over{2}(:)) | (B._over{2}(:)));
+              if (any (dummy)),
+                if (itercol),
+                  error ("Incompatible column vs row names");
+                else
+                  error ("Incompatible column names");
+                endif
+              endif
+              dummy = A._over{2} > B._over{idxB};
+              if (any (dummy)),
+                C._name{2}(dummy) = B._name{idxB}(dummy);
+                C._over{2}(dummy) = B._over{idxB}(dummy);
+              endif
+            endif
+          else
+            if (nargout > 2 && ~isempty (B._name{idxB})),
+              C._name{2} = B._name{idxB}; C._over{2} = B._over{idxB}; 
+            endif
+          endif
+        endif
 
-	if (isempty(A._src) && nargout > 2 && !isempty(B._src)), 
-	  C._src = B._src;
-	endif
-	if (isempty(A._cmt) && nargout > 2 && !isempty(B._cmt)), 
-	  C._cmt = B._cmt;
-	endif
+        if (isempty (A._src) && nargout > 2 && ~isempty (B._src)), 
+          C._src = B._src;
+        endif
+        if (isempty (A._cmt) && nargout > 2 && ~isempty (B._cmt)), 
+          C._cmt = B._cmt;
+        endif
       else %# B is not a df
-	if (nargout > 2 && isempty(C)),
-	  C = df_allmeta(A);
-	endif
+        if (nargout > 2 && isempty (C)),
+          C = df_allmeta (A);
+        endif
       endif
     else %# A is not a df
       if (nargout > 2), 
-	if (all(Csize==size(B)(1:2))),
-	  C = df_allmeta(B, Csize); 
-	else
-	  C = df_allmeta(B); 
-	endif         
+        if (all (Csize == size (B)(1:2))),
+          C = df_allmeta (B, Csize); 
+        else
+          C = df_allmeta (B); 
+        endif         
       endif
     endif
   else %# both arg are  scalar
-    if (nargout > 2),
-      if (isa(A, 'dataframe')) 
-	C = df_allmeta(A);     
+    if (nargout > 2)
+      if (isa (A, 'dataframe')) 
+        C = df_allmeta (A);     
       else
-	C = df_allmeta(B); 
+        C = df_allmeta (B); 
       endif
     endif
   endif

Modified: trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_check_char_array.m
===================================================================
--- trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_check_char_array.m	2012-03-11 20:34:47 UTC (rev 9816)
+++ trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_check_char_array.m	2012-03-11 20:53:31 UTC (rev 9817)
@@ -26,27 +26,27 @@
   %# $Id$
   %#
   
-  if 2 == nargin, required = [nelem 1]; endif
+  if (2 == nargin) required = [nelem 1]; endif
 
-  if nelem < required(1),
-    error("Too many elements to assign");
+  if (nelem < required(1))
+    error ("Too many elements to assign");
   endif
 
   %# a zero-length element is still considered as a space by char
-  if isempty(x), x = ' '; endif 
+  if (isempty (x)) x = ' '; endif 
 
-  if size(x, 1) < max(required(1), nelem)
+  if (size (x, 1) < max (required(1), nelem))
     %# pad vertically
-    dummy = repmat(' ', nelem-size(x, 1), 1);
-    resu = char(x, dummy);
+    dummy = repmat (' ', nelem-size (x, 1), 1);
+    resu = char (x, dummy);
   else
     resu = x;
   endif
       
-  if size(resu, 2) < required(2),
+  if (size (resu, 2) < required(2))
     %# pad horizontally
-    dummy = repmat(' ', nelem, required(2)-size(resu, 2));
-    resu = horzcat(resu, dummy);
+    dummy = repmat (' ', nelem, required(2)-size (resu, 2));
+    resu = horzcat (resu, dummy);
   endif
 
 endfunction

Modified: trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_colmeta.m
===================================================================
--- trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_colmeta.m	2012-03-11 20:34:47 UTC (rev 9816)
+++ trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_colmeta.m	2012-03-11 20:53:31 UTC (rev 9817)
@@ -28,15 +28,15 @@
   %# $Id: df_func.m 7943 2010-11-24 15:33:54Z cdemills $
   %#
 
-  resu = dataframe([]);
+  resu = dataframe ([]);
 
   resu._cnt(2) = df._cnt(2);
   resu._name{2} = df._name{2};
   resu._over{2} = df._over{2};
   resu._type = df._type;
   %# init it with the right orientation
-  resu._data = cell(size(df._data));
-  resu._rep = cell(size(df._rep));
+  resu._data = cell (size (df._data));
+  resu._rep = cell (size (df._rep));
   resu._src  = df._src;
   resu._cmt  = df._cmt;
 

Modified: trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_cow.m
===================================================================
--- trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_cow.m	2012-03-11 20:34:47 UTC (rev 9816)
+++ trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_cow.m	2012-03-11 20:53:31 UTC (rev 9817)
@@ -29,50 +29,50 @@
   %# $Id$
   %#
 
-  if length(col) > 1,
-    error("df_cow must work on a column-by-column basis");
+  if (length (col) > 1)
+    error ("df_cow must work on a column-by-column basis");
   endif
   
-  if (1 == length(S.subs)),
+  if (1 == length (S.subs)),
     inds = 1; 
   else
     inds = S.subs{2};
   endif
 
-  if (!isnumeric(inds)), 
-    if !strcmp(inds, ':'),
-      error("Unknown sheet selector %s", inds);
+  if (~isnumeric(inds)) 
+    if (~strcmp (inds, ':'))
+      error ("Unknown sheet selector %s", inds);
     endif
-    inds = 1:length(df._rep(col));
+    inds = 1:length (df._rep(col));
   endif
 
-  for indi = inds(:).',
+  for indi = (inds(:).')
     dummy = df._rep{col}; dummy(indi) = 0;
-    [t1, t2] = ismember(df._rep{col}(indi)(:), dummy);
-    for indj = t2(find(t2)), %# Copy-On-Write
+    [t1, t2] = ismember (df._rep{col}(indi)(:), dummy);
+    for indj = (t2(find (t2))) %# Copy-On-Write
       %# determines the index for the next column
-      t1 = 1+max(df._rep{col}); 
+      t1 = 1 + max (df._rep{col}); 
       %# duplicate the touched column
-      df._data{col} = horzcat(df._data{col}, \
-                              df._data{col}(:, df._rep{col}(indj)));  
-      if (indi > 1),
+      df._data{col} = horzcat (df._data{col}, \
+                               df._data{col}(:, df._rep{col}(indj)));  
+      if (indi > 1)
         %# a new column has been created
         df._rep{col}(indi) = t1;
       else
         %# update repetition index aliasing this one
-        df._rep{col}(find(dummy == indi)) = t1;
+        df._rep{col}(find (dummy == indi)) = t1;
       endif
     endfor
   endfor
 
   %# reorder S
-  if (length(S.subs) > 1),
-    if (S.subs{2} != 1 || length(S.subs{2}) > 1), 
+  if (length (S.subs) > 1)
+    if (S.subs{2} ~= 1 || length (S.subs{2}) > 1), 
       %# adapt sheet index according to df_rep
       S.subs{2} = df._rep{col}(S.subs{2});
     endif
   endif
 
-  df = df_thirddim(df);
+  df = df_thirddim (df);
 
 endfunction

Modified: trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_func.m
===================================================================
--- trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_func.m	2012-03-11 20:34:47 UTC (rev 9816)
+++ trunk/octave-forge/extra/dataframe/inst/@dataframe/private/df_func.m	2012-03-11 20:53:31 UTC (rev 9817)
@@ -32,191 +32,191 @@
   %# $Id$
   %#
 
-  [A, B, resu] = df_basecomp(A, B, itercol, func);
+  [A, B, resu] = df_basecomp (A, B, itercol, func);
   itercol = itercol(1); %# drop second value
 
-  if (isa(B, 'dataframe'))
-    if (!isa(A, 'dataframe')),
-      if (isscalar(A)),
-        for indi = resu._cnt(2):-1:1,
+  if (isa (B, 'dataframe'))
+    if (~isa (A, 'dataframe')),
+      if (isscalar (A)),
+        for indi = (resu._cnt(2):-1:1)
           switch resu._type{indi}
             case "char"
-              resu._data{indi} = feval(func, A, char(B._data{indi}));
+              resu._data{indi} = feval (func, A, char (B._data{indi}));
             otherwise
-              resu._data{indi} = feval(func, A, B._data{indi});
+              resu._data{indi} = feval (func, A, B._data{indi});
           endswitch
         endfor
         resu._rep = B._rep;
       else
-        if (whole(1) && !whole(2)),
-          for indi = resu._cnt(2):-1:1,
+        if (whole(1) && ~whole(2))
+          for indi = (resu._cnt(2):-1:1)
             switch resu._type{indi}
               case "char"
-                resu._data{indi} = feval(func, A, \
-                                         char(B._data{indi}(:, B._rep{indi})));
+                resu._data{indi} = feval (func, A, \
+                                          char (B._data{indi}(:, B._rep{indi})));
               otherwise
-                resu._data{indi} = feval(func, A, \
-                                         B._data{indi}(:, B._rep{indi}));
+                resu._data{indi} = feval (func, A, \
+                                          B._data{indi}(:, B._rep{indi}));
             endswitch
-            resu._rep{indi} = 1:size(resu._data{indi}, 2);
+            resu._rep{indi} = 1:size (resu._data{indi}, 2);
           endfor
-        elseif (itercol && !whole(2)),
-          for indi = resu._cnt(2):-1:1,
+        elseif (itercol && ~whole(2)),
+          for indi = (resu._cnt(2):-1:1)
             switch resu._type{indi}
               case "char"
-                resu._data{indi} = feval(func, squeeze(A(:, indi, :)), \
-                                         char(B._data{indi}(:, B._rep{indi})));
+                resu._data{indi} = feval (func, squeeze (A(:, indi, :)), \
+                                          char (B._data{indi}(:, B._rep{indi})));
               otherwise
-                resu._data{indi} = feval(func, squeeze(A(:, indi, :)), \
-                                         B._data{indi}(:, B._rep{indi}));
+                resu._data{indi} = feval (func, squeeze (A(:, indi, :)), \
+                                          B._data{indi}(:, B._rep{indi}));
             endswitch
-            resu._rep{indi} = 1:size(resu._data{indi}, 2);
+            resu._rep{indi} = 1:size (resu._data{indi}, 2);
           endfor
-        elseif (!whole(2)),
-          warning("no 3D yet");
-          for indi = resu._cnt(2):-1:1,
+        elseif (~whole(2)),
+          warning ("no 3D yet");
+          for indi = (resu._cnt(2):-1:1)
             switch resu._type{indi}
               case "char"
-                resu._data{indi} = feval(func, A(indi, :), char(B._data{indi}));
+                resu._data{indi} = feval (func, A(indi, :), char (B._data{indi}));
               otherwise
-                resu._data{indi} = feval(func, A(indi, :), B._data{indi});
+                resu._data{indi} = feval (func, A(indi, :), B._data{indi});
             endswitch
           endfor
         else
-          dummy = feval(func, A, df_whole(B));
-          for indi = resu._cnt(2):-1:1, %# store column-wise
-            resu._data{indi} = sq...
 
[truncated message content]

[Octave-cvsupdate] SF.net SVN: octave:[9816] trunk/octave-forge/main/io/NEWS

From: <prn...@us...> - 2012-03-11 20:34:53

Revision: 9816
          http://octave.svn.sourceforge.net/octave/?rev=9816&view=rev
Author:   prnienhuis
Date:     2012-03-11 20:34:47 +0000 (Sun, 11 Mar 2012)
Log Message:
-----------
First version of NEWS

Added Paths:
-----------
    trunk/octave-forge/main/io/NEWS

Added: trunk/octave-forge/main/io/NEWS
===================================================================
--- trunk/octave-forge/main/io/NEWS	                        (rev 0)
+++ trunk/octave-forge/main/io/NEWS	2012-03-11 20:34:47 UTC (rev 9816)
@@ -0,0 +1,96 @@
+Summary of important user-visible changes for releases of the io package
+
+===============================================================================
+io-1.0.18   Release Date: TBA   Release Manager: Philip Nienhuis
+===============================================================================
+
+** Bug fixes:
+--- odsfinfo: fixed "wrong type argument `cell'" bug when run interactively.
+--- xlsopen, odsopen: fixed messed up screen output due to UNO usage warning.
+
+** Adapted to internal LibreOffice-3.5-final changes.
+
+** Tried OpenXLS-6.0.7.jar. Reads OK, still unusable for writing .xls files.
+
+===============================================================================
+io-1.0.17   Release Date: 2012-02-27   Release Manager: Philip Nienhuis
+===============================================================================
+
+** Bug fixes:
+--- oct2ods, oct2xls, odswrite default range input arg. These functions may not
+    have worked properly for two years (!)
+
+** Fixed support for odfdom v.0.8.7 (ODS). Note: the OTK interface only works
+  well with xercesImpl.jar 2.9.1 (Sep 14, 2009)
+
+** Many small bug fixes & documentation updated to actual functionality.
+
+** Fixed "seealso" texinfo header string in almost all functions.
+
+** Added formal test scripts to "internal functions" section.
+
+===============================================================================
+io-1.0.16   Release Date: 2012-01-19   Release Manager: Philip Nienhuis
+===============================================================================
+
+** Bug fixing release
+
+** PKG_ADD now expects Java spreadsheet class libs (.jars) in /lib/java
+  (for MinGW)
+
+===============================================================================
+io-1.0.15   Release Date: 2011-10-02   Release Manager: Philip Nienhuis
+===============================================================================
+
+io-1.0.15 is primarily a bug fix release and a snapshot / wrap-up of current 
+  development status (some still a bit experimental). It mainly comprises:
+
+** A number of bug fixes (incl. some serious ones, notably with .ods/OOo Calc);
+
+** Some mainly cosmetic improvements to existing code; less verbosity;
+
+** pch2mat (reading & transforming Nastran PCH files, contributed by 
+  B. Oytun Peksel);
+
+** object2json.m (creating a json description string of objects, contributed
+  by Daniel Torre). This was already silently introduced in io-1.0.14;
+
+** A scripted troubleshooting / classpath setup tool for spreadsheet I/O
+  support (chk_spreadsheet_support.m);
+
+** Experimental OXS support (OpenXLS) for reading Excel xls (BIFF8).
+  OpenXLS is -let's say- a little bit lacking: For reading it is faster than
+  JXL. However, while OXS write support has been coded (and works) I had to
+  disable it as the OXS Java classes won't release the file handle so Octave
+  will hang upon closing :-(  I'm stuck with this so I just release it as-is;
+
+** Experimental UNO support, i.e. invoking OpenOffice.org (or clones like 
+  LibreOffice) behind the scenes to read spreadsheet files, much like 
+  ActiveX/COM for MS-Excel. This is also based on Java. The first time you
+  use UNO, OOo has to be loaded and you'll have to be patient, but once loaded
+  (and in the OS cache) you'll see the pros:
+  --* Very fast;
+  --* Much lower Java memory usage as OOo loads the spreadsheet in its own 
+      memory chunk (not Octave's) => much bigger spreadsheet capacity;
+  --* You can read *all* formats supported by OOo: .ods, .xls, .csv, .xlsx,
+      .sxc, .dbf, Lotus wk1, Quattro Pro, ......; and it doesn't really matter
+      whether xlsopen of odsopen is used.
+  Of course all this wonderful stuff comes at a prize:
+  --* After closing the spreadsheet file (odsclose, xlsclose) ALL OOo
+      invocations will be closed, also those started outside Octave. This is 
+      due to "the way OpenOffice works" (quoted from OOo dev forum), especially
+      through Java. There are other ways to close OOo but they'll hang Octave;
+  --* The Java UNO classes supplied with e.g. LibreOffice aren't kept quite
+      up-to-date with the main program. As a consequence, with e.g.,
+      LibreOffice 3.4 the main LO window will pop up (it can't be hidden). I 
+      filed a bug report for this 
+      (https://bugs.freedesktop.org/show_bug.cgi?id=40991) but I haven't seen
+      it being picked up yet. Another example: while LO 3.3.1's row capacity
+      was already > 106, it took until LO 3.4 before this capacity was
+      implemented in the Java UNO classes.
+  Like with OXS, I'm a bit stuck here - all this has to be fixed upstream.
+
+Hint:
+for older Octave versions (< 3.4.0) you can install io-1.0.15 using the -nodeps
+  flag. You'll then loose the old and buggy textread and csv/dlm-read/write
+  functions but I'd consider that as no big loss.

This was sent by the SourceForge.net collaborative development platform, the world's largest Open Source development site.

[Octave-cvsupdate] SF.net SVN: octave:[9815] trunk/octave-forge/main/queueing

From: <mma...@us...> - 2012-03-11 16:44:24

Revision: 9815
          http://octave.svn.sourceforge.net/octave/?rev=9815&view=rev
Author:   mmarzolla
Date:     2012-03-11 16:44:18 +0000 (Sun, 11 Mar 2012)
Log Message:
-----------
improvements to the documentation

Modified Paths:
--------------
    trunk/octave-forge/main/queueing/doc/markovchains.txi
    trunk/octave-forge/main/queueing/doc/queueing.html
    trunk/octave-forge/main/queueing/doc/queueing.pdf
    trunk/octave-forge/main/queueing/inst/ctmc.m

Modified: trunk/octave-forge/main/queueing/doc/markovchains.txi
===================================================================
--- trunk/octave-forge/main/queueing/doc/markovchains.txi	2012-03-11 15:45:11 UTC (rev 9814)
+++ trunk/octave-forge/main/queueing/doc/markovchains.txi	2012-03-11 16:44:18 UTC (rev 9815)
@@ -60,11 +60,7 @@
 
 The transition probability matrix @math{\bf P} must satisfy the
 following two properties: (1) @math{P_{i, j} @geq{} 0} for all
-@math{i, j}, and (2) @math{\sum_{j=1}^N P_{i,j} = 1}. We denote with
-@math{{\bf \pi}(n) = (\pi_1(n), \pi_2(n), @dots{}, \pi_N(n) )} the
-@emph{state occupancy probability vector} at step
-@math{n}. @math{\pi_i(n)} denotes the probability that the system is
-in state @math{i} at step @math{n}.
+@math{i, j}, and (2) @math{\sum_{j=1}^N P_{i,j} = 1}. 
 
 @c
 @DOCSTRING(dtmc_check_P)
@@ -74,6 +70,11 @@
 @c
 @subsection State occupancy probabilities
 
+We denote with @math{{\bf \pi}(n) = (\pi_1(n), \pi_2(n), @dots{},
+\pi_N(n) )} the @emph{state occupancy probability vector} at step
+@math{n}. @math{\pi_i(n)} denotes the probability that the system is
+in state @math{i} at step @math{n}.
+
 Given the transition probability matrix @math{\bf P} and the initial
 state occupancy probability vector @math{{\bf \pi}(0) = (\pi_1(0),
 \pi_2(0), @dots{}, \pi_N(0))} at step 0, the state occupancy
@@ -97,7 +98,8 @@
 occupancy probability} @math{{\bf \pi} = \lim_{n \rightarrow +\infty}
 {\bf \pi}(n)}, which is independent from the initial state occupancy
 @math{{\bf \pi}(0)}. The stationary state occupancy probability vector
-@math{\bf \pi} satisfies @math{{\bf \pi} = {\bf \pi} {\bf P}}.
+@math{\bf \pi} satisfies @math{{\bf \pi} = {\bf \pi} {\bf P}}
+and @math{\sum_{i=1}^N \pi_i = 1}
 
 @c
 @DOCSTRING(dtmc)
@@ -148,6 +150,27 @@
 @node Continuous-Time Markov Chains
 @section Continuous-Time Markov Chains
 
+A stochastic process @math{@{X(t), t @geq{} 0@}} is a continuous-time
+Markov chain if, for all integers @math{n}, and for any sequence
+@math{t_0, t_1 , \ldots , t_n, t_{n+1}} such that @math{t_0 < t_1 <
+\ldots < t_n < t_{n+1}}, we have
+
+@iftex
+@tex
+$$P(X_{t_{n+1}} = x_{n+1}\ |\ X(t_n) = x_n, X(t_{n-1}) = x_{n-1}, \ldots, X(t_0) = x_0) = P(X(t_{n+1}) = x_{n+1}\ |\ X(t_n) = x_n)$$
+@end tex
+@end iftex
+@ifnottex
+@math{P(X_{n+1} = x_{n+1} | X_n = x_n, X_{n-1} = x_{n-1}, ..., X_0 = x_0) = P(X_{n+1} = x_{n+1} | X_n = x_n)}
+@end ifnottex
+
+A continuous-time Markov chain is defined according to an
+@emph{infinitesimal generator matrix} @math{{\bf Q} = [Q_{i,j}]} such
+that for each @math{i \neq j}, @math{Q_{i, j}} is the transition rate
+from state @math{i} to state @math{j}. The elements @math{Q_{i, i}}
+must be defined in such a way that the infinitesimal generator matrix
+@math{\bf Q} satisfies the property @math{\sum_{j=1}^N Q_{i,j} = 0}.
+
 @DOCSTRING(ctmc_check_Q)
 
 @menu
@@ -162,6 +185,37 @@
 @node State occupancy probabilities
 @subsection State occupancy probabilities
 
+Similarly to the discrete case, we denote with @math{{\bf \pi}(t) =
+(\pi_1(t), \pi_2(t), @dots{}, \pi_N(t) )} the @emph{state occupancy
+probability vector} at time @math{t}. @math{\pi_i(t)} denotes the
+probability that the system is in state @math{i} at time @math{t @geq{} 0}.
+
+Given the infinitesimal generator matrix @math{\bf Q} and the initial
+state occupancy probability vector @math{{\bf \pi}(0) = (\pi_1(0),
+\pi_2(0), @dots{}, \pi_N(0))}, the state occupancy probability vector
+@math{{\bf \pi}(t)} at time @math{t} can be computed as:
+
+@iftex
+@tex
+$${\bf \pi}(t) = {\bf \pi}(0) \exp( {\bf Q} t )$$
+@end tex
+@end iftex
+@ifnottex
+@example
+@group
+\pi(t) = \pi(0) exp(Qt)
+@end group
+@end example
+@end ifnottex
+
+@noindent where @math{\exp( {\bf Q} t )} is the matrix exponential
+of @math{{\bf Q} t}. Under certain conditions, there exists a
+@emph{stationary state occupancy probability} @math{{\bf \pi} =
+\lim_{t \rightarrow +\infty} {\bf \pi}(t)}, which is independent from
+the initial state occupancy @math{{\bf \pi}(0)}. The stationary state
+occupancy probability vector @math{\bf \pi} satisfies 
+@math{{\bf \pi} {\bf Q} = {\bf 0}} and @math{\sum_{i=1}^N \pi_i = 1}.
+
 @DOCSTRING(ctmc)
 
 @noindent @strong{EXAMPLE}
@@ -195,7 +249,7 @@
 (L_1(t), L_2(t), \ldots L_N(t))} such that @math{L_i(t)} is the
 expected sojourn time in state @math{i} during the interval
 @math{[0,t)}, assuming that the initial occupancy probability at time
-0 was @math{{\bf \pi}(0)}. Then, @math{{\bf L}(t)} is the solution of
+0 was @math{{\bf \pi}(0)}. @math{{\bf L}(t)} is the solution of
 the following differential equation:
 
 @iftex
@@ -213,10 +267,27 @@
 @end example
 @end ifnottex
 
-The function @code{ctmc_exps} can be used to compute @math{{\bf
-L}(t)}, by using the @code{lsode} Octave function to solve the above
-linear differential equation.
+Alternatively, @math{{\bf L}(t)} can also be expressed in integral
+form as:
 
+@iftex
+@tex
+$$ {\bf L}(t) = \int_{u=0}^t {\bf \pi}(u) du$$
+@end tex
+@end iftex
+@ifnottex
+@example
+@group
+       / t
+L(t) = |      pi(u) du
+       / u=0
+@end group
+@end example
+@end ifnottex
+
+@noindent where @math{{\bf \pi}(t) = {\bf \pi}(0) \exp({\bf Q}t)} is
+the state occupancy probability at time @math{t}.
+
 @DOCSTRING(ctmc_exps)
 
 @noindent @strong{EXAMPLE}
@@ -225,7 +296,7 @@
 rate from state @math{i} to state @math{i+1} is @math{\lambda_i = i
 \lambda} (@math{i=1, 2, 3}), with @math{\lambda = 0.5}. The following
 code computes the expected sojourn time in state @math{i},
-given the initial occupancy probability @math{p_0=(1,0,0,0)}. 
+given the initial occupancy probability @math{{\bf \pi}_0=(1,0,0,0)}. 
 
 @example
 @group

Modified: trunk/octave-forge/main/queueing/doc/queueing.html
===================================================================
--- trunk/octave-forge/main/queueing/doc/queueing.html	2012-03-11 15:45:11 UTC (rev 9814)
+++ trunk/octave-forge/main/queueing/doc/queueing.html	2012-03-11 16:44:18 UTC (rev 9815)
@@ -811,11 +811,7 @@
 
    <p>The transition probability matrix \bf P must satisfy the
 following two properties: (1) P_i, j &ge; 0 for all
-i, j, and (2) \sum_j=1^N P_i,j = 1. We denote with
-\bf \pi(n) = (\pi_1(n), \pi_2(n), <small class="dots">...</small>, \pi_N(n) ) the
-<em>state occupancy probability vector</em> at step
-n. \pi_i(n) denotes the probability that the system is
-in state i at step n.
+i, j, and (2) \sum_j=1^N P_i,j = 1.
 
    <p><a name="doc_002ddtmc_005fcheck_005fP"></a>
 
@@ -832,7 +828,12 @@
 
 <h4 class="subsection">4.1.1 State occupancy probabilities</h4>
 
-<p>Given the transition probability matrix \bf P and the initial
+<p>We denote with \bf \pi(n) = (\pi_1(n), \pi_2(n), <small class="dots">...</small>,
+\pi_N(n) ) the <em>state occupancy probability vector</em> at step
+n. \pi_i(n) denotes the probability that the system is
+in state i at step n.
+
+   <p>Given the transition probability matrix \bf P and the initial
 state occupancy probability vector \bf \pi(0) = (\pi_1(0),
 \pi_2(0), <small class="dots">...</small>, \pi_N(0)) at step 0, the state occupancy
 probability vector \bf \pi(n) at step n can be
@@ -844,7 +845,8 @@
 occupancy probability</em> \bf \pi = \lim_n \rightarrow +\infty
 \bf \pi(n), which is independent from the initial state occupancy
 \bf \pi(0). The stationary state occupancy probability vector
-\bf \pi satisfies \bf \pi = \bf \pi \bf P.
+\bf \pi satisfies \bf \pi = \bf \pi \bf P
+and \sum_i=1^N \pi_i = 1
 
    <p><a name="doc_002ddtmc"></a>
 
@@ -1009,8 +1011,22 @@
 
 <h3 class="section">4.2 Continuous-Time Markov Chains</h3>
 
-<p><a name="doc_002dctmc_005fcheck_005fQ"></a>
+<p>A stochastic process {X(t), t &ge; 0} is a continuous-time
+Markov chain if, for all integers n, and for any sequence
+t_0, t_1 , \ldots , t_n, t_n+1 such that t_0 &lt; t_1 &lt;
+\ldots &lt; t_n &lt; t_n+1, we have
 
+   <p>P(X_n+1 = x_n+1 | X_n = x_n, X_n-1 = x_n-1, ..., X_0 = x_0) = P(X_n+1 = x_n+1 | X_n = x_n)
+
+   <p>A continuous-time Markov chain is defined according to an
+<em>infinitesimal generator matrix</em> \bf Q = [Q_i,j] such
+that for each i \neq j, Q_i, j is the transition rate
+from state i to state j. The elements Q_i, i
+must be defined in such a way that the infinitesimal generator matrix
+\bf Q satisfies the property \sum_j=1^N Q_i,j = 0.
+
+   <p><a name="doc_002dctmc_005fcheck_005fQ"></a>
+
 <div class="defun">
 &mdash; Function File: [<var>result</var> <var>err</var>] = <b>ctmc_check_Q</b> (<var>Q</var>)<var><a name="index-ctmc_005fcheck_005fQ-16"></a></var><br>
 <blockquote>
@@ -1041,11 +1057,31 @@
 
 <h4 class="subsection">4.2.1 State occupancy probabilities</h4>
 
-<p><a name="doc_002dctmc"></a>
+<p>Similarly to the discrete case, we denote with \bf \pi(t) =
+(\pi_1(t), \pi_2(t), <small class="dots">...</small>, \pi_N(t) ) the <em>state occupancy
+probability vector</em> at time t. \pi_i(t) denotes the
+probability that the system is in state i at time t &ge; 0.
 
+   <p>Given the infinitesimal generator matrix \bf Q and the initial
+state occupancy probability vector \bf \pi(0) = (\pi_1(0),
+\pi_2(0), <small class="dots">...</small>, \pi_N(0)), the state occupancy probability vector
+\bf \pi(t) at time t can be computed as:
+
+<pre class="example">     \pi(t) = \pi(0) exp(Qt)
+</pre>
+   <p class="noindent">where \exp( \bf Q t ) is the matrix exponential
+of \bf Q t. Under certain conditions, there exists a
+<em>stationary state occupancy probability</em> \bf \pi =
+\lim_t \rightarrow +\infty \bf \pi(t), which is independent from
+the initial state occupancy \bf \pi(0). The stationary state
+occupancy probability vector \bf \pi satisfies
+\bf \pi \bf Q = \bf 0 and \sum_i=1^N \pi_i = 1.
+
+   <p><a name="doc_002dctmc"></a>
+
 <div class="defun">
 &mdash; Function File: <var>p</var> = <b>ctmc</b> (<var>Q</var>)<var><a name="index-ctmc-18"></a></var><br>
-&mdash; Function File: <var>p</var> = <b>ctmc</b> (<var>Q, t. q0</var>)<var><a name="index-ctmc-19"></a></var><br>
+&mdash; Function File: <var>p</var> = <b>ctmc</b> (<var>Q, t. p0</var>)<var><a name="index-ctmc-19"></a></var><br>
 <blockquote>
         <p><a name="index-Markov-chain_002c-continuous-time-20"></a><a name="index-Continuous-time-Markov-chain-21"></a><a name="index-Markov-chain_002c-state-occupancy-probabilities-22"></a><a name="index-Stationary-probabilities-23"></a>
 With a single argument, compute the stationary state occupancy
@@ -1080,7 +1116,7 @@
 satisfies the equation p\bf Q = 0 and \sum_i=1^N p_i = 1. 
 If this function is invoked with three arguments, <var>p</var><code>(i)</code>
 is the probability that the system is in state i at time <var>t</var>,
-given the initial occupancy probabilities <var>q0</var>.
+given the initial occupancy probabilities <var>p0</var>.
 
         </dl>
 
@@ -1152,17 +1188,23 @@
 (L_1(t), L_2(t), \ldots L_N(t)) such that L_i(t) is the
 expected sojourn time in state i during the interval
 [0,t), assuming that the initial occupancy probability at time
-0 was \bf \pi(0). Then, \bf L(t) is the solution of
+0 was \bf \pi(0). \bf L(t) is the solution of
 the following differential equation:
 
 <pre class="example">      dL
       --(t) = L(t) Q + pi(0),    L(0) = 0
       dt
 </pre>
-   <p>The function <code>ctmc_exps</code> can be used to compute \bf
-L(t), by using the <code>lsode</code> Octave function to solve the above
-linear differential equation.
+   <p>Alternatively, \bf L(t) can also be expressed in integral
+form as:
 
+<pre class="example">            / t
+     L(t) = |      pi(u) du
+            / u=0
+</pre>
+   <p class="noindent">where \bf \pi(t) = \bf \pi(0) \exp(\bf Qt) is
+the state occupancy probability at time t.
+
    <p><a name="doc_002dctmc_005fexps"></a>
 
 <div class="defun">
@@ -1212,7 +1254,7 @@
 rate from state i to state i+1 is \lambda_i = i
 \lambda (i=1, 2, 3), with \lambda = 0.5. The following
 code computes the expected sojourn time in state i,
-given the initial occupancy probability p_0=(1,0,0,0).
+given the initial occupancy probability \bf \pi_0=(1,0,0,0).
 
 <pre class="example"><pre class="verbatim">      lambda = 0.5;
       N = 4;

Modified: trunk/octave-forge/main/queueing/doc/queueing.pdf
===================================================================
(Binary files differ)

Modified: trunk/octave-forge/main/queueing/inst/ctmc.m
===================================================================
--- trunk/octave-forge/main/queueing/inst/ctmc.m	2012-03-11 15:45:11 UTC (rev 9814)
+++ trunk/octave-forge/main/queueing/inst/ctmc.m	2012-03-11 16:44:18 UTC (rev 9815)
@@ -18,7 +18,7 @@
 ## -*- texinfo -*-
 ##
 ## @deftypefn {Function File} {@var{p} =} ctmc (@var{Q})
-## @deftypefnx {Function File} {@var{p} =} ctmc (@var{Q}, @var{t}. @var{q0})
+## @deftypefnx {Function File} {@var{p} =} ctmc (@var{Q}, @var{t}. @var{p0})
 ##
 ## @cindex Markov chain, continuous time
 ## @cindex Continuous time Markov chain
@@ -63,7 +63,7 @@
 ## satisfies the equation @math{p{\bf Q} = 0} and @math{\sum_{i=1}^N p_i = 1}.
 ## If this function is invoked with three arguments, @code{@var{p}(i)}
 ## is the probability that the system is in state @math{i} at time @var{t},
-## given the initial occupancy probabilities @var{q0}.
+## given the initial occupancy probabilities @var{p0}.
 ##
 ## @end table
 ##
@@ -72,7 +72,7 @@
 ## Author: Moreno Marzolla <marzolla(at)cs.unibo.it>
 ## Web: http://www.moreno.marzolla.name/
 
-function q = ctmc( Q, t, q0 )
+function q = ctmc( Q, t, p0 )
 
   persistent epsilon = 10*eps;
 
@@ -91,17 +91,17 @@
   endif
 
   if ( nargin > 2 )
-    ( isvector(q0) && length(q0) == N && all(q0>=0) && abs(sum(q0)-1.0)<epsilon ) || \
-        usage( "q0 must be a probability vector" );   
-    q0 = q0(:)'; # make q0 a row vector
+    ( isvector(p0) && length(p0) == N && all(p0>=0) && abs(sum(p0)-1.0)<epsilon ) || \
+        usage( "p0 must be a probability vector" );   
+    p0 = p0(:)'; # make p0 a row vector
   else
-    q0 = ones(1,N) / N;
+    p0 = ones(1,N) / N;
   endif
 
   if ( nargin == 1 )
     q = __ctmc_steady_state( Q );
   else
-    q = __ctmc_transient(Q, t, q0 );
+    q = __ctmc_transient(Q, t, p0 );
   endif
 
 endfunction
@@ -132,8 +132,8 @@
 endfunction
 
 ## Helper function, compute transient probability
-function q = __ctmc_transient( Q, t, q0 )
-  q = q0*expm(Q*t);
+function q = __ctmc_transient( Q, t, p0 )
+  q = p0*expm(Q*t);
 endfunction
 
 %!test

This was sent by the SourceForge.net collaborative development platform, the world's largest Open Source development site.

[Octave-cvsupdate] SF.net SVN: octave:[9814] trunk/octave-forge/main/queueing

From: <mma...@us...> - 2012-03-11 15:45:22

Revision: 9814
          http://octave.svn.sourceforge.net/octave/?rev=9814&view=rev
Author:   mmarzolla
Date:     2012-03-11 15:45:11 +0000 (Sun, 11 Mar 2012)
Log Message:
-----------
added function ctmc_check_Q()

Modified Paths:
--------------
    trunk/octave-forge/main/queueing/ChangeLog
    trunk/octave-forge/main/queueing/DESCRIPTION
    trunk/octave-forge/main/queueing/Makefile
    trunk/octave-forge/main/queueing/NEWS
    trunk/octave-forge/main/queueing/doc/markovchains.txi
    trunk/octave-forge/main/queueing/doc/queueing.html
    trunk/octave-forge/main/queueing/doc/queueing.pdf
    trunk/octave-forge/main/queueing/inst/ctmc.m
    trunk/octave-forge/main/queueing/inst/ctmc_exps.m
    trunk/octave-forge/main/queueing/inst/ctmc_fpt.m
    trunk/octave-forge/main/queueing/inst/ctmc_mtta.m
    trunk/octave-forge/main/queueing/inst/ctmc_taexps.m
    trunk/octave-forge/main/queueing/inst/dtmc.m
    trunk/octave-forge/main/queueing/inst/dtmc_check_P.m
    trunk/octave-forge/main/queueing/inst/dtmc_fpt.m
    trunk/octave-forge/main/queueing/inst/qnmvablo.m
    trunk/octave-forge/main/queueing/inst/qnvisits.m

Added Paths:
-----------
    trunk/octave-forge/main/queueing/inst/ctmc_check_Q.m
    trunk/octave-forge/main/queueing/inst/dtmc_is_irreducible.m

Modified: trunk/octave-forge/main/queueing/ChangeLog
===================================================================
--- trunk/octave-forge/main/queueing/ChangeLog	2012-03-11 11:20:31 UTC (rev 9813)
+++ trunk/octave-forge/main/queueing/ChangeLog	2012-03-11 15:45:11 UTC (rev 9814)
@@ -1,18 +1,19 @@
-2012-02-XX Moreno Marzolla <mar...@cs...>
+2012-03-XX Moreno Marzolla <mar...@cs...>
 
 	* Version 1.X.0 released
 	* Fixed bug in qnvisits() which made the function behave incorrectly
 	  under particular degenerate cases.
 	* Fixed bug in ctmc_exps() (wrong initial value in call to lsode)
-	* Function ctmc_exps() can now also compute the expected sojourn time
+	* ctmc_exps() can now also compute the expected sojourn time
 	  until absorption for absorbing CTMCs.
-	* Function ctmc_exps() and ctmc_taexps() accept a scalar as second
+	* ctmc_exps() and ctmc_taexps() accept a scalar as second
 	  argument; the old syntax is still supported, but may be deprecated
 	  in future releases.
-	* Function ctmc_bd() now returns the infinitesimal generator matrix
+	* ctmc_bd() now returns the infinitesimal generator matrix
 	  of the birth-death process, not the steady-state solution.
-	* Function ctmc_bd_solve() has been removed
-	* New function dtmc_bd()
+	* ctmc_bd_solve() has been removed
+	* dtmc_bd() has been added
+	* ctmc_check_Q() has been added
 	* Miscellaneous fixes/improvements to the documentation
 
 2012-02-04 Moreno Marzolla <mar...@cs...>

Modified: trunk/octave-forge/main/queueing/DESCRIPTION
===================================================================
--- trunk/octave-forge/main/queueing/DESCRIPTION	2012-03-11 11:20:31 UTC (rev 9813)
+++ trunk/octave-forge/main/queueing/DESCRIPTION	2012-03-11 15:45:11 UTC (rev 9814)
@@ -1,6 +1,6 @@
 Name: queueing
 Version: 1.X.0
-Date: 2012-02-XX
+Date: 2012-03-XX
 Author: Moreno Marzolla <mar...@cs...>
 Maintainer: Moreno Marzolla <mar...@cs...>
 Title: Queueing networks and Markov chains analysis package for GNU Octave

Modified: trunk/octave-forge/main/queueing/Makefile
===================================================================
--- trunk/octave-forge/main/queueing/Makefile	2012-03-11 11:20:31 UTC (rev 9813)
+++ trunk/octave-forge/main/queueing/Makefile	2012-03-11 15:45:11 UTC (rev 9814)
@@ -1,5 +1,5 @@
 VERSIONNUM=1.X.0
-VERSIONDATE="2012-02-XX"
+VERSIONDATE="2012-03-XX"
 PROGNAME=queueing
 
 DISTNAME=$(PROGNAME)-$(VERSIONNUM)

Modified: trunk/octave-forge/main/queueing/NEWS
===================================================================
--- trunk/octave-forge/main/queueing/NEWS	2012-03-11 11:20:31 UTC (rev 9813)
+++ trunk/octave-forge/main/queueing/NEWS	2012-03-11 15:45:11 UTC (rev 9814)
@@ -15,6 +15,8 @@
 
 ** Function ctmc_bd_solve() has been removed
 
+** New function ctmc_check_Q() added
+
 Summary of important user-visible changes for queueing-1.0.0
 ------------------------------------------------------------------------------
 

Modified: trunk/octave-forge/main/queueing/doc/markovchains.txi
===================================================================
--- trunk/octave-forge/main/queueing/doc/markovchains.txi	2012-03-11 11:20:31 UTC (rev 9813)
+++ trunk/octave-forge/main/queueing/doc/markovchains.txi	2012-03-11 15:45:11 UTC (rev 9814)
@@ -67,6 +67,11 @@
 in state @math{i} at step @math{n}.
 
 @c
+@DOCSTRING(dtmc_check_P)
+
+@c
+@c
+@c
 @subsection State occupancy probabilities
 
 Given the transition probability matrix @math{\bf P} and the initial
@@ -143,6 +148,8 @@
 @node Continuous-Time Markov Chains
 @section Continuous-Time Markov Chains
 
+@DOCSTRING(ctmc_check_Q)
+
 @menu
 * State occupancy probabilities::
 * Birth-Death process::
@@ -319,5 +326,6 @@
 @c
 @node First Passage Times
 @subsection First Passage Times
+
 @DOCSTRING(ctmc_fpt)
 

Modified: trunk/octave-forge/main/queueing/doc/queueing.html
===================================================================
--- trunk/octave-forge/main/queueing/doc/queueing.html	2012-03-11 11:20:31 UTC (rev 9813)
+++ trunk/octave-forge/main/queueing/doc/queueing.html	2012-03-11 15:45:11 UTC (rev 9814)
@@ -817,6 +817,19 @@
 n. \pi_i(n) denotes the probability that the system is
 in state i at step n.
 
+   <p><a name="doc_002ddtmc_005fcheck_005fP"></a>
+
+<div class="defun">
+&mdash; Function File: [<var>result</var> <var>err</var>] = <b>dtmc_check_P</b> (<var>P</var>)<var><a name="index-dtmc_005fcheck_005fP-1"></a></var><br>
+<blockquote>
+        <p><a name="index-Markov-chain_002c-discrete-time-2"></a>
+If <var>P</var> is a valid transition probability matrix, return
+the size (number of rows or columns) of <var>P</var>. If <var>P</var> is not
+a transition probability matrix, set <var>result</var> to zero, and
+<var>err</var> to an appropriate error string.
+
+        </blockquote></div>
+
 <h4 class="subsection">4.1.1 State occupancy probabilities</h4>
 
 <p>Given the transition probability matrix \bf P and the initial
@@ -836,10 +849,10 @@
    <p><a name="doc_002ddtmc"></a>
 
 <div class="defun">
-&mdash; Function File: <var>p</var> = <b>dtmc</b> (<var>P</var>)<var><a name="index-dtmc-1"></a></var><br>
-&mdash; Function File: <var>p</var> = <b>dtmc</b> (<var>P, n, p0</var>)<var><a name="index-dtmc-2"></a></var><br>
+&mdash; Function File: <var>p</var> = <b>dtmc</b> (<var>P</var>)<var><a name="index-dtmc-3"></a></var><br>
+&mdash; Function File: <var>p</var> = <b>dtmc</b> (<var>P, n, p0</var>)<var><a name="index-dtmc-4"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-discrete-time-3"></a><a name="index-Discrete-time-Markov-chain-4"></a><a name="index-Markov-chain_002c-stationary-probabilities-5"></a><a name="index-Stationary-probabilities-6"></a>
+        <p><a name="index-Markov-chain_002c-discrete-time-5"></a><a name="index-Discrete-time-Markov-chain-6"></a><a name="index-Markov-chain_002c-stationary-probabilities-7"></a><a name="index-Stationary-probabilities-8"></a>
 With a single argument, compute the steady-state probability vector
 <var>p</var><code>(1), ..., </code><var>p</var><code>(N)</code> for a
 Discrete-Time Markov Chain given the N \times N transition
@@ -900,9 +913,9 @@
 <p><a name="doc_002ddtmc_005fbd"></a>
 
 <div class="defun">
-&mdash; Function File: <var>P</var> = <b>dtmc_bd</b> (<var>birth, death</var>)<var><a name="index-dtmc_005fbd-7"></a></var><br>
+&mdash; Function File: <var>P</var> = <b>dtmc_bd</b> (<var>birth, death</var>)<var><a name="index-dtmc_005fbd-9"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-discrete-time-8"></a><a name="index-Birth_002ddeath-process-9"></a>
+        <p><a name="index-Markov-chain_002c-discrete-time-10"></a><a name="index-Birth_002ddeath-process-11"></a>
 Returns the N \times N transition probability matrix P
 for a birth-death process with given rates.
 
@@ -942,10 +955,10 @@
    <p><a name="doc_002ddtmc_005ffpt"></a>
 
 <div class="defun">
-&mdash; Function File: <var>M</var> = <b>dtmc_fpt</b> (<var>P</var>)<var><a name="index-dtmc_005ffpt-10"></a></var><br>
-&mdash; Function File: <var>m</var> = <b>dtmc_fpt</b> (<var>P, i, j</var>)<var><a name="index-dtmc_005ffpt-11"></a></var><br>
+&mdash; Function File: <var>M</var> = <b>dtmc_fpt</b> (<var>P</var>)<var><a name="index-dtmc_005ffpt-12"></a></var><br>
+&mdash; Function File: <var>m</var> = <b>dtmc_fpt</b> (<var>P, i, j</var>)<var><a name="index-dtmc_005ffpt-13"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-discrete-time-12"></a><a name="index-First-passage-times-13"></a>
+        <p><a name="index-Markov-chain_002c-discrete-time-14"></a><a name="index-First-passage-times-15"></a>
 If called with a single argument, computes the mean first passage
 times <var>M</var><code>(i,j)</code>, that are the average number of transitions before
 state <var>j</var> is reached, starting from state <var>i</var>, for all
@@ -971,9 +984,11 @@
         <p><strong>OUTPUTS</strong>
 
           <dl>
-<dt><var>M</var><dd>If this function is called with a single argument, the result
+<dt><var>M</var><dd>If this function is called with a single argument,
 <var>M</var><code>(i,j)</code> is the average number of transitions before state
-<var>j</var> is reached for the first time, starting from state <var>i</var>.
+<var>j</var> is reached for the first time, starting from state <var>i</var>. 
+<var>M</var><code>(i,i)</code> is the <em>mean recurrence time</em>, and
+represents the average time needed to return to state <var>i</var>.
 
           <br><dt><var>m</var><dd>If this function is called with three arguments, the result <var>m</var>
 is the average number of transitions before state <var>j</var> is visited
@@ -994,6 +1009,19 @@
 
 <h3 class="section">4.2 Continuous-Time Markov Chains</h3>
 
+<p><a name="doc_002dctmc_005fcheck_005fQ"></a>
+
+<div class="defun">
+&mdash; Function File: [<var>result</var> <var>err</var>] = <b>ctmc_check_Q</b> (<var>Q</var>)<var><a name="index-ctmc_005fcheck_005fQ-16"></a></var><br>
+<blockquote>
+        <p><a name="index-Markov-chain_002c-continuous-time-17"></a>
+If <var>Q</var> is a valid infinitesimal generator matrix, return
+the size (number of rows or columns) of <var>Q</var>. If <var>Q</var> is not
+an infinitesimal generator matrix, set <var>result</var> to zero, and
+<var>err</var> to an appropriate error string.
+
+        </blockquote></div>
+
 <ul class="menu">
 <li><a accesskey="1" href="#State-occupancy-probabilities">State occupancy probabilities</a>
 <li><a accesskey="2" href="#Birth_002dDeath-process">Birth-Death process</a>
@@ -1016,10 +1044,10 @@
 <p><a name="doc_002dctmc"></a>
 
 <div class="defun">
-&mdash; Function File: <var>p</var> = <b>ctmc</b> (<var>Q</var>)<var><a name="index-ctmc-14"></a></var><br>
-&mdash; Function File: <var>p</var> = <b>ctmc</b> (<var>Q, t. q0</var>)<var><a name="index-ctmc-15"></a></var><br>
+&mdash; Function File: <var>p</var> = <b>ctmc</b> (<var>Q</var>)<var><a name="index-ctmc-18"></a></var><br>
+&mdash; Function File: <var>p</var> = <b>ctmc</b> (<var>Q, t. q0</var>)<var><a name="index-ctmc-19"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-16"></a><a name="index-Continuous-time-Markov-chain-17"></a><a name="index-Markov-chain_002c-state-occupancy-probabilities-18"></a><a name="index-Stationary-probabilities-19"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-20"></a><a name="index-Continuous-time-Markov-chain-21"></a><a name="index-Markov-chain_002c-state-occupancy-probabilities-22"></a><a name="index-Stationary-probabilities-23"></a>
 With a single argument, compute the stationary state occupancy
 probability vector <var>p</var>(1), <small class="dots">...</small>, <var>p</var>(N) for a
 Continuous-Time Markov Chain with infinitesimal generator matrix
@@ -1082,9 +1110,9 @@
 <p><a name="doc_002dctmc_005fbd"></a>
 
 <div class="defun">
-&mdash; Function File: <var>Q</var> = <b>ctmc_bd</b> (<var>birth, death</var>)<var><a name="index-ctmc_005fbd-20"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>ctmc_bd</b> (<var>birth, death</var>)<var><a name="index-ctmc_005fbd-24"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-21"></a><a name="index-Birth_002ddeath-process-22"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-25"></a><a name="index-Birth_002ddeath-process-26"></a>
 Returns the N \times N infinitesimal generator matrix Q
 for a birth-death process with given rates.
 
@@ -1138,10 +1166,10 @@
    <p><a name="doc_002dctmc_005fexps"></a>
 
 <div class="defun">
-&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, t, p </var>)<var><a name="index-ctmc_005fexps-23"></a></var><br>
-&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fexps-24"></a></var><br>
+&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, t, p </var>)<var><a name="index-ctmc_005fexps-27"></a></var><br>
+&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fexps-28"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-25"></a><a name="index-Expected-sojourn-time-26"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-29"></a><a name="index-Expected-sojourn-time-30"></a>
 With three arguments, compute the expected times <var>L</var><code>(i)</code>
 spent in each state i during the time interval
 [0,t], assuming that the state occupancy probabilities
@@ -1221,9 +1249,9 @@
 <p><a name="doc_002dctmc_005ftaexps"></a>
 
 <div class="defun">
-&mdash; Function File: <var>M</var> = <b>ctmc_taexps</b> (<var>Q, t, p</var>)<var><a name="index-ctmc_005ftaexps-27"></a></var><br>
+&mdash; Function File: <var>M</var> = <b>ctmc_taexps</b> (<var>Q, t, p</var>)<var><a name="index-ctmc_005ftaexps-31"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-28"></a><a name="index-Time_002dalveraged-sojourn-time-29"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-32"></a><a name="index-Time_002dalveraged-sojourn-time-33"></a>
 Compute the <em>time-averaged sojourn time</em> <var>M</var><code>(i)</code>,
 defined as the fraction of the time interval [0,t] spent in
 state i, assuming that the state occupancy probabilities at
@@ -1306,9 +1334,9 @@
    <p><a name="doc_002dctmc_005fmtta"></a>
 
 <div class="defun">
-&mdash; Function File: <var>t</var> = <b>ctmc_mtta</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fmtta-30"></a></var><br>
+&mdash; Function File: <var>t</var> = <b>ctmc_mtta</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fmtta-34"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-31"></a><a name="index-Mean-time-to-absorption-32"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-35"></a><a name="index-Mean-time-to-absorption-36"></a>
 Compute the Mean-Time to Absorption (MTTA) of the CTMC described by
 the infinitesimal generator matrix <var>Q</var>, starting from initial
 occupancy probabilities <var>p</var>. If there are no absorbing states, this
@@ -1369,7 +1397,7 @@
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998.
 
-   <p><a name="index-Bolch_002c-G_002e-33"></a><a name="index-Greiner_002c-S_002e-34"></a><a name="index-de-Meer_002c-H_002e-35"></a><a name="index-Trivedi_002c-K_002e-36"></a>
+   <p><a name="index-Bolch_002c-G_002e-37"></a><a name="index-Greiner_002c-S_002e-38"></a><a name="index-de-Meer_002c-H_002e-39"></a><a name="index-Trivedi_002c-K_002e-40"></a>
 <div class="node">
 <a name="First-Passage-Times"></a>
 <p><hr>
@@ -1383,10 +1411,10 @@
 <p><a name="doc_002dctmc_005ffpt"></a>
 
 <div class="defun">
-&mdash; Function File: <var>M</var> = <b>ctmc_fpt</b> (<var>Q</var>)<var><a name="index-ctmc_005ffpt-37"></a></var><br>
-&mdash; Function File: <var>m</var> = <b>ctmc_fpt</b> (<var>Q, i, j</var>)<var><a name="index-ctmc_005ffpt-38"></a></var><br>
+&mdash; Function File: <var>M</var> = <b>ctmc_fpt</b> (<var>Q</var>)<var><a name="index-ctmc_005ffpt-41"></a></var><br>
+&mdash; Function File: <var>m</var> = <b>ctmc_fpt</b> (<var>Q, i, j</var>)<var><a name="index-ctmc_005ffpt-42"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-39"></a><a name="index-First-passage-times-40"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-43"></a><a name="index-First-passage-times-44"></a>
 If called with a single argument, computes the mean first passage
 times <var>M</var><code>(i,j)</code>, the average times before state <var>j</var> is
 reached, starting from state <var>i</var>, for all 1 \leq i, j \leq
@@ -1492,9 +1520,9 @@
    <p><a name="doc_002dqnmm1"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmm1</b> (<var>lambda, mu</var>)<var><a name="index-qnmm1-41"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmm1</b> (<var>lambda, mu</var>)<var><a name="index-qnmm1-45"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002f1_007d-system-42"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002f1_007d-system-46"></a>
 Compute utilization, response time, average number of requests
 and throughput for a M/M/1 queue.
 
@@ -1539,7 +1567,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.3.
 
-   <p><a name="index-Bolch_002c-G_002e-43"></a><a name="index-Greiner_002c-S_002e-44"></a><a name="index-de-Meer_002c-H_002e-45"></a><a name="index-Trivedi_002c-K_002e-46"></a>
+   <p><a name="index-Bolch_002c-G_002e-47"></a><a name="index-Greiner_002c-S_002e-48"></a><a name="index-de-Meer_002c-H_002e-49"></a><a name="index-Trivedi_002c-K_002e-50"></a>
 <!-- M/M/m -->
 <div class="node">
 <a name="The-M%2fM%2fm-System"></a>
@@ -1565,10 +1593,10 @@
    <p><a name="doc_002dqnmmm"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu</var>)<var><a name="index-qnmmm-47"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu, m</var>)<var><a name="index-qnmmm-48"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu</var>)<var><a name="index-qnmmm-51"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu, m</var>)<var><a name="index-qnmmm-52"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002fm_007d-system-49"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002fm_007d-system-53"></a>
 Compute utilization, response time, average number of requests in
 service and throughput for a M/M/m queue, a queueing
 system with m identical service centers connected to a single queue.
@@ -1620,7 +1648,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.5.
 
-   <p><a name="index-Bolch_002c-G_002e-50"></a><a name="index-Greiner_002c-S_002e-51"></a><a name="index-de-Meer_002c-H_002e-52"></a><a name="index-Trivedi_002c-K_002e-53"></a>
+   <p><a name="index-Bolch_002c-G_002e-54"></a><a name="index-Greiner_002c-S_002e-55"></a><a name="index-de-Meer_002c-H_002e-56"></a><a name="index-Trivedi_002c-K_002e-57"></a>
 <!-- M/M/inf -->
 <div class="node">
 <a name="The-M%2fM%2finf-System"></a>
@@ -1643,7 +1671,7 @@
    <p><a name="doc_002dqnmminf"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmminf</b> (<var>lambda, mu</var>)<var><a name="index-qnmminf-54"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmminf</b> (<var>lambda, mu</var>)<var><a name="index-qnmminf-58"></a></var><br>
 <blockquote>
         <p>Compute utilization, response time, average number of requests and
 throughput for a M/M/\infty queue. This is a system with an
@@ -1651,7 +1679,7 @@
 system is always stable, regardless the values of the arrival and
 service rates.
 
-        <p><a name="index-g_t_0040math_007bM_002fM_002f_007dinf-system-55"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002f_007dinf-system-59"></a>
 
         <p><strong>INPUTS</strong>
 
@@ -1669,7 +1697,7 @@
 different from the utilization, which in the case of M/M/\infty
 centers is always zero.
 
-          <p><a name="index-traffic-intensity-56"></a>
+          <p><a name="index-traffic-intensity-60"></a>
 <br><dt><var>R</var><dd>Service center response time.
 
           <br><dt><var>Q</var><dd>Average number of requests in the system (which is equal to the
@@ -1697,7 +1725,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.4.
 
-   <p><a name="index-Bolch_002c-G_002e-57"></a><a name="index-Greiner_002c-S_002e-58"></a><a name="index-de-Meer_002c-H_002e-59"></a><a name="index-Trivedi_002c-K_002e-60"></a>
+   <p><a name="index-Bolch_002c-G_002e-61"></a><a name="index-Greiner_002c-S_002e-62"></a><a name="index-de-Meer_002c-H_002e-63"></a><a name="index-Trivedi_002c-K_002e-64"></a>
 <!-- M/M/1/k -->
 <div class="node">
 <a name="The-M%2fM%2f1%2fK-System"></a>
@@ -1721,9 +1749,9 @@
    <p><a name="doc_002dqnmm1k"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmm1k</b> (<var>lambda, mu, K</var>)<var><a name="index-qnmm1k-61"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmm1k</b> (<var>lambda, mu, K</var>)<var><a name="index-qnmm1k-65"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002f1_002fK_007d-system-62"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002f1_002fK_007d-system-66"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/M/1/K finite capacity system. In a
 M/M/1/K queue there is a single server; the maximum number of
@@ -1790,9 +1818,9 @@
    <p><a name="doc_002dqnmmmk"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmmmk</b> (<var>lambda, mu, m, K</var>)<var><a name="index-qnmmmk-63"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmmmk</b> (<var>lambda, mu, m, K</var>)<var><a name="index-qnmmmk-67"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002fm_002fK_007d-system-64"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002fm_002fK_007d-system-68"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/M/m/K finite capacity system. In a
 M/M/m/K system there are m \geq 1 identical service
@@ -1850,7 +1878,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.6.
 
-   <p><a name="index-Bolch_002c-G_002e-65"></a><a name="index-Greiner_002c-S_002e-66"></a><a name="index-de-Meer_002c-H_002e-67"></a><a name="index-Trivedi_002c-K_002e-68"></a>
+   <p><a name="index-Bolch_002c-G_002e-69"></a><a name="index-Greiner_002c-S_002e-70"></a><a name="index-de-Meer_002c-H_002e-71"></a><a name="index-Trivedi_002c-K_002e-72"></a>
 
 <!-- Approximate M/M/m -->
 <div class="node">
@@ -1872,9 +1900,9 @@
    <p><a name="doc_002dqnammm"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnammm</b> (<var>lambda, mu</var>)<var><a name="index-qnammm-69"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnammm</b> (<var>lambda, mu</var>)<var><a name="index-qnammm-73"></a></var><br>
 <blockquote>
-        <p><a name="index-Asymmetric-_0040math_007bM_002fM_002fm_007d-system-70"></a>
+        <p><a name="index-Asymmetric-_0040math_007bM_002fM_002fm_007d-system-74"></a>
 Compute <em>approximate</em> utilization, response time, average number
 of requests in service and throughput for an asymmetric  M/M/m
 queue. In this system there are m different service centers
@@ -1921,7 +1949,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998
 
-   <p><a name="index-Bolch_002c-G_002e-71"></a><a name="index-Greiner_002c-S_002e-72"></a><a name="index-de-Meer_002c-H_002e-73"></a><a name="index-Trivedi_002c-K_002e-74"></a>
+   <p><a name="index-Bolch_002c-G_002e-75"></a><a name="index-Greiner_002c-S_002e-76"></a><a name="index-de-Meer_002c-H_002e-77"></a><a name="index-Trivedi_002c-K_002e-78"></a>
 <div class="node">
 <a name="The-M%2fG%2f1-System"></a>
 <a name="The-M_002fG_002f1-System"></a>
@@ -1937,9 +1965,9 @@
 <p><a name="doc_002dqnmg1"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmg1</b> (<var>lambda, xavg, x2nd</var>)<var><a name="index-qnmg1-75"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmg1</b> (<var>lambda, xavg, x2nd</var>)<var><a name="index-qnmg1-79"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fG_002f1_007d-system-76"></a>
+        <p><a name="index-g_t_0040math_007bM_002fG_002f1_007d-system-80"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/G/1 system. The service time distribution
 is described by its mean <var>xavg</var>, and by its second moment
@@ -1996,9 +2024,9 @@
 <p><a name="doc_002dqnmh1"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmh1</b> (<var>lambda, mu, alpha</var>)<var><a name="index-qnmh1-77"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmh1</b> (<var>lambda, mu, alpha</var>)<var><a name="index-qnmh1-81"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fH_005fm_002f1_007d-system-78"></a>
+        <p><a name="index-g_t_0040math_007bM_002fH_005fm_002f1_007d-system-82"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/H_m/1 system. In this system, the customer
 service times have hyper-exponential distribution:
@@ -2080,7 +2108,7 @@
 <li><a accesskey="6" href="#Utility-functions">Utility functions</a>:                    Utility functions to compute miscellaneous quantities
 </ul>
 
-<p><a name="index-queueing-networks-79"></a>
+<p><a name="index-queueing-networks-83"></a>
 <!-- INTRODUCTION -->
 <div class="node">
 <a name="Introduction-to-QNs"></a>
@@ -2341,13 +2369,13 @@
    <p><a name="doc_002dqnmknode"></a>
 
 <div class="defun">
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S</var>)<var><a name="index-qnmknode-80"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S, m</var>)<var><a name="index-qnmknode-81"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/1-lcfs-pr", S</var>)<var><a name="index-qnmknode-82"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S</var>)<var><a name="index-qnmknode-83"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S, s2</var>)<var><a name="index-qnmknode-84"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S</var>)<var><a name="index-qnmknode-85"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S, s2</var>)<var><a name="index-qnmknode-86"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S</var>)<var><a name="index-qnmknode-84"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S, m</var>)<var><a name="index-qnmknode-85"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/1-lcfs-pr", S</var>)<var><a name="index-qnmknode-86"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S</var>)<var><a name="index-qnmknode-87"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S, s2</var>)<var><a name="index-qnmknode-88"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S</var>)<var><a name="index-qnmknode-89"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S, s2</var>)<var><a name="index-qnmknode-90"></a></var><br>
 <blockquote>
         <p>Creates a node; this function can be used together with
 <code>qnsolve</code>. It is possible to create either single-class nodes
@@ -2416,10 +2444,10 @@
    <p><a name="doc_002dqnsolve"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V</var>)<var><a name="index-qnsolve-87"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V, Z</var>)<var><a name="index-qnsolve-88"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"open", lambda, QQ, V</var>)<var><a name="index-qnsolve-89"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"mixed", lambda, N, QQ, V</var>)<var><a name="index-qnsolve-90"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V</var>)<var><a name="index-qnsolve-91"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V, Z</var>)<var><a name="index-qnsolve-92"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"open", lambda, QQ, V</var>)<var><a name="index-qnsolve-93"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"mixed", lambda, N, QQ, V</var>)<var><a name="index-qnsolve-94"></a></var><br>
 <blockquote>
         <p>General evaluator of QN models. Networks can be open,
 closed or mixed; single as well as multiclass networks are supported.
@@ -2597,11 +2625,11 @@
    <p><a name="doc_002dqnjackson"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P </var>)<var><a name="index-qnjackson-91"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P, m </var>)<var><a name="index-qnjackson-92"></a></var><br>
-&mdash; Function File: <var>pr</var> = <b>qnjackson</b> (<var>lambda, S, P, m, k</var>)<var><a name="index-qnjackson-93"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P </var>)<var><a name="index-qnjackson-95"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P, m </var>)<var><a name="index-qnjackson-96"></a></var><br>
+&mdash; Function File: <var>pr</var> = <b>qnjackson</b> (<var>lambda, S, P, m, k</var>)<var><a name="index-qnjackson-97"></a></var><br>
 <blockquote>
-        <p><a name="index-open-network_002c-single-class-94"></a><a name="index-Jackson-network-95"></a>
+        <p><a name="index-open-network_002c-single-class-98"></a><a name="index-Jackson-network-99"></a>
 With three or four input parameters, this function computes the
 steady-state occupancy probabilities for a Jackson network. With five
 input parameters, this function computes the steady-state probability
@@ -2683,7 +2711,7 @@
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998, pp. 284&ndash;287.
 
-   <p><a name="index-Bolch_002c-G_002e-96"></a><a name="index-Greiner_002c-S_002e-97"></a><a name="index-de-Meer_002c-H_002e-98"></a><a name="index-Trivedi_002c-K_002e-99"></a>
+   <p><a name="index-Bolch_002c-G_002e-100"></a><a name="index-Greiner_002c-S_002e-101"></a><a name="index-de-Meer_002c-H_002e-102"></a><a name="index-Trivedi_002c-K_002e-103"></a>
 
 <h4 class="subsection">6.3.2 The Convolution Algorithm</h4>
 
@@ -2717,10 +2745,10 @@
    <p><a name="doc_002dqnconvolution"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V</var>)<var><a name="index-qnconvolution-100"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V, m</var>)<var><a name="index-qnconvolution-101"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V</var>)<var><a name="index-qnconvolution-104"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V, m</var>)<var><a name="index-qnconvolution-105"></a></var><br>
 <blockquote>
-        <p><a name="index-closed-network-102"></a><a name="index-normalization-constant-103"></a><a name="index-convolution-algorithm-104"></a>
+        <p><a name="index-closed-network-106"></a><a name="index-normalization-constant-107"></a><a name="index-convolution-algorithm-108"></a>
 This function implements the <em>convolution algorithm</em> for
 computing steady-state performance measures of product-form,
 single-class closed queueing networks. Load-independent service
@@ -2811,20 +2839,20 @@
 16, number 9, september 1973,
 pp. 527&ndash;531. <a href="http://doi.acm.org/10.1145/362342.362345">http://doi.acm.org/10.1145/362342.362345</a>
 
-   <p><a name="index-Buzen_002c-J_002e-P_002e-105"></a>
+   <p><a name="index-Buzen_002c-J_002e-P_002e-109"></a>
 This implementation is based on G. Bolch, S. Greiner, H. de Meer and
 K. Trivedi, <cite>Queueing Networks and Markov Chains: Modeling and
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998, pp. 313&ndash;317.
 
-   <p><a name="index-Bolch_002c-G_002e-106"></a><a name="index-Greiner_002c-S_002e-107"></a><a name="index-de-Meer_002c-H_002e-108"></a><a name="index-Trivedi_002c-K_002e-109"></a>
+   <p><a name="index-Bolch_002c-G_002e-110"></a><a name="index-Greiner_002c-S_002e-111"></a><a name="index-de-Meer_002c-H_002e-112"></a><a name="index-Trivedi_002c-K_002e-113"></a>
 <!-- Convolution for load-dependent service centers -->
 <a name="doc_002dqnconvolutionld"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolutionld</b> (<var>N, S, V</var>)<var><a name="index-qnconvolutionld-110"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolutionld</b> (<var>N, S, V</var>)<var><a name="index-qnconvolutionld-114"></a></var><br>
 <blockquote>
-        <p><a name="index-closed-network-111"></a><a name="index-normalization-constant-112"></a><a name="index-convolution-algorithm-113"></a><a name="index-load_002ddependent-service-center-114"></a>
+        <p><a name="index-closed-network-115"></a><a name="index-normalization-constant-116"></a><a name="index-convolution-algorithm-117"></a><a name="index-load_002ddependent-service-center-118"></a>
 This function implements the <em>convolution algorithm</em> for
 product-form, single-class closed queueing networks with general
 load-dependent service centers.
@@ -2884,7 +2912,7 @@
 Purdue University, feb, 1981 (revised). 
 <a href="http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-354.pdf">http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-354.pdf</a>
 
-   <p><a name="index-Schwetman_002c-H_002e-115"></a>
+   <p><a name="index-Schwetman_002c-H_002e-119"></a>
 M. Reiser, H. Kobayashi, <cite>On The Convolution Algorithm for
 Separable Queueing Networks</cite>, In Proceedings of the 1976 ACM
 SIGMETRICS Conference on Computer Performance Modeling Measurement and
@@ -2892,7 +2920,7 @@
 1976). SIGMETRICS '76. ACM, New York, NY,
 pp. 109&ndash;117. <a href="http://doi.acm.org/10.1145/800200.806187">http://doi.acm.org/10.1145/800200.806187</a>
 
-   <p><a name="index-Reiser_002c-M_002e-116"></a><a name="index-Kobayashi_002c-H_002e-117"></a>
+   <p><a name="index-Reiser_002c-M_002e-120"></a><a name="index-Kobayashi_002c-H_002e-121"></a>
 This implementation is based on G. Bolch, S. Greiner, H. de Meer and
 K. Trivedi, <cite>Queueing Networks and Markov Chains: Modeling and
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
@@ -2904,7 +2932,7 @@
 function f_i defined in Schwetman, <code>Some Computational
 Aspects of Queueing Network Models</code>.
 
-   <p><a name="index-Bolch_002c-G_002e-118"></a><a name="index-Greiner_002c-S_002e-119"></a><a name="index-de-Meer_002c-H_002e-120"></a><a name="index-Trivedi_002c-K_002e-121"></a>
+   <p><a name="index-Bolch_002c-G_002e-122"></a><a name="index-Greiner_002c-S_002e-123"></a><a name="index-de-Meer_002c-H_002e-124"></a><a name="index-Trivedi_002c-K_002e-125"></a>
 
 <h4 class="subsection">6.3.3 Open networks</h4>
 
@@ -2912,10 +2940,10 @@
 <p><a name="doc_002dqnopensingle"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V</var>)<var><a name="index-qnopensingle-122"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopensingle-123"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V</var>)<var><a name="index-qnopensingle-126"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopensingle-127"></a></var><br>
 <blockquote>
-        <p><a name="index-open-network_002c-single-class-124"></a><a name="index-BCMP-network-125"></a>
+        <p><a name="index-open-network_002c-single-class-128"></a><a name="index-BCMP-network-129"></a>
 Analyze open, single class BCMP queueing networks.
 
         <p>This function works for a subset of BCMP single-class open networks
@@ -3008,16 +3036,16 @@
 Networks and Markov Chains: Modeling and Performance Evaluation with
 Computer Science Applications</cite>, Wiley, 1998.
 
-   <p><a name="index-Bolch_002c-G_002e-126"></a><a name="index-Greiner_002c-S_002e-127"></a><a name="index-de-Meer_002c-H_002e-128"></a><a name="index-Trivedi_002c-K_002e-129"></a>
+   <p><a name="index-Bolch_002c-G_002e-130"></a><a name="index-Greiner_002c-S_002e-131"></a><a name="index-de-Meer_002c-H_002e-132"></a><a name="index-Trivedi_002c-K_002e-133"></a>
 
 <!-- Open network with multiple classes -->
    <p><a name="doc_002dqnopenmulti"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V</var>)<var><a name="index-qnopenmulti-130"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopenmulti-131"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V</var>)<var><a name="index-qnopenmulti-134"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopenmulti-135"></a></var><br>
 <blockquote>
-        <p><a name="index-open-network_002c-multiple-classes-132"></a>
+        <p><a name="index-open-network_002c-multiple-classes-136"></a>
 Exact analysis of open, multiple-class BCMP networks. The network can
 be made of <em>single-server</em> queueing centers (FCFS, LCFS-PR or
 PS) or delay centers (IS). This function assumes a network with
@@ -3082,7 +3110,7 @@
 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In
 particular, see section 7.4.1 ("Open Model Solution Techniques").
 
-   <p><a name="index-Lazowska_002c-E_002e-D_002e-133"></a><a name="index-Zahorjan_002c-J_002e-134"></a><a name="index-Graham_002c-G_002e-S_002e-135"></a><a name="index-Sevcik_002c-K_002e-C_002e-136"></a>
+   <p><a name="index-Lazowska_002c-E_002e-D_002e-137"></a><a name="index-Zahorjan_002c-J_002e-138"></a><a name="index-Graham_002c-G_002e-S_002e-139"></a><a name="index-Sevcik_002c-K_002e-C_002e-140"></a>
 
 <h4 class="subsection">6.3.4 Closed Networks</h4>
 
@@ -3090,11 +3118,11 @@
 <p><a name="doc_002dqnclosedsinglemva"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemva-137"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemva-138"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemva-139"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemva-141"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemva-142"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemva-143"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-140"></a><a name="index-closed-network_002c-single-class-141"></a><a name="index-normalization-constant-142"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-144"></a><a name="index-closed-network_002c-single-class-145"></a><a name="index-normalization-constant-146"></a>
 Analyze closed, single class queueing networks using the exact Mean
 Value Analysis (MVA) algorithm. The following queueing disciplines
 are supported: FCFS, LCFS-PR, PS and IS (Infinite Server). This
@@ -3195,7 +3223,7 @@
 Multichain Queuing Networks</cite>, Journal of the ACM, vol. 27, n. 2, April
 1980, pp. 313&ndash;322. <a href="http://doi.acm.org/10.1145/322186.322195">http://doi.acm.org/10.1145/322186.322195</a>
 
-   <p><a name="index-Reiser_002c-M_002e-143"></a><a name="index-Lavenberg_002c-S_002e-S_002e-144"></a>
+   <p><a name="index-Reiser_002c-M_002e-147"></a><a name="index-Lavenberg_002c-S_002e-S_002e-148"></a>
 This implementation is described in R. Jain , <cite>The Art of Computer
 Systems Performance Analysis</cite>, Wiley, 1991, p. 577.  Multi-server nodes
 <!-- and the computation of @math{G(N)}, -->
@@ -3204,15 +3232,15 @@
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998, Section 8.2.1, "Single Class Queueing Networks".
 
-   <p><a name="index-Jain_002c-R_002e-145"></a><a name="index-Bolch_002c-G_002e-146"></a><a name="index-Greiner_002c-S_002e-147"></a><a name="index-de-Meer_002c-H_002e-148"></a><a name="index-Trivedi_002c-K_002e-149"></a>
+   <p><a name="index-Jain_002c-R_002e-149"></a><a name="index-Bolch_002c-G_002e-150"></a><a name="index-Greiner_002c-S_002e-151"></a><a name="index-de-Meer_002c-H_002e-152"></a><a name="index-Trivedi_002c-K_002e-153"></a>
 <!-- MVA for single class, closed networks with load dependent servers -->
 <a name="doc_002dqnclosedsinglemvald"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvald-150"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V, Z</var>)<var><a name="index-qnclosedsinglemvald-151"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvald-154"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V, Z</var>)<var><a name="index-qnclosedsinglemvald-155"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-152"></a><a name="index-closed-network_002c-single-class-153"></a><a name="index-load_002ddependent-service-center-154"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-156"></a><a name="index-closed-network_002c-single-class-157"></a><a name="index-load_002ddependent-service-center-158"></a>
 Exact MVA algorithm for closed, single class queueing networks
 with load-dependent service centers. This function supports
 FCFS, LCFS-PR, PS and IS nodes. For networks with only fixed-rate
@@ -3270,15 +3298,15 @@
 1998, Section 8.2.4.1, &ldquo;Networks with Load-Deèpendent Service: Closed
 Networks&rdquo;.
 
-   <p><a name="index-Bolch_002c-G_002e-155"></a><a name="index-Greiner_002c-S_002e-156"></a><a name="index-de-Meer_002c-H_002e-157"></a><a name="index-Trivedi_002c-K_002e-158"></a>
+   <p><a name="index-Bolch_002c-G_002e-159"></a><a name="index-Greiner_002c-S_002e-160"></a><a name="index-de-Meer_002c-H_002e-161"></a><a name="index-Trivedi_002c-K_002e-162"></a>
 <!-- CMVA for single class, closed networks with a single load dependent servers -->
 <a name="doc_002dqncmva"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V</var>)<var><a name="index-qncmva-159"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V, Z</var>)<var><a name="index-qncmva-160"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V</var>)<var><a name="index-qncmva-163"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V, Z</var>)<var><a name="index-qncmva-164"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-161"></a><a name="index-CMVA-162"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-165"></a><a name="index-CMVA-166"></a>
 Implementation of the Conditional MVA (CMVA) algorithm, a numerically
 stable variant of MVA for load-dependent servers. CMVA is described
 in G. Casale, <cite>A Note on Stable Flow-Equivalent Aggregation in
@@ -3332,19 +3360,19 @@
 closed networks</cite>. Queueing Syst. Theory Appl., 60:193–202, December
 2008.
 
-   <p><a name="index-Casale_002c-G_002e-163"></a>
+   <p><a name="index-Casale_002c-G_002e-167"></a>
 <!-- Approximate MVA for single class, closed networks -->
 
    <p><a name="doc_002dqnclosedsinglemvaapprox"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvaapprox-164"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemvaapprox-165"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemvaapprox-166"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedsinglemvaapprox-167"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedsinglemvaapprox-168"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvaapprox-168"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemvaapprox-169"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemvaapprox-170"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedsinglemvaapprox-171"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedsinglemvaapprox-172"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-169"></a><a name="index-Approximate-MVA-170"></a><a name="index-Closed-network_002c-single-class-171"></a><a name="index-Closed-network_002c-approximate-analysis-172"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-173"></a><a name="index-Approximate-MVA-174"></a><a name="index-Closed-network_002c-single-class-175"></a><a name="index-Closed-network_002c-approximate-analysis-176"></a>
 Analyze closed, single class queueing networks using the Approximate
 Mean Value Analysis (MVA) algorithm. This function is based on
 approximating the number of customers seen at center k when a
@@ -3423,20 +3451,20 @@
 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In
 particular, see section 6.4.2.2 ("Approximate Solution Techniques").
 
-   <p><a name="index-Lazowska_002c-E_002e-D_002e-173"></a><a name="index-Zahorjan_002c-J_002e-174"></a><a name="index-Graham_002c-G_002e-S_002e-175"></a><a name="index-Sevcik_002c-K_002e-C_002e-176"></a>
+   <p><a name="index-Lazowska_002c-E_002e-D_002e-177"></a><a name="index-Zahorjan_002c-J_002e-178"></a><a name="index-Graham_002c-G_002e-S_002e-179"></a><a name="index-Sevcik_002c-K_002e-C_002e-180"></a>
 
 <!-- MVA for multiple class, closed networks -->
    <p><a name="doc_002dqnclosedmultimva"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S </var>)<var><a name="index-qnclosedmultimva-177"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimva-178"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimva-179"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimva-180"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P</var>)<var><a name="index-qnclosedmultimva-181"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P, m</var>)<var><a name="index-qnclosedmultimva-182"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S </var>)<var><a name="index-qnclosedmultimva-181"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimva-182"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimva-183"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimva-184"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P</var>)<var><a name="index-qnclosedmultimva-185"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P, m</var>)<var><a name="index-qnclosedmultimva-186"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-183"></a><a name="index-closed-network_002c-multiple-classes-184"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-187"></a><a name="index-closed-network_002c-multiple-classes-188"></a>
 Analyze closed, multiclass queueing networks with K service
 centers and C independent customer classes (chains) using the
 Mean Value Analysys (MVA) algorithm.
@@ -3566,7 +3594,7 @@
 Multichain Queuing Networks</cite>, Journal of the ACM, vol. 27, n. 2, April
 1980, pp. 313&ndash;322. <a href="http://doi.acm.org/10.1145/322186.322195">http://doi.acm.org/10.1145/322186.322195</a>
 
-   <p><a name="index-Reiser_002c-M_002e-185"></a><a name="index-Lavenberg_002c-S_002e-S_002e-186"></a>
+   <p><a name="index-Reiser_002c-M_002e-189"></a><a name="index-Lavenberg_002c-S_002e-S_002e-190"></a>
 This implementation is based on G. Bolch, S. Greiner, H. de Meer and
 K. Trivedi, <cite>Queueing Networks and Markov Chains: Modeling and
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
@@ -3576,18 +3604,18 @@
 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In
 particular, see section 7.4.2.1 ("Exact Solution Techniques").
 
-   <p><a name="index-Bolch_002c-G_002e-187"></a><a name="index-Greiner_002c-S_002e-188"></a><a name="index-de-Meer_002c-H_002e-189"></a><a name="index-Trivedi_002c-K_002e-190"></a><a name="index-Lazowska_002c-E_002e-D_002e-191"></a><a name="index-Zahorjan_002c-J_002e-192"></a><a name="index-Graham_002c-G_002e-S_002e-193"></a><a name="index-Sevcik_002c-K_002e-C_002e-194"></a>
+   <p><a name="index-Bolch_002c-G_002e-191"></a><a name="index-Greiner_002c-S_002e-192"></a><a name="index-de-Meer_002c-H_002e-193"></a><a name="index-Trivedi_002c-K_002e-194"></a><a name="index-Lazowska_002c-E_002e-D_002e-195"></a><a name="index-Zahorjan_002c-J_002e-196"></a><a name="index-Graham_002c-G_002e-S_002e-197"></a><a name="index-Sevcik_002c-K_002e-C_002e-198"></a>
 <!-- Approximate MVA, with Bard-Schweitzer approximation -->
 <a name="doc_002dqnclosedmultimvaapprox"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimvaapprox-195"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimvaapprox-196"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimvaapprox-197"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedmultimvaapprox-198"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedmultimvaapprox-199"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimvaapprox-199"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimvaapprox-200"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimvaapprox-201"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedmultimvaapprox-202"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedmultimvaapprox-203"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-200"></a><a name="index-Approximate-MVA-201"></a><a name="index-Closed-network_002c-multiple-classes-202"></a><a name="index-Closed-network_002c-approximate-analysis-203"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-204"></a><a name="index-Approximate-MVA-205"></a><a name="index-Closed-network_002c-multiple-classes-206"></a><a name="index-Closed-network_002c-approximate-analysis-207"></a>
 Analyze closed, multiclass queueing networks with K service
 centers and C customer classes using the approximate Mean
 Value Analysys (MVA) algorithm.
@@ -3672,12 +3700,12 @@
 proc. 4th Int. Symp. on Modelling and Performance Evaluation of
 Computer Systems, feb. 1979, pp. 51&ndash;62.
 
-   <p><a name="index-Bard_002c-Y_002e-204"></a>
+   <p><a name="index-Bard_002c-Y_002e-208"></a>
 P. Schweitzer, <cite>Approximate Analysis of Multiclass Closed
 Networks of Queues</cite>, Proc. Int. Conf. on Stochastic Control and
 Optimization, jun 1979, pp. 25&ndash;29.
 
-   <p><a name="index-Schweitzer_002c-P_002e-205"></a>
+   <p><a name="index-Schweitzer_002c-P_002e-209"></a>
 This implementation is based on Edward D. Lazowska, John Zahorjan, G. 
 Scott Graham, and Kenneth C. Sevcik, <cite>Quantitative System
 Performance: Computer System Analysis Using Queueing Network Models</cite>,
@@ -3688,7 +3716,7 @@
 described above, as it computes the average response times R
 instead of the residence times.
 
-   <p><a name="index-Lazowska_002c-E_002e-D_002e-206"></a><a name="index-Zahorjan_002c-J_002e-207"></a><a name="index-Graham_002c-G_002e-S_002e-208"></a><a name="index-Sevcik_002c-K_002e-C_002e-209"></a>
+   <p><a name="index-Lazowska_002c-E_002e-D_002e-210"></a><a name="index-Zahorjan_002c-J_002e-211"></a><a name="index-Graham_002c-G_002e-S_002e-212"></a><a name="index-Sevcik_002c-K_002e-C_002e-213"></a>
 
 <h4 class="subsection">6.3.5 Mixed Networks</h4>
 
@@ -3696,9 +3724,9 @@
 <p...
 
[truncated message content]

[Octave-cvsupdate] SF.net SVN: octave:[9813] trunk/octave-forge/main/queueing

From: <mma...@us...> - 2012-03-11 11:20:42

Revision: 9813
          http://octave.svn.sourceforge.net/octave/?rev=9813&view=rev
Author:   mmarzolla
Date:     2012-03-11 11:20:31 +0000 (Sun, 11 Mar 2012)
Log Message:
-----------
New function dtmc_bd() added; misc fixes and improvements

Modified Paths:
--------------
    trunk/octave-forge/main/queueing/ChangeLog
    trunk/octave-forge/main/queueing/DESCRIPTION
    trunk/octave-forge/main/queueing/Makefile
    trunk/octave-forge/main/queueing/NEWS
    trunk/octave-forge/main/queueing/doc/INSTALL
    trunk/octave-forge/main/queueing/doc/markovchains.txi
    trunk/octave-forge/main/queueing/doc/queueing.html
    trunk/octave-forge/main/queueing/doc/queueing.pdf
    trunk/octave-forge/main/queueing/doc/summary.txi
    trunk/octave-forge/main/queueing/inst/ctmc_bd.m
    trunk/octave-forge/main/queueing/inst/ctmc_exps.m
    trunk/octave-forge/main/queueing/inst/qnmm1k.m
    trunk/octave-forge/main/queueing/inst/qnmmmk.m
    trunk/octave-forge/main/queueing/inst/qnvisits.m

Added Paths:
-----------
    trunk/octave-forge/main/queueing/inst/dtmc_bd.m

Removed Paths:
-------------
    trunk/octave-forge/main/queueing/inst/ctmc_bd_solve.m

Modified: trunk/octave-forge/main/queueing/ChangeLog
===================================================================
--- trunk/octave-forge/main/queueing/ChangeLog	2012-03-10 20:51:31 UTC (rev 9812)
+++ trunk/octave-forge/main/queueing/ChangeLog	2012-03-11 11:20:31 UTC (rev 9813)
@@ -1,6 +1,6 @@
 2012-02-XX Moreno Marzolla <mar...@cs...>
 
-	* Version 1.0.X released
+	* Version 1.X.0 released
 	* Fixed bug in qnvisits() which made the function behave incorrectly
 	  under particular degenerate cases.
 	* Fixed bug in ctmc_exps() (wrong initial value in call to lsode)
@@ -9,6 +9,10 @@
 	* Function ctmc_exps() and ctmc_taexps() accept a scalar as second
 	  argument; the old syntax is still supported, but may be deprecated
 	  in future releases.
+	* Function ctmc_bd() now returns the infinitesimal generator matrix
+	  of the birth-death process, not the steady-state solution.
+	* Function ctmc_bd_solve() has been removed
+	* New function dtmc_bd()
 	* Miscellaneous fixes/improvements to the documentation
 
 2012-02-04 Moreno Marzolla <mar...@cs...>

Modified: trunk/octave-forge/main/queueing/DESCRIPTION
===================================================================
--- trunk/octave-forge/main/queueing/DESCRIPTION	2012-03-10 20:51:31 UTC (rev 9812)
+++ trunk/octave-forge/main/queueing/DESCRIPTION	2012-03-11 11:20:31 UTC (rev 9813)
@@ -1,6 +1,6 @@
 Name: queueing
-Version: 1.0.0
-Date: 2012-02-04
+Version: 1.X.0
+Date: 2012-02-XX
 Author: Moreno Marzolla <mar...@cs...>
 Maintainer: Moreno Marzolla <mar...@cs...>
 Title: Queueing networks and Markov chains analysis package for GNU Octave

Modified: trunk/octave-forge/main/queueing/Makefile
===================================================================
--- trunk/octave-forge/main/queueing/Makefile	2012-03-10 20:51:31 UTC (rev 9812)
+++ trunk/octave-forge/main/queueing/Makefile	2012-03-11 11:20:31 UTC (rev 9813)
@@ -1,5 +1,5 @@
-VERSIONNUM=1.0.0
-VERSIONDATE="2012-02-04"
+VERSIONNUM=1.X.0
+VERSIONDATE="2012-02-XX"
 PROGNAME=queueing
 
 DISTNAME=$(PROGNAME)-$(VERSIONNUM)

Modified: trunk/octave-forge/main/queueing/NEWS
===================================================================
--- trunk/octave-forge/main/queueing/NEWS	2012-03-10 20:51:31 UTC (rev 9812)
+++ trunk/octave-forge/main/queueing/NEWS	2012-03-11 11:20:31 UTC (rev 9813)
@@ -1,4 +1,4 @@
-Summary of important user-visible changes for queueing-1.0.X
+Summary of important user-visible changes for queueing-1.X.0
 
 ** Function ctmc_exps() can now compute the expected sojourn time
    until absorption for absorming CTMC
@@ -7,6 +7,14 @@
    the second argument (time). The old syntax is still supported,
    but may be deprecated in the future.
 
+** Function ctmc_bd() now returns the infinitesimal generator matrix Q
+   of the birth-death process with given rates, not the steady-state
+   solution.
+
+** New function dtmc_bd() added
+
+** Function ctmc_bd_solve() has been removed
+
 Summary of important user-visible changes for queueing-1.0.0
 ------------------------------------------------------------------------------
 

Modified: trunk/octave-forge/main/queueing/doc/INSTALL
===================================================================
--- trunk/octave-forge/main/queueing/doc/INSTALL	2012-03-10 20:51:31 UTC (rev 9812)
+++ trunk/octave-forge/main/queueing/doc/INSTALL	2012-03-11 11:20:31 UTC (rev 9813)
@@ -16,7 +16,7 @@
 1.1 Installation through Octave package management system
 =========================================================
 
-The most recent version of `queueing' is 1.0.0 and can be downloaded
+The most recent version of `queueing' is 1.X.0 and can be downloaded
 from Octave-Forge
 
    `http://octave.sourceforge.net/queueing/'
@@ -37,13 +37,13 @@
      octave:1>pkg list queueing
      Package Name  | Version | Installation directory
      --------------+---------+-----------------------
-         queueing *|   1.0.0 | /home/moreno/octave/queueing-1.0.0
+         queueing *|   1.X.0 | /home/moreno/octave/queueing-1.X.0
 
    Alternatively, you can first download `queueing' from Octave-Forge;
 then, to install the package in the system-wide location issue this
 command at the Octave prompt:
 
-     octave:1> pkg install _queueing-1.0.0.tar.gz_
+     octave:1> pkg install _queueing-1.X.0.tar.gz_
 
 (you may need to start Octave as root in order to allow the
 installation to copy the files to the target locations). After this,
@@ -52,7 +52,7 @@
 
    If you do not have root access, you can do a local install using:
 
-     octave:1> pkg install -local queueing-1.0.0.tar.gz
+     octave:1> pkg install -local queueing-1.X.0.tar.gz
 
    This will install `queueing' within your home directory, and the
 package will be available to your user only. *Note:* Octave version
@@ -69,8 +69,8 @@
 If you want to manually install `queueing' in a custom location, you
 can download the tarball and unpack it somewhere:
 
-     tar xvfz queueing-1.0.0.tar.gz
-     cd queueing-1.0.0/queueing/
+     tar xvfz queueing-1.X.0.tar.gz
+     cd queueing-1.X.0/queueing/
 
    Copy all `.m' files from the `inst/' directory to some target
 location. Then, start Octave with the `-p' option to add the target

Modified: trunk/octave-forge/main/queueing/doc/markovchains.txi
===================================================================
--- trunk/octave-forge/main/queueing/doc/markovchains.txi	2012-03-10 20:51:31 UTC (rev 9812)
+++ trunk/octave-forge/main/queueing/doc/markovchains.txi	2012-03-11 11:20:31 UTC (rev 9813)
@@ -66,6 +66,9 @@
 @math{n}. @math{\pi_i(n)} denotes the probability that the system is
 in state @math{i} at step @math{n}.
 
+@c
+@subsection State occupancy probabilities
+
 Given the transition probability matrix @math{\bf P} and the initial
 state occupancy probability vector @math{{\bf \pi}(0) = (\pi_1(0),
 \pi_2(0), @dots{}, \pi_N(0))} at step 0, the state occupancy
@@ -91,6 +94,7 @@
 @math{{\bf \pi}(0)}. The stationary state occupancy probability vector
 @math{\bf \pi} satisfies @math{{\bf \pi} = {\bf \pi} {\bf P}}.
 
+@c
 @DOCSTRING(dtmc)
 
 @noindent @strong{EXAMPLE}
@@ -101,6 +105,13 @@
 @end group
 @end example
 
+@subsection Birth-Death process
+
+@c
+@DOCSTRING(dtmc_bd)
+
+@subsection First passage times
+
 The First Passage Time @math{M_{i j}} is defined as the average
 number of transitions needed to visit state @math{j} for the first
 time, starting from state @math{i}. Matrix @math{\bf M} satisfies the
@@ -123,6 +134,7 @@
 @end example
 @end ifnottex
 
+@c
 @DOCSTRING(dtmc_fpt)
 
 @c
@@ -132,16 +144,16 @@
 @section Continuous-Time Markov Chains
 
 @menu
-* CTMC Stationary Probability::
+* State occupancy probabilities::
 * Birth-Death process::
 * Expected Sojourn Time::
 * Time-Averaged Expected Sojourn Time::
 * Expected Time to Absorption::
-* CTMC First Passage Times::
+* First Passage Times::
 @end menu
 
-@node CTMC Stationary Probability
-@subsection Stationary Probability
+@node State occupancy probabilities
+@subsection State occupancy probabilities
 
 @DOCSTRING(ctmc)
 
@@ -305,7 +317,7 @@
 @c
 @c
 @c
-@node CTMC First Passage Times
+@node First Passage Times
 @subsection First Passage Times
 @DOCSTRING(ctmc_fpt)
 

Modified: trunk/octave-forge/main/queueing/doc/queueing.html
===================================================================
--- trunk/octave-forge/main/queueing/doc/queueing.html	2012-03-10 20:51:31 UTC (rev 9812)
+++ trunk/octave-forge/main/queueing/doc/queueing.html	2012-03-11 11:20:31 UTC (rev 9813)
@@ -55,14 +55,19 @@
 <li><a name="toc_Markov-Chains" href="#Markov-Chains">4 Markov Chains</a>
 <ul>
 <li><a href="#Discrete_002dTime-Markov-Chains">4.1 Discrete-Time Markov Chains</a>
+<ul>
+<li><a href="#Discrete_002dTime-Markov-Chains">4.1.1 State occupancy probabilities</a>
+<li><a href="#Discrete_002dTime-Markov-Chains">4.1.2 Birth-Death process</a>
+<li><a href="#Discrete_002dTime-Markov-Chains">4.1.3 First passage times</a>
+</li></ul>
 <li><a href="#Continuous_002dTime-Markov-Chains">4.2 Continuous-Time Markov Chains</a>
 <ul>
-<li><a href="#CTMC-Stationary-Probability">4.2.1 Stationary Probability</a>
+<li><a href="#State-occupancy-probabilities">4.2.1 State occupancy probabilities</a>
 <li><a href="#Birth_002dDeath-process">4.2.2 Birth-Death process</a>
 <li><a href="#Expected-Sojourn-Time">4.2.3 Expected Sojourn Time</a>
 <li><a href="#Time_002dAveraged-Expected-Sojourn-Time">4.2.4 Time-Averaged Expected Sojourn Time</a>
 <li><a href="#Expected-Time-to-Absorption">4.2.5 Expected Time to Absorption</a>
-<li><a href="#CTMC-First-Passage-Times">4.2.6 First Passage Times</a>
+<li><a href="#First-Passage-Times">4.2.6 First Passage Times</a>
 </li></ul>
 </li></ul>
 <li><a name="toc_Single-Station-Queueing-Systems" href="#Single-Station-Queueing-Systems">5 Single Station Queueing Systems</a>
@@ -121,7 +126,7 @@
 <h2 class="unnumbered">queueing</h2>
 
 <p>This manual documents how to install and run the Queueing Toolbox. 
-It corresponds to version 1.0.0 of the package.
+It corresponds to version 1.X.0 of the package.
 
 <!--  -->
 <ul class="menu">
@@ -189,8 +194,7 @@
      <li>Approximate MVA for closed, single-class networks with blocking
 (MVABLO algorithm by F. Akyildiz);
 
-     <li>Computation of Asymptotic Bounds, Balanced System Bounds
-and Geometric Bounds;
+     <li>Asymptotic Bounds, Balanced System Bounds and Geometric Bounds;
 
    </ul>
 
@@ -209,15 +213,15 @@
 <li>M/H_m/1 (Hyperexponential service time distribution)
 </ul>
 
-   <p>Functions for Markov chain analysis are also provided (discrete and
-continuous time Markov chains are supported):
+   <p>Functions for Markov chain analysis are also provided, for discrete-time
+chains (DTMC) or continuous-time chains (CTMC):
 
      <ul>
-<li>Birth-death process;
-<li>Computation of transient and steady-state occupancy probabilities;
-<li>Computation of mean time to absorption;
-<li>Computation of time-averages sojourn time. 
-<li>Computation of mean passage times
+<li>Birth-death process (DTMC and CTMC);
+<li>Transient and steady-state occupancy probabilities (DTMC and CTMC);
+<li>Mean time to absorption (CTMC);
+<li>Time-averaged sojourn times (CTMC);
+<li>First passage times (DTMC and CTMC).
 
    </ul>
 
@@ -308,7 +312,7 @@
 
 <h3 class="section">2.1 Installation through Octave package management system</h3>
 
-<p>The most recent version of <code>queueing</code> is 1.0.0 and can
+<p>The most recent version of <code>queueing</code> is 1.X.0 and can
 be downloaded from Octave-Forge
 
    <p><a href="http://octave.sourceforge.net/queueing/">http://octave.sourceforge.net/queueing/</a>
@@ -330,13 +334,13 @@
 <pre class="example">     octave:1&gt;<kbd>pkg list queueing</kbd>
      Package Name  | Version | Installation directory
      --------------+---------+-----------------------
-         queueing *|   1.0.0 | /home/moreno/octave/queueing-1.0.0
+         queueing *|   1.X.0 | /home/moreno/octave/queueing-1.X.0
 </pre>
    <p>Alternatively, you can first download <code>queueing</code> from
 Octave-Forge; then, to install the package in the system-wide
 location issue this command at the Octave prompt:
 
-<pre class="example">     octave:1&gt; <kbd>pkg install </kbd><em>queueing-1.0.0.tar.gz</em>
+<pre class="example">     octave:1&gt; <kbd>pkg install </kbd><em>queueing-1.X.0.tar.gz</em>
 </pre>
    <p class="noindent">(you may need to start Octave as root in order to allow the
 installation to copy the files to the target locations). After this,
@@ -345,7 +349,7 @@
 
    <p>If you do not have root access, you can do a local install using:
 
-<pre class="example">     octave:1&gt; <kbd>pkg install -local queueing-1.0.0.tar.gz</kbd>
+<pre class="example">     octave:1&gt; <kbd>pkg install -local queueing-1.X.0.tar.gz</kbd>
 </pre>
    <p>This will install <code>queueing</code> within your home directory, and the
 package will be available to your user only. <strong>Note:</strong> Octave
@@ -371,8 +375,8 @@
 <p>If you want to manually install <code>queueing</code> in a custom location,
 you can download the tarball and unpack it somewhere:
 
-<pre class="example">     <kbd>tar xvfz queueing-1.0.0.tar.gz</kbd>
-     <kbd>cd queueing-1.0.0/queueing/</kbd>
+<pre class="example">     <kbd>tar xvfz queueing-1.X.0.tar.gz</kbd>
+     <kbd>cd queueing-1.X.0/queueing/</kbd>
 </pre>
    <p>Copy all <code>.m</code> files from the <samp><span class="file">inst/</span></samp> directory to some
 target location. Then, start Octave with the <samp><span class="option">-p</span></samp> option to add
@@ -813,7 +817,9 @@
 n. \pi_i(n) denotes the probability that the system is
 in state i at step n.
 
-   <p>Given the transition probability matrix \bf P and the initial
+<h4 class="subsection">4.1.1 State occupancy probabilities</h4>
+
+<p>Given the transition probability matrix \bf P and the initial
 state occupancy probability vector \bf \pi(0) = (\pi_1(0),
 \pi_2(0), <small class="dots">...</small>, \pi_N(0)) at step 0, the state occupancy
 probability vector \bf \pi(n) at step n can be
@@ -889,7 +895,40 @@
             T, ss(2)*ones(size(T)), "r;Steady State;" );
       xlabel("Time Step");</pre>
 </pre>
-   <p>The First Passage Time M_i j is defined as the average
+   <h4 class="subsection">4.1.2 Birth-Death process</h4>
+
+<p><a name="doc_002ddtmc_005fbd"></a>
+
+<div class="defun">
+&mdash; Function File: <var>P</var> = <b>dtmc_bd</b> (<var>birth, death</var>)<var><a name="index-dtmc_005fbd-7"></a></var><br>
+<blockquote>
+        <p><a name="index-Markov-chain_002c-discrete-time-8"></a><a name="index-Birth_002ddeath-process-9"></a>
+Returns the N \times N transition probability matrix P
+for a birth-death process with given rates.
+
+        <p><strong>INPUTS</strong>
+
+          <dl>
+<dt><var>birth</var><dd>Vector with N-1 elements, where <var>birth</var><code>(i)</code> is the
+transition probability from state i to state i+1.
+
+          <br><dt><var>death</var><dd>Vector with N-1 elements, where <var>death</var><code>(i)</code> is the
+transition probability from state i+1 to state i.
+
+        </dl>
+
+        <p><strong>OUTPUTS</strong>
+
+          <dl>
+<dt><var>P</var><dd>Transition probability matrix for the birth-death process.
+
+        </dl>
+
+        </blockquote></div>
+
+<h4 class="subsection">4.1.3 First passage times</h4>
+
+<p>The First Passage Time M_i j is defined as the average
 number of transitions needed to visit state j for the first
 time, starting from state i. Matrix \bf M satisfies the
 property that
@@ -903,10 +942,10 @@
    <p><a name="doc_002ddtmc_005ffpt"></a>
 
 <div class="defun">
-&mdash; Function File: <var>M</var> = <b>dtmc_fpt</b> (<var>P</var>)<var><a name="index-dtmc_005ffpt-7"></a></var><br>
-&mdash; Function File: <var>m</var> = <b>dtmc_fpt</b> (<var>P, i, j</var>)<var><a name="index-dtmc_005ffpt-8"></a></var><br>
+&mdash; Function File: <var>M</var> = <b>dtmc_fpt</b> (<var>P</var>)<var><a name="index-dtmc_005ffpt-10"></a></var><br>
+&mdash; Function File: <var>m</var> = <b>dtmc_fpt</b> (<var>P, i, j</var>)<var><a name="index-dtmc_005ffpt-11"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-discrete-time-9"></a><a name="index-First-passage-times-10"></a>
+        <p><a name="index-Markov-chain_002c-discrete-time-12"></a><a name="index-First-passage-times-13"></a>
 If called with a single argument, computes the mean first passage
 times <var>M</var><code>(i,j)</code>, that are the average number of transitions before
 state <var>j</var> is reached, starting from state <var>i</var>, for all
@@ -956,31 +995,31 @@
 <h3 class="section">4.2 Continuous-Time Markov Chains</h3>
 
 <ul class="menu">
-<li><a accesskey="1" href="#CTMC-Stationary-Probability">CTMC Stationary Probability</a>
+<li><a accesskey="1" href="#State-occupancy-probabilities">State occupancy probabilities</a>
 <li><a accesskey="2" href="#Birth_002dDeath-process">Birth-Death process</a>
 <li><a accesskey="3" href="#Expected-Sojourn-Time">Expected Sojourn Time</a>
 <li><a accesskey="4" href="#Time_002dAveraged-Expected-Sojourn-Time">Time-Averaged Expected Sojourn Time</a>
 <li><a accesskey="5" href="#Expected-Time-to-Absorption">Expected Time to Absorption</a>
-<li><a accesskey="6" href="#CTMC-First-Passage-Times">CTMC First Passage Times</a>
+<li><a accesskey="6" href="#First-Passage-Times">First Passage Times</a>
 </ul>
 
 <div class="node">
-<a name="CTMC-Stationary-Probability"></a>
+<a name="State-occupancy-probabilities"></a>
 <p><hr>
 Next:&nbsp;<a rel="next" accesskey="n" href="#Birth_002dDeath-process">Birth-Death process</a>,
 Up:&nbsp;<a rel="up" accesskey="u" href="#Continuous_002dTime-Markov-Chains">Continuous-Time Markov Chains</a>
 
 </div>
 
-<h4 class="subsection">4.2.1 Stationary Probability</h4>
+<h4 class="subsection">4.2.1 State occupancy probabilities</h4>
 
 <p><a name="doc_002dctmc"></a>
 
 <div class="defun">
-&mdash; Function File: <var>p</var> = <b>ctmc</b> (<var>Q</var>)<var><a name="index-ctmc-11"></a></var><br>
-&mdash; Function File: <var>p</var> = <b>ctmc</b> (<var>Q, t. q0</var>)<var><a name="index-ctmc-12"></a></var><br>
+&mdash; Function File: <var>p</var> = <b>ctmc</b> (<var>Q</var>)<var><a name="index-ctmc-14"></a></var><br>
+&mdash; Function File: <var>p</var> = <b>ctmc</b> (<var>Q, t. q0</var>)<var><a name="index-ctmc-15"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-13"></a><a name="index-Continuous-time-Markov-chain-14"></a><a name="index-Markov-chain_002c-state-occupancy-probabilities-15"></a><a name="index-Stationary-probabilities-16"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-16"></a><a name="index-Continuous-time-Markov-chain-17"></a><a name="index-Markov-chain_002c-state-occupancy-probabilities-18"></a><a name="index-Stationary-probabilities-19"></a>
 With a single argument, compute the stationary state occupancy
 probability vector <var>p</var>(1), <small class="dots">...</small>, <var>p</var>(N) for a
 Continuous-Time Markov Chain with infinitesimal generator matrix
@@ -1033,7 +1072,7 @@
 <a name="Birth_002dDeath-process"></a>
 <p><hr>
 Next:&nbsp;<a rel="next" accesskey="n" href="#Expected-Sojourn-Time">Expected Sojourn Time</a>,
-Previous:&nbsp;<a rel="previous" accesskey="p" href="#CTMC-Stationary-Probability">CTMC Stationary Probability</a>,
+Previous:&nbsp;<a rel="previous" accesskey="p" href="#State-occupancy-probabilities">State occupancy probabilities</a>,
 Up:&nbsp;<a rel="up" accesskey="u" href="#Continuous_002dTime-Markov-Chains">Continuous-Time Markov Chains</a>
 
 </div>
@@ -1043,11 +1082,11 @@
 <p><a name="doc_002dctmc_005fbd"></a>
 
 <div class="defun">
-&mdash; Function File: <var>p</var> = <b>ctmc_bd</b> (<var>birth, death</var>)<var><a name="index-ctmc_005fbd-17"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>ctmc_bd</b> (<var>birth, death</var>)<var><a name="index-ctmc_005fbd-20"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-18"></a><a name="index-Birth_002ddeath-process-19"></a>
-Compute the steady-state solution of a birth-death process with state
-space (1, <small class="dots">...</small>, N).
+        <p><a name="index-Markov-chain_002c-continuous-time-21"></a><a name="index-Birth_002ddeath-process-22"></a>
+Returns the N \times N infinitesimal generator matrix Q
+for a birth-death process with given rates.
 
         <p><strong>INPUTS</strong>
 
@@ -1063,8 +1102,7 @@
         <p><strong>OUTPUTS</strong>
 
           <dl>
-<dt><var>p</var><dd><var>p</var><code>(i)</code> is the steady-state probability that the system is
-in state i, i=1, <small class="dots">...</small>, N.
+<dt><var>Q</var><dd>Infinitesimal generator matrix for the birth-death process.
 
         </dl>
 
@@ -1100,10 +1138,10 @@
    <p><a name="doc_002dctmc_005fexps"></a>
 
 <div class="defun">
-&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, t, p </var>)<var><a name="index-ctmc_005fexps-20"></a></var><br>
-&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fexps-21"></a></var><br>
+&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, t, p </var>)<var><a name="index-ctmc_005fexps-23"></a></var><br>
+&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fexps-24"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-22"></a><a name="index-Expected-sojourn-time-23"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-25"></a><a name="index-Expected-sojourn-time-26"></a>
 With three arguments, compute the expected times <var>L</var><code>(i)</code>
 spent in each state i during the time interval
 [0,t], assuming that the state occupancy probabilities
@@ -1130,9 +1168,9 @@
 
           <dl>
 <dt><var>L</var><dd>If this function is called with three arguments, <var>L</var><code>(i)</code> is
-the expected time spent in state j during the interval
+the expected time spent in state i during the interval
 [0,t]. If this function is called with two arguments
-<var>L</var><code>(i)</code> is the expected time spent in state i until
+<var>L</var><code>(i)</code> is either the expected time spent in state i until
 absorption (if i is a transient state), or zero
 (if <var>i</var> is an absorbing state).
 
@@ -1183,9 +1221,9 @@
 <p><a name="doc_002dctmc_005ftaexps"></a>
 
 <div class="defun">
-&mdash; Function File: <var>M</var> = <b>ctmc_taexps</b> (<var>Q, t, p</var>)<var><a name="index-ctmc_005ftaexps-24"></a></var><br>
+&mdash; Function File: <var>M</var> = <b>ctmc_taexps</b> (<var>Q, t, p</var>)<var><a name="index-ctmc_005ftaexps-27"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-25"></a><a name="index-Time_002dalveraged-sojourn-time-26"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-28"></a><a name="index-Time_002dalveraged-sojourn-time-29"></a>
 Compute the <em>time-averaged sojourn time</em> <var>M</var><code>(i)</code>,
 defined as the fraction of the time interval [0,t] spent in
 state i, assuming that the state occupancy probabilities at
@@ -1242,7 +1280,7 @@
    <div class="node">
 <a name="Expected-Time-to-Absorption"></a>
 <p><hr>
-Next:&nbsp;<a rel="next" accesskey="n" href="#CTMC-First-Passage-Times">CTMC First Passage Times</a>,
+Next:&nbsp;<a rel="next" accesskey="n" href="#First-Passage-Times">First Passage Times</a>,
 Previous:&nbsp;<a rel="previous" accesskey="p" href="#Time_002dAveraged-Expected-Sojourn-Time">Time-Averaged Expected Sojourn Time</a>,
 Up:&nbsp;<a rel="up" accesskey="u" href="#Continuous_002dTime-Markov-Chains">Continuous-Time Markov Chains</a>
 
@@ -1268,9 +1306,9 @@
    <p><a name="doc_002dctmc_005fmtta"></a>
 
 <div class="defun">
-&mdash; Function File: <var>t</var> = <b>ctmc_mtta</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fmtta-27"></a></var><br>
+&mdash; Function File: <var>t</var> = <b>ctmc_mtta</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fmtta-30"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-28"></a><a name="index-Mean-time-to-absorption-29"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-31"></a><a name="index-Mean-time-to-absorption-32"></a>
 Compute the Mean-Time to Absorption (MTTA) of the CTMC described by
 the infinitesimal generator matrix <var>Q</var>, starting from initial
 occupancy probabilities <var>p</var>. If there are no absorbing states, this
@@ -1331,9 +1369,9 @@
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998.
 
-   <p><a name="index-Bolch_002c-G_002e-30"></a><a name="index-Greiner_002c-S_002e-31"></a><a name="index-de-Meer_002c-H_002e-32"></a><a name="index-Trivedi_002c-K_002e-33"></a>
+   <p><a name="index-Bolch_002c-G_002e-33"></a><a name="index-Greiner_002c-S_002e-34"></a><a name="index-de-Meer_002c-H_002e-35"></a><a name="index-Trivedi_002c-K_002e-36"></a>
 <div class="node">
-<a name="CTMC-First-Passage-Times"></a>
+<a name="First-Passage-Times"></a>
 <p><hr>
 Previous:&nbsp;<a rel="previous" accesskey="p" href="#Expected-Time-to-Absorption">Expected Time to Absorption</a>,
 Up:&nbsp;<a rel="up" accesskey="u" href="#Continuous_002dTime-Markov-Chains">Continuous-Time Markov Chains</a>
@@ -1345,10 +1383,10 @@
 <p><a name="doc_002dctmc_005ffpt"></a>
 
 <div class="defun">
-&mdash; Function File: <var>M</var> = <b>ctmc_fpt</b> (<var>Q</var>)<var><a name="index-ctmc_005ffpt-34"></a></var><br>
-&mdash; Function File: <var>m</var> = <b>ctmc_fpt</b> (<var>Q, i, j</var>)<var><a name="index-ctmc_005ffpt-35"></a></var><br>
+&mdash; Function File: <var>M</var> = <b>ctmc_fpt</b> (<var>Q</var>)<var><a name="index-ctmc_005ffpt-37"></a></var><br>
+&mdash; Function File: <var>m</var> = <b>ctmc_fpt</b> (<var>Q, i, j</var>)<var><a name="index-ctmc_005ffpt-38"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-36"></a><a name="index-First-passage-times-37"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-39"></a><a name="index-First-passage-times-40"></a>
 If called with a single argument, computes the mean first passage
 times <var>M</var><code>(i,j)</code>, the average times before state <var>j</var> is
 reached, starting from state <var>i</var>, for all 1 \leq i, j \leq
@@ -1454,9 +1492,9 @@
    <p><a name="doc_002dqnmm1"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmm1</b> (<var>lambda, mu</var>)<var><a name="index-qnmm1-38"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmm1</b> (<var>lambda, mu</var>)<var><a name="index-qnmm1-41"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002f1_007d-system-39"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002f1_007d-system-42"></a>
 Compute utilization, response time, average number of requests
 and throughput for a M/M/1 queue.
 
@@ -1501,7 +1539,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.3.
 
-   <p><a name="index-Bolch_002c-G_002e-40"></a><a name="index-Greiner_002c-S_002e-41"></a><a name="index-de-Meer_002c-H_002e-42"></a><a name="index-Trivedi_002c-K_002e-43"></a>
+   <p><a name="index-Bolch_002c-G_002e-43"></a><a name="index-Greiner_002c-S_002e-44"></a><a name="index-de-Meer_002c-H_002e-45"></a><a name="index-Trivedi_002c-K_002e-46"></a>
 <!-- M/M/m -->
 <div class="node">
 <a name="The-M%2fM%2fm-System"></a>
@@ -1527,10 +1565,10 @@
    <p><a name="doc_002dqnmmm"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu</var>)<var><a name="index-qnmmm-44"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu, m</var>)<var><a name="index-qnmmm-45"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu</var>)<var><a name="index-qnmmm-47"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu, m</var>)<var><a name="index-qnmmm-48"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002fm_007d-system-46"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002fm_007d-system-49"></a>
 Compute utilization, response time, average number of requests in
 service and throughput for a M/M/m queue, a queueing
 system with m identical service centers connected to a single queue.
@@ -1582,7 +1620,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.5.
 
-   <p><a name="index-Bolch_002c-G_002e-47"></a><a name="index-Greiner_002c-S_002e-48"></a><a name="index-de-Meer_002c-H_002e-49"></a><a name="index-Trivedi_002c-K_002e-50"></a>
+   <p><a name="index-Bolch_002c-G_002e-50"></a><a name="index-Greiner_002c-S_002e-51"></a><a name="index-de-Meer_002c-H_002e-52"></a><a name="index-Trivedi_002c-K_002e-53"></a>
 <!-- M/M/inf -->
 <div class="node">
 <a name="The-M%2fM%2finf-System"></a>
@@ -1605,7 +1643,7 @@
    <p><a name="doc_002dqnmminf"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmminf</b> (<var>lambda, mu</var>)<var><a name="index-qnmminf-51"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmminf</b> (<var>lambda, mu</var>)<var><a name="index-qnmminf-54"></a></var><br>
 <blockquote>
         <p>Compute utilization, response time, average number of requests and
 throughput for a M/M/\infty queue. This is a system with an
@@ -1613,7 +1651,7 @@
 system is always stable, regardless the values of the arrival and
 service rates.
 
-        <p><a name="index-g_t_0040math_007bM_002fM_002f_007dinf-system-52"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002f_007dinf-system-55"></a>
 
         <p><strong>INPUTS</strong>
 
@@ -1631,7 +1669,7 @@
 different from the utilization, which in the case of M/M/\infty
 centers is always zero.
 
-          <p><a name="index-traffic-intensity-53"></a>
+          <p><a name="index-traffic-intensity-56"></a>
 <br><dt><var>R</var><dd>Service center response time.
 
           <br><dt><var>Q</var><dd>Average number of requests in the system (which is equal to the
@@ -1659,7 +1697,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.4.
 
-   <p><a name="index-Bolch_002c-G_002e-54"></a><a name="index-Greiner_002c-S_002e-55"></a><a name="index-de-Meer_002c-H_002e-56"></a><a name="index-Trivedi_002c-K_002e-57"></a>
+   <p><a name="index-Bolch_002c-G_002e-57"></a><a name="index-Greiner_002c-S_002e-58"></a><a name="index-de-Meer_002c-H_002e-59"></a><a name="index-Trivedi_002c-K_002e-60"></a>
 <!-- M/M/1/k -->
 <div class="node">
 <a name="The-M%2fM%2f1%2fK-System"></a>
@@ -1683,9 +1721,9 @@
    <p><a name="doc_002dqnmm1k"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmm1k</b> (<var>lambda, mu, K</var>)<var><a name="index-qnmm1k-58"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmm1k</b> (<var>lambda, mu, K</var>)<var><a name="index-qnmm1k-61"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002f1_002fK_007d-system-59"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002f1_002fK_007d-system-62"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/M/1/K finite capacity system. In a
 M/M/1/K queue there is a single server; the maximum number of
@@ -1752,9 +1790,9 @@
    <p><a name="doc_002dqnmmmk"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmmmk</b> (<var>lambda, mu, m, K</var>)<var><a name="index-qnmmmk-60"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmmmk</b> (<var>lambda, mu, m, K</var>)<var><a name="index-qnmmmk-63"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002fm_002fK_007d-system-61"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002fm_002fK_007d-system-64"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/M/m/K finite capacity system. In a
 M/M/m/K system there are m \geq 1 identical service
@@ -1812,7 +1850,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.6.
 
-   <p><a name="index-Bolch_002c-G_002e-62"></a><a name="index-Greiner_002c-S_002e-63"></a><a name="index-de-Meer_002c-H_002e-64"></a><a name="index-Trivedi_002c-K_002e-65"></a>
+   <p><a name="index-Bolch_002c-G_002e-65"></a><a name="index-Greiner_002c-S_002e-66"></a><a name="index-de-Meer_002c-H_002e-67"></a><a name="index-Trivedi_002c-K_002e-68"></a>
 
 <!-- Approximate M/M/m -->
 <div class="node">
@@ -1834,9 +1872,9 @@
    <p><a name="doc_002dqnammm"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnammm</b> (<var>lambda, mu</var>)<var><a name="index-qnammm-66"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnammm</b> (<var>lambda, mu</var>)<var><a name="index-qnammm-69"></a></var><br>
 <blockquote>
-        <p><a name="index-Asymmetric-_0040math_007bM_002fM_002fm_007d-system-67"></a>
+        <p><a name="index-Asymmetric-_0040math_007bM_002fM_002fm_007d-system-70"></a>
 Compute <em>approximate</em> utilization, response time, average number
 of requests in service and throughput for an asymmetric  M/M/m
 queue. In this system there are m different service centers
@@ -1883,7 +1921,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998
 
-   <p><a name="index-Bolch_002c-G_002e-68"></a><a name="index-Greiner_002c-S_002e-69"></a><a name="index-de-Meer_002c-H_002e-70"></a><a name="index-Trivedi_002c-K_002e-71"></a>
+   <p><a name="index-Bolch_002c-G_002e-71"></a><a name="index-Greiner_002c-S_002e-72"></a><a name="index-de-Meer_002c-H_002e-73"></a><a name="index-Trivedi_002c-K_002e-74"></a>
 <div class="node">
 <a name="The-M%2fG%2f1-System"></a>
 <a name="The-M_002fG_002f1-System"></a>
@@ -1899,9 +1937,9 @@
 <p><a name="doc_002dqnmg1"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmg1</b> (<var>lambda, xavg, x2nd</var>)<var><a name="index-qnmg1-72"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmg1</b> (<var>lambda, xavg, x2nd</var>)<var><a name="index-qnmg1-75"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fG_002f1_007d-system-73"></a>
+        <p><a name="index-g_t_0040math_007bM_002fG_002f1_007d-system-76"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/G/1 system. The service time distribution
 is described by its mean <var>xavg</var>, and by its second moment
@@ -1958,9 +1996,9 @@
 <p><a name="doc_002dqnmh1"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmh1</b> (<var>lambda, mu, alpha</var>)<var><a name="index-qnmh1-74"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmh1</b> (<var>lambda, mu, alpha</var>)<var><a name="index-qnmh1-77"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fH_005fm_002f1_007d-system-75"></a>
+        <p><a name="index-g_t_0040math_007bM_002fH_005fm_002f1_007d-system-78"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/H_m/1 system. In this system, the customer
 service times have hyper-exponential distribution:
@@ -2042,7 +2080,7 @@
 <li><a accesskey="6" href="#Utility-functions">Utility functions</a>:                    Utility functions to compute miscellaneous quantities
 </ul>
 
-<p><a name="index-queueing-networks-76"></a>
+<p><a name="index-queueing-networks-79"></a>
 <!-- INTRODUCTION -->
 <div class="node">
 <a name="Introduction-to-QNs"></a>
@@ -2303,13 +2341,13 @@
    <p><a name="doc_002dqnmknode"></a>
 
 <div class="defun">
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S</var>)<var><a name="index-qnmknode-77"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S, m</var>)<var><a name="index-qnmknode-78"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/1-lcfs-pr", S</var>)<var><a name="index-qnmknode-79"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S</var>)<var><a name="index-qnmknode-80"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S, s2</var>)<var><a name="index-qnmknode-81"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S</var>)<var><a name="index-qnmknode-82"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S, s2</var>)<var><a name="index-qnmknode-83"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S</var>)<var><a name="index-qnmknode-80"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S, m</var>)<var><a name="index-qnmknode-81"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/1-lcfs-pr", S</var>)<var><a name="index-qnmknode-82"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S</var>)<var><a name="index-qnmknode-83"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S, s2</var>)<var><a name="index-qnmknode-84"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S</var>)<var><a name="index-qnmknode-85"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S, s2</var>)<var><a name="index-qnmknode-86"></a></var><br>
 <blockquote>
         <p>Creates a node; this function can be used together with
 <code>qnsolve</code>. It is possible to create either single-class nodes
@@ -2378,10 +2416,10 @@
    <p><a name="doc_002dqnsolve"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V</var>)<var><a name="index-qnsolve-84"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V, Z</var>)<var><a name="index-qnsolve-85"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"open", lambda, QQ, V</var>)<var><a name="index-qnsolve-86"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"mixed", lambda, N, QQ, V</var>)<var><a name="index-qnsolve-87"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V</var>)<var><a name="index-qnsolve-87"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V, Z</var>)<var><a name="index-qnsolve-88"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"open", lambda, QQ, V</var>)<var><a name="index-qnsolve-89"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"mixed", lambda, N, QQ, V</var>)<var><a name="index-qnsolve-90"></a></var><br>
 <blockquote>
         <p>General evaluator of QN models. Networks can be open,
 closed or mixed; single as well as multiclass networks are supported.
@@ -2559,11 +2597,11 @@
    <p><a name="doc_002dqnjackson"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P </var>)<var><a name="index-qnjackson-88"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P, m </var>)<var><a name="index-qnjackson-89"></a></var><br>
-&mdash; Function File: <var>pr</var> = <b>qnjackson</b> (<var>lambda, S, P, m, k</var>)<var><a name="index-qnjackson-90"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P </var>)<var><a name="index-qnjackson-91"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P, m </var>)<var><a name="index-qnjackson-92"></a></var><br>
+&mdash; Function File: <var>pr</var> = <b>qnjackson</b> (<var>lambda, S, P, m, k</var>)<var><a name="index-qnjackson-93"></a></var><br>
 <blockquote>
-        <p><a name="index-open-network_002c-single-class-91"></a><a name="index-Jackson-network-92"></a>
+        <p><a name="index-open-network_002c-single-class-94"></a><a name="index-Jackson-network-95"></a>
 With three or four input parameters, this function computes the
 steady-state occupancy probabilities for a Jackson network. With five
 input parameters, this function computes the steady-state probability
@@ -2645,7 +2683,7 @@
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998, pp. 284&ndash;287.
 
-   <p><a name="index-Bolch_002c-G_002e-93"></a><a name="index-Greiner_002c-S_002e-94"></a><a name="index-de-Meer_002c-H_002e-95"></a><a name="index-Trivedi_002c-K_002e-96"></a>
+   <p><a name="index-Bolch_002c-G_002e-96"></a><a name="index-Greiner_002c-S_002e-97"></a><a name="index-de-Meer_002c-H_002e-98"></a><a name="index-Trivedi_002c-K_002e-99"></a>
 
 <h4 class="subsection">6.3.2 The Convolution Algorithm</h4>
 
@@ -2679,10 +2717,10 @@
    <p><a name="doc_002dqnconvolution"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V</var>)<var><a name="index-qnconvolution-97"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V, m</var>)<var><a name="index-qnconvolution-98"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V</var>)<var><a name="index-qnconvolution-100"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V, m</var>)<var><a name="index-qnconvolution-101"></a></var><br>
 <blockquote>
-        <p><a name="index-closed-network-99"></a><a name="index-normalization-constant-100"></a><a name="index-convolution-algorithm-101"></a>
+        <p><a name="index-closed-network-102"></a><a name="index-normalization-constant-103"></a><a name="index-convolution-algorithm-104"></a>
 This function implements the <em>convolution algorithm</em> for
 computing steady-state performance measures of product-form,
 single-class closed queueing networks. Load-independent service
@@ -2773,20 +2811,20 @@
 16, number 9, september 1973,
 pp. 527&ndash;531. <a href="http://doi.acm.org/10.1145/362342.362345">http://doi.acm.org/10.1145/362342.362345</a>
 
-   <p><a name="index-Buzen_002c-J_002e-P_002e-102"></a>
+   <p><a name="index-Buzen_002c-J_002e-P_002e-105"></a>
 This implementation is based on G. Bolch, S. Greiner, H. de Meer and
 K. Trivedi, <cite>Queueing Networks and Markov Chains: Modeling and
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998, pp. 313&ndash;317.
 
-   <p><a name="index-Bolch_002c-G_002e-103"></a><a name="index-Greiner_002c-S_002e-104"></a><a name="index-de-Meer_002c-H_002e-105"></a><a name="index-Trivedi_002c-K_002e-106"></a>
+   <p><a name="index-Bolch_002c-G_002e-106"></a><a name="index-Greiner_002c-S_002e-107"></a><a name="index-de-Meer_002c-H_002e-108"></a><a name="index-Trivedi_002c-K_002e-109"></a>
 <!-- Convolution for load-dependent service centers -->
 <a name="doc_002dqnconvolutionld"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolutionld</b> (<var>N, S, V</var>)<var><a name="index-qnconvolutionld-107"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolutionld</b> (<var>N, S, V</var>)<var><a name="index-qnconvolutionld-110"></a></var><br>
 <blockquote>
-        <p><a name="index-closed-network-108"></a><a name="index-normalization-constant-109"></a><a name="index-convolution-algorithm-110"></a><a name="index-load_002ddependent-service-center-111"></a>
+        <p><a name="index-closed-network-111"></a><a name="index-normalization-constant-112"></a><a name="index-convolution-algorithm-113"></a><a name="index-load_002ddependent-service-center-114"></a>
 This function implements the <em>convolution algorithm</em> for
 product-form, single-class closed queueing networks with general
 load-dependent service centers.
@@ -2846,7 +2884,7 @@
 Purdue University, feb, 1981 (revised). 
 <a href="http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-354.pdf">http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-354.pdf</a>
 
-   <p><a name="index-Schwetman_002c-H_002e-112"></a>
+   <p><a name="index-Schwetman_002c-H_002e-115"></a>
 M. Reiser, H. Kobayashi, <cite>On The Convolution Algorithm for
 Separable Queueing Networks</cite>, In Proceedings of the 1976 ACM
 SIGMETRICS Conference on Computer Performance Modeling Measurement and
@@ -2854,7 +2892,7 @@
 1976). SIGMETRICS '76. ACM, New York, NY,
 pp. 109&ndash;117. <a href="http://doi.acm.org/10.1145/800200.806187">http://doi.acm.org/10.1145/800200.806187</a>
 
-   <p><a name="index-Reiser_002c-M_002e-113"></a><a name="index-Kobayashi_002c-H_002e-114"></a>
+   <p><a name="index-Reiser_002c-M_002e-116"></a><a name="index-Kobayashi_002c-H_002e-117"></a>
 This implementation is based on G. Bolch, S. Greiner, H. de Meer and
 K. Trivedi, <cite>Queueing Networks and Markov Chains: Modeling and
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
@@ -2866,7 +2904,7 @@
 function f_i defined in Schwetman, <code>Some Computational
 Aspects of Queueing Network Models</code>.
 
-   <p><a name="index-Bolch_002c-G_002e-115"></a><a name="index-Greiner_002c-S_002e-116"></a><a name="index-de-Meer_002c-H_002e-117"></a><a name="index-Trivedi_002c-K_002e-118"></a>
+   <p><a name="index-Bolch_002c-G_002e-118"></a><a name="index-Greiner_002c-S_002e-119"></a><a name="index-de-Meer_002c-H_002e-120"></a><a name="index-Trivedi_002c-K_002e-121"></a>
 
 <h4 class="subsection">6.3.3 Open networks</h4>
 
@@ -2874,10 +2912,10 @@
 <p><a name="doc_002dqnopensingle"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V</var>)<var><a name="index-qnopensingle-119"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopensingle-120"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V</var>)<var><a name="index-qnopensingle-122"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopensingle-123"></a></var><br>
 <blockquote>
-        <p><a name="index-open-network_002c-single-class-121"></a><a name="index-BCMP-network-122"></a>
+        <p><a name="index-open-network_002c-single-class-124"></a><a name="index-BCMP-network-125"></a>
 Analyze open, single class BCMP queueing networks.
 
         <p>This function works for a subset of BCMP single-class open networks
@@ -2970,16 +3008,16 @@
 Networks and Markov Chains: Modeling and Performance Evaluation with
 Computer Science Applications</cite>, Wiley, 1998.
 
-   <p><a name="index-Bolch_002c-G_002e-123"></a><a name="index-Greiner_002c-S_002e-124"></a><a name="index-de-Meer_002c-H_002e-125"></a><a name="index-Trivedi_002c-K_002e-126"></a>
+   <p><a name="index-Bolch_002c-G_002e-126"></a><a name="index-Greiner_002c-S_002e-127"></a><a name="index-de-Meer_002c-H_002e-128"></a><a name="index-Trivedi_002c-K_002e-129"></a>
 
 <!-- Open network with multiple classes -->
    <p><a name="doc_002dqnopenmulti"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V</var>)<var><a name="index-qnopenmulti-127"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopenmulti-128"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V</var>)<var><a name="index-qnopenmulti-130"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopenmulti-131"></a></var><br>
 <blockquote>
-        <p><a name="index-open-network_002c-multiple-classes-129"></a>
+        <p><a name="index-open-network_002c-multiple-classes-132"></a>
 Exact analysis of open, multiple-class BCMP networks. The network can
 be made of <em>single-server</em> queueing centers (FCFS, LCFS-PR or
 PS) or delay centers (IS). This function assumes a network with
@@ -3044,7 +3082,7 @@
 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In
 particular, see section 7.4.1 ("Open Model Solution Techniques").
 
-   <p><a name="index-Lazowska_002c-E_002e-D_002e-130"></a><a name="index-Zahorjan_002c-J_002e-131"></a><a name="index-Graham_002c-G_002e-S_002e-132"></a><a name="index-Sevcik_002c-K_002e-C_002e-133"></a>
+   <p><a name="index-Lazowska_002c-E_002e-D_002e-133"></a><a name="index-Zahorjan_002c-J_002e-134"></a><a name="index-Graham_002c-G_002e-S_002e-135"></a><a name="index-Sevcik_002c-K_002e-C_002e-136"></a>
 
 <h4 class="subsection">6.3.4 Closed Networks</h4>
 
@@ -3052,11 +3090,11 @@
 <p><a name="doc_002dqnclosedsinglemva"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemva-134"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemva-135"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemva-136"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemva-137"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemva-138"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemva-139"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-137"></a><a name="index-closed-network_002c-single-class-138"></a><a name="index-normalization-constant-139"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-140"></a><a name="index-closed-network_002c-single-class-141"></a><a name="index-normalization-constant-142"></a>
 Analyze closed, single class queueing networks using the exact Mean
 Value Analysis (MVA) algorithm. The following queueing disciplines
 are supported: FCFS, LCFS-PR, PS and IS (Infinite Server). This
@@ -3157,7 +3195,7 @@
 Multichain Queuing Networks</cite>, Journal of the ACM, vol. 27, n. 2, April
 1980, pp. 313&ndash;322. <a href="http://doi.acm.org/10.1145/322186.322195">http://doi.acm.org/10.1145/322186.322195</a>
 
-   <p><a name="index-Reiser_002c-M_002e-140"></a><a name="index-Lavenberg_002c-S_002e-S_002e-141"></a>
+   <p><a name="index-Reiser_002c-M_002e-143"></a><a name="index-Lavenberg_002c-S_002e-S_002e-144"></a>
 This implementation is described in R. Jain , <cite>The Art of Computer
 Systems Performance Analysis</cite>, Wiley, 1991, p. 577.  Multi-server nodes
 <!-- and the computation of @math{G(N)}, -->
@@ -3166,15 +3204,15 @@
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998, Section 8.2.1, "Single Class Queueing Networks".
 
-   <p><a name="index-Jain_002c-R_002e-142"></a><a name="index-Bolch_002c-G_002e-143"></a><a name="index-Greiner_002c-S_002e-144"></a><a name="index-de-Meer_002c-H_002e-145"></a><a name="index-Trivedi_002c-K_002e-146"></a>
+   <p><a name="index-Jain_002c-R_002e-145"></a><a name="index-Bolch_002c-G_002e-146"></a><a name="index-Greiner_002c-S_002e-147"></a><a name="index-de-Meer_002c-H_002e-148"></a><a name="index-Trivedi_002c-K_002e-149"></a>
 <!-- MVA for single class, closed networks with load dependent servers -->
 <a name="doc_002dqnclosedsinglemvald"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvald-147"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V, Z</var>)<var><a name="index-qnclosedsinglemvald-148"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvald-150"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V, Z</var>)<var><a name="index-qnclosedsinglemvald-151"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-149"></a><a name="index-closed-network_002c-single-class-150"></a><a name="index-load_002ddependent-service-center-151"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-152"></a><a name="index-closed-network_002c-single-class-153"></a><a name="index-load_002ddependent-service-center-154"></a>
 Exact MVA algorithm for closed, single class queueing networks
 with load-dependent service centers. This function supports
 FCFS, LCFS-PR, PS and IS nodes. For networks with only fixed-rate
@@ -3232,15 +3270,15 @@
 1998, Section 8.2.4.1, &ldquo;Networks with Load-Deèpendent Service: Closed
 Networks&rdquo;.
 
-   <p><a name="index-Bolch_002c-G_002e-152"></a><a name="index-Greiner_002c-S_002e-153"></a><a name="index-de-Meer_002c-H_002e-154"></a><a name="index-Trivedi_002c-K_002e-155"></a>
+   <p><a name="index-Bolch_002c-G_002e-155"></a><a name="index-Greiner_002c-S_002e-156"></a><a name="index-de-Meer_002c-H_002e-157"></a><a name="index-Trivedi_002c-K_002e-158"></a>
 <!-- CMVA for single class, closed networks with a single load dependent servers -->
 <a name="doc_002dqncmva"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V</var>)<var><a name="index-qncmva-156"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V, Z</var>)<var><a name="index-qncmva-157"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V</var>)<var><a name="index-qncmva-159"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V, Z</var>)<var><a name="index-qncmva-160"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-158"></a><a name="index-CMVA-159"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-161"></a><a name="index-CMVA-162"></a>
 Implementation of the Conditional MVA (CMVA) algorithm, a numerically
 stable variant of MVA for load-dependent servers. CMVA is described
 in G. Casale, <cite>A Note on Stable Flow-Equivalent Aggregation in
@@ -3294,19 +3332,19 @@
 closed networks</cite>. Queueing Syst. Theory Appl., 60:193–202, December
 2008.
 
-   <p><a name="index-Casale_002c-G_002e-160"></a>
+   <p><a name="index-Casale_002c-G_002e-163"></a>
 <!-- Approximate MVA for single class, closed networks -->
 
    <p><a name="doc_002dqnclosedsinglemvaapprox"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvaapprox-161"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemvaapprox-162"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemvaapprox-163"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedsinglemvaapprox-164"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedsinglemvaapprox-165"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvaapprox-164"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemvaapprox-165"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemvaapprox-166"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedsinglemvaapprox-167"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedsinglemvaapprox-168"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-166"></a><a name="index-Approximate-MVA-167"></a><a name="index-Closed-network_002c-single-class-168"></a><a name="index-Closed-network_002c-approximate-analysis-169"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-169"></a><a name="index-Approximate-MVA-170"></a><a name="index-Closed-n...
 
[truncated message content]

[Octave-cvsupdate] SF.net SVN: octave:[9812] trunk/octave-forge/main/queueing/doc

From: <mma...@us...> - 2012-03-10 20:51:37

Revision: 9812
          http://octave.svn.sourceforge.net/octave/?rev=9812&view=rev
Author:   mmarzolla
Date:     2012-03-10 20:51:31 +0000 (Sat, 10 Mar 2012)
Log Message:
-----------
updated documentation

Modified Paths:
--------------
    trunk/octave-forge/main/queueing/doc/queueing.html
    trunk/octave-forge/main/queueing/doc/queueing.pdf

Modified: trunk/octave-forge/main/queueing/doc/queueing.html
===================================================================
--- trunk/octave-forge/main/queueing/doc/queueing.html	2012-03-10 20:27:25 UTC (rev 9811)
+++ trunk/octave-forge/main/queueing/doc/queueing.html	2012-03-10 20:51:31 UTC (rev 9812)
@@ -1154,13 +1154,16 @@
       death = zeros(1,N-1);
       Q = diag(birth,1)+diag(death,-1);
       Q -= diag(sum(Q,2));
-      tt = linspace(0,10,100);
+      t = linspace(0,10,100);
       p0 = zeros(1,N); p0(1)=1;
-      L = ctmc_exps(Q,tt,p0);
-      plot( tt, L(:,1), ";State 1;", "linewidth", 2, \
-            tt, L(:,2), ";State 2;", "linewidth", 2, \
-            tt, L(:,3), ";State 3;", "linewidth", 2, \
-            tt, L(:,4), ";State 4 (absorbing);", "linewidth", 2);
+      L = zeros(length(t),N);
+      for i=1:length(t)
+        L(i,:) = ctmc_exps(Q,t(i),p0);
+      endfor
+      plot( t, L(:,1), ";State 1;", "linewidth", 2, \
+            t, L(:,2), ";State 2;", "linewidth", 2, \
+            t, L(:,3), ";State 3;", "linewidth", 2, \
+            t, L(:,4), ";State 4;", "linewidth", 2 );
       legend("location","northwest");
       xlabel("Time");
       ylabel("Expected sojourn time");</pre>
@@ -1222,9 +1225,12 @@
       death = zeros(1,N-1);
       Q = diag(birth,1)+diag(death,-1);
       Q -= diag(sum(Q,2));
-      t = linspace(1e-3,50,500);
+      t = linspace(1e-5,30,100);
       p = zeros(1,N); p(1)=1;
-      M = ctmc_taexps(Q,t,p);
+      M = zeros(length(t),N);
+      for i=1:length(t)
+        M(i,:) = ctmc_taexps(Q,t(i),p);
+      endfor
       plot(t, M(:,1), ";State 1;", "linewidth", 2, \
            t, M(:,2), ";State 2;", "linewidth", 2, \
            t, M(:,3), ";State 3;", "linewidth", 2, \
@@ -1316,7 +1322,7 @@
       death = [ 3 4 5 ] * mu;
       Q = diag(death,-1);
       Q -= diag(sum(Q,2));
-      t = ctmc_mtta(Q,[0 0 0 1])</pre>    &rArr; t = 78.333
+      [t L] = ctmc_mtta(Q,[0 0 0 1])</pre>    &rArr; t = 78.333
 </pre>
    <p class="noindent"><strong>REFERENCES</strong>
 

Modified: trunk/octave-forge/main/queueing/doc/queueing.pdf
===================================================================
(Binary files differ)

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[Octave-cvsupdate] SF.net SVN: octave:[9811] trunk/octave-forge/main/queueing

From: <mma...@us...> - 2012-03-10 20:27:32

Revision: 9811
          http://octave.svn.sourceforge.net/octave/?rev=9811&view=rev
Author:   mmarzolla
Date:     2012-03-10 20:27:25 +0000 (Sat, 10 Mar 2012)
Log Message:
-----------
New signature for ctmc_exps() and ctmc_taexps()

Modified Paths:
--------------
    trunk/octave-forge/main/queueing/ChangeLog
    trunk/octave-forge/main/queueing/NEWS
    trunk/octave-forge/main/queueing/doc/queueing.html
    trunk/octave-forge/main/queueing/doc/queueing.pdf
    trunk/octave-forge/main/queueing/inst/ctmc_exps.m
    trunk/octave-forge/main/queueing/inst/ctmc_mtta.m
    trunk/octave-forge/main/queueing/inst/ctmc_taexps.m

Modified: trunk/octave-forge/main/queueing/ChangeLog
===================================================================
--- trunk/octave-forge/main/queueing/ChangeLog	2012-03-10 19:46:27 UTC (rev 9810)
+++ trunk/octave-forge/main/queueing/ChangeLog	2012-03-10 20:27:25 UTC (rev 9811)
@@ -6,6 +6,9 @@
 	* Fixed bug in ctmc_exps() (wrong initial value in call to lsode)
 	* Function ctmc_exps() can now also compute the expected sojourn time
 	  until absorption for absorbing CTMCs.
+	* Function ctmc_exps() and ctmc_taexps() accept a scalar as second
+	  argument; the old syntax is still supported, but may be deprecated
+	  in future releases.
 	* Miscellaneous fixes/improvements to the documentation
 
 2012-02-04 Moreno Marzolla <mar...@cs...>

Modified: trunk/octave-forge/main/queueing/NEWS
===================================================================
--- trunk/octave-forge/main/queueing/NEWS	2012-03-10 19:46:27 UTC (rev 9810)
+++ trunk/octave-forge/main/queueing/NEWS	2012-03-10 20:27:25 UTC (rev 9811)
@@ -3,6 +3,10 @@
 ** Function ctmc_exps() can now compute the expected sojourn time
    until absorption for absorming CTMC
 
+** Functions ctmc_exps() and ctmc_taexps() now accept a scalar as
+   the second argument (time). The old syntax is still supported,
+   but may be deprecated in the future.
+
 Summary of important user-visible changes for queueing-1.0.0
 ------------------------------------------------------------------------------
 

Modified: trunk/octave-forge/main/queueing/doc/queueing.html
===================================================================
--- trunk/octave-forge/main/queueing/doc/queueing.html	2012-03-10 19:46:27 UTC (rev 9810)
+++ trunk/octave-forge/main/queueing/doc/queueing.html	2012-03-10 20:27:25 UTC (rev 9811)
@@ -1100,15 +1100,15 @@
    <p><a name="doc_002dctmc_005fexps"></a>
 
 <div class="defun">
-&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, tt, p </var>)<var><a name="index-ctmc_005fexps-20"></a></var><br>
+&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, t, p </var>)<var><a name="index-ctmc_005fexps-20"></a></var><br>
 &mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fexps-21"></a></var><br>
 <blockquote>
         <p><a name="index-Markov-chain_002c-continuous-time-22"></a><a name="index-Expected-sojourn-time-23"></a>
-With three arguments, compute the expected time <var>L</var><code>(t,j)</code>
-spent in each state j during the time interval
-<code>[0,</code><var>tt</var><code>(t))</code>, assuming that at time 0 the state occupancy
-probability was <var>p</var>. With two arguments, compute the expected
-time <var>L</var><code>(j)</code> spent in each state j until absorption.
+With three arguments, compute the expected times <var>L</var><code>(i)</code>
+spent in each state i during the time interval
+[0,t], assuming that the state occupancy probabilities
+at time 0 are <var>p</var>. With two arguments, compute the expected time
+<var>L</var><code>(i)</code> spent in each state i until absorption.
 
         <p><strong>INPUTS</strong>
 
@@ -1118,10 +1118,7 @@
 &le; i \neq j &le; N. The matrix <var>Q</var> must also satisfy the
 condition \sum_j=1^N Q_ij = 0.
 
-          <br><dt><var>tt</var><dd>This parameter is a vector used for numerical integration. The first
-element <var>tt</var><code>(1)</code> must be 0, and the last element
-<var>tt</var><code>(end)</code> must be the upper bound of the interval
-[0,t) of interest (<var>tt</var><code>(end) == t</code>).
+          <br><dt><var>t</var><dd>Time
 
           <br><dt><var>p</var><dd>Initial occupancy probability vector; <var>p</var><code>(i)</code> is the
 probability the system is in state i at time 0, i = 1,
@@ -1132,14 +1129,12 @@
         <p><strong>OUTPUTS</strong>
 
           <dl>
-<dt><var>L</var><dd>If this function is called with three arguments, <var>L</var> is a matrix
-of size <code>[length(</code><var>tt</var><code>), N]</code> where <var>L</var><code>(t,j)</code> is the
-expected time spent in state j during the interval
-<code>[0,</code><var>tt</var><code>(t)]</code>. If this function is called with two
-arguments, <var>L</var> is a vector with N elements where
-<var>L</var><code>(j)</code> is the expected time spent in state j until
-absorption, if j is a transient state. If j
-is an absorbing state, <var>L</var><code>(j) = 0</code>.
+<dt><var>L</var><dd>If this function is called with three arguments, <var>L</var><code>(i)</code> is
+the expected time spent in state j during the interval
+[0,t]. If this function is called with two arguments
+<var>L</var><code>(i)</code> is the expected time spent in state i until
+absorption (if i is a transient state), or zero
+(if <var>i</var> is an absorbing state).
 
         </dl>
 
@@ -1185,13 +1180,13 @@
 <p><a name="doc_002dctmc_005ftaexps"></a>
 
 <div class="defun">
-&mdash; Function File: <var>M</var> = <b>ctmc_taexps</b> (<var>Q, tt, p</var>)<var><a name="index-ctmc_005ftaexps-24"></a></var><br>
+&mdash; Function File: <var>M</var> = <b>ctmc_taexps</b> (<var>Q, t, p</var>)<var><a name="index-ctmc_005ftaexps-24"></a></var><br>
 <blockquote>
         <p><a name="index-Markov-chain_002c-continuous-time-25"></a><a name="index-Time_002dalveraged-sojourn-time-26"></a>
-Compute the <em>time-averaged sojourn time</em> <var>M</var><code>(t,j)</code>,
-defined as the fraction of the time interval <code>[0,</code><var>tt</var><code>(t))</code> spent in
-state j, assuming that at time 0 the state occupancy
-probability was <var>p</var>.
+Compute the <em>time-averaged sojourn time</em> <var>M</var><code>(i)</code>,
+defined as the fraction of the time interval [0,t] spent in
+state i, assuming that the state occupancy probabilities at
+time 0 are <var>p</var>.
 
         <p><strong>INPUTS</strong>
 
@@ -1199,15 +1194,9 @@
 <dt><var>Q</var><dd>Infinitesimal generator matrix. <var>Q</var><code>(i,j)</code> is the transition
 rate from state i to state j,
 1 &le; i \neq j &le; N. The
-matrix <var>Q</var> must also satisfy the condition <code>sum(</code><var>Q</var><code>,2) == 0</code>
+matrix <var>Q</var> must also satisfy the condition \sum_j=1^N Q_ij = 0
 
-          <br><dt><var>tt</var><dd>This parameter is a vector used for numerical integration of the
-sujourn time. The first element <var>tt</var><code>(1)</code> must be slightly
-larger than 0, and the
-last element <var>tt</var><code>(end)</code> must be the upper limit of the
-interval [0,t) of interest (<var>tt</var><code>(end) == t</code>). 
-This vector is used by the ODE solver to compute the solution
-<var>M</var>.
+          <br><dt><var>t</var><dd>Time
 
           <br><dt><var>p</var><dd><var>p</var><code>(i)</code> is the probability that, at time 0, the system was in
 state i, for all i = 1, <small class="dots">...</small>, N
@@ -1217,10 +1206,9 @@
         <p><strong>OUTPUTS</strong>
 
           <dl>
-<dt><var>M</var><dd><var>M</var><code>(t,j)</code> is the expected fraction of time spent in state
-j during the interval [0,tt(t)) assuming that the state
-occupancy probability at time zero was <var>p</var>. <code>1 &le;
-</code><var>t</var><code> &le; length(</code><var>tt</var><code>)</code>
+<dt><var>M</var><dd><var>M</var><code>(i)</code> is the expected fraction of time spent in state
+i during the interval [0,t] assuming that the state
+occupancy probability at time zero is <var>p</var>.
 
         </dl>
 
@@ -1279,7 +1267,7 @@
         <p><a name="index-Markov-chain_002c-continuous-time-28"></a><a name="index-Mean-time-to-absorption-29"></a>
 Compute the Mean-Time to Absorption (MTTA) of the CTMC described by
 the infinitesimal generator matrix <var>Q</var>, starting from initial
-occupancy probability <var>p</var>. If there are no absorbing states, this
+occupancy probabilities <var>p</var>. If there are no absorbing states, this
 function fails with an error.
 
         <p><strong>INPUTS</strong>

Modified: trunk/octave-forge/main/queueing/doc/queueing.pdf
===================================================================
(Binary files differ)

Modified: trunk/octave-forge/main/queueing/inst/ctmc_exps.m
===================================================================
--- trunk/octave-forge/main/queueing/inst/ctmc_exps.m	2012-03-10 19:46:27 UTC (rev 9810)
+++ trunk/octave-forge/main/queueing/inst/ctmc_exps.m	2012-03-10 20:27:25 UTC (rev 9811)
@@ -17,17 +17,17 @@
 
 ## -*- texinfo -*-
 ##
-## @deftypefn {Function File} {@var{L} =} ctmc_exps (@var{Q}, @var{tt}, @var{p} )
+## @deftypefn {Function File} {@var{L} =} ctmc_exps (@var{Q}, @var{t}, @var{p} )
 ## @deftypefnx {Function File} {@var{L} =} ctmc_exps (@var{Q}, @var{p})
 ##
 ## @cindex Markov chain, continuous time
 ## @cindex Expected sojourn time
 ##
-## With three arguments, compute the expected time @code{@var{L}(t,j)}
-## spent in each state @math{j} during the time interval
-## @code{[0,@var{tt}(t))}, assuming that at time 0 the state occupancy
-## probability was @var{p}. With two arguments, compute the expected
-## time @code{@var{L}(j)} spent in each state @math{j} until absorption.
+## With three arguments, compute the expected times @code{@var{L}(i)}
+## spent in each state @math{i} during the time interval
+## @math{[0,t]}, assuming that the state occupancy probabilities
+## at time 0 are @var{p}. With two arguments, compute the expected time
+## @code{@var{L}(i)} spent in each state @math{i} until absorption.
 ##
 ## @strong{INPUTS}
 ##
@@ -39,11 +39,8 @@
 ## @leq{} i \neq j @leq{} N}. The matrix @var{Q} must also satisfy the
 ## condition @math{\sum_{j=1}^N Q_{ij} = 0}.
 ##
-## @item tt
-## This parameter is a vector used for numerical integration. The first
-## element @code{@var{tt}(1)} must be 0, and the last element
-## @code{@var{tt}(end)} must be the upper bound of the interval
-## @math{[0,t)} of interest (@code{@var{tt}(end) == @math{t}}).
+## @item t
+## Time
 ##
 ## @item p
 ## Initial occupancy probability vector; @code{@var{p}(i)} is the
@@ -57,14 +54,12 @@
 ## @table @var
 ##
 ## @item L
-## If this function is called with three arguments, @var{L} is a matrix
-## of size @code{[length(@var{tt}), N]} where @code{@var{L}(t,j)} is the
-## expected time spent in state @math{j} during the interval
-## @code{[0,@var{tt}(t)]}. If this function is called with two
-## arguments, @var{L} is a vector with @math{N} elements where
-## @code{@var{L}(j)} is the expected time spent in state @math{j} until
-## absorption, if @math{j} is a transient state. If @math{j}
-## is an absorbing state, @code{@var{L}(j) = 0}.
+## If this function is called with three arguments, @code{@var{L}(i)} is
+## the expected time spent in state @math{j} during the interval
+## @math{[0,t]}. If this function is called with two arguments
+## @code{@var{L}(i)} is the expected time spent in state @math{i} until
+## absorption (if @math{i} is a transient state), or zero
+## (if @var{i} is an absorbing state).
 ##
 ## @end table
 ##
@@ -85,12 +80,12 @@
       usage( "Q must be a square matrix" );
 
   ( norm( sum(Q,2), "inf" ) < epsilon ) || \
-      error( "Q is not an infinitesimal generator matrix" );
+      usage( "Q is not an infinitesimal generator matrix" );
 
   if ( nargin == 2 )
     p = varargin{1};
   else
-    tt = varargin{1};
+    t = varargin{1};
     p = varargin{2};
   endif
 
@@ -98,15 +93,27 @@
       usage( "p must be a probability vector" );
 
   if ( nargin == 3 ) 
-    ( isvector(tt) && abs(tt(1)) < epsilon ) || \
-	usage( "tt must be a vector, and tt(1) must be 0.0" );
-    tt = tt(:)'; # make tt a row vector
-    p = p(:)'; # make p a row vector
-    ff = @(x,t) (x(:)'*Q+p);
-    fj = @(x,t) (Q);
-    L = lsode( {ff, fj}, zeros(size(p)), tt );
+    if ( isscalar(t) )
+      (t >= 0 ) || \
+	  usage( "t must be >= 0" );
+      ## F(x) are the transient state occupancy probabilities at time x.
+      ## It is known that F(x) = p*expm(Q*x) (see function ctmc()).
+      F = @(x) (p*expm(Q*x));
+      L = quadv(F,0,t);
+    else
+      ## FIXME: deprecate this?
+      ( isvector(t) && abs(t(1)) < epsilon ) || \
+	  usage( "t must be a vector, and t(1) must be 0.0" );
+      t = t(:)'; # make tt a row vector
+      p = p(:)'; # make p a row vector
+      ff = @(x,t) (x(:)'*Q+p);
+      fj = @(x,t) (Q);
+      L = lsode( {ff, fj}, zeros(size(p)), t );
+    endif
   else
 #{
+    ## This code is left for information only
+
     ## F(t) are the transient state occupancy probabilities at time t.
     ## It is known that F(t) = p*expm(Q*t) (see function ctmc()).
     ## The expected times spent in each state until absorption can
@@ -138,6 +145,10 @@
     L(nzrows) = LN;
   endif
 endfunction
+%!test
+%! Q = [-1 1; 1 -1];
+%! L = ctmc_exps(Q,10,[1 0]);
+%! L = ctmc_exps(Q,linspace(0,10,100),[1 0]);
 
 %!demo
 %! lambda = 0.5;
@@ -146,18 +157,16 @@
 %! death = zeros(1,N-1);
 %! Q = diag(birth,1)+diag(death,-1);
 %! Q -= diag(sum(Q,2));
-%! tt = linspace(0,10,100);
+%! t = linspace(0,10,100);
 %! p0 = zeros(1,N); p0(1)=1;
-%! L = ctmc_exps(Q,tt,p0);
-%! #L2 = 0*L;
-%! #for i=1:length(tt)
-%! #  L2(i,:) = quadv( @(t) (p0*expm(Q*t)) , 0, tt(i) );
-%! #endfor
-%! plot( tt, L(:,1), ";State 1;", "linewidth", 2, \
-%! #      tt, L2(:,1), "+;State 1 (quadv);", "markersize", 8, \
-%!       tt, L(:,2), ";State 2;", "linewidth", 2, \
-%!       tt, L(:,3), ";State 3;", "linewidth", 2, \
-%!       tt, L(:,4), ";State 4 (absorbing);", "linewidth", 2);
+%! L = zeros(length(t),N);
+%! for i=1:length(t)
+%!   L(i,:) = ctmc_exps(Q,t(i),p0);
+%! endfor
+%! plot( t, L(:,1), ";State 1;", "linewidth", 2, \
+%!       t, L(:,2), ";State 2;", "linewidth", 2, \
+%!       t, L(:,3), ";State 3;", "linewidth", 2, \
+%!       t, L(:,4), ";State 4;", "linewidth", 2 );
 %! legend("location","northwest");
 %! xlabel("Time");
 %! ylabel("Expected sojourn time");

Modified: trunk/octave-forge/main/queueing/inst/ctmc_mtta.m
===================================================================
--- trunk/octave-forge/main/queueing/inst/ctmc_mtta.m	2012-03-10 19:46:27 UTC (rev 9810)
+++ trunk/octave-forge/main/queueing/inst/ctmc_mtta.m	2012-03-10 20:27:25 UTC (rev 9811)
@@ -24,7 +24,7 @@
 ##
 ## Compute the Mean-Time to Absorption (MTTA) of the CTMC described by
 ## the infinitesimal generator matrix @var{Q}, starting from initial
-## occupancy probability @var{p}. If there are no absorbing states, this
+## occupancy probabilities @var{p}. If there are no absorbing states, this
 ## function fails with an error.
 ##
 ## @strong{INPUTS}
@@ -71,8 +71,8 @@
   
   N = rows(Q);
 
-  all( abs( sum(Q,2) ) < epsilon )  || \
-      usage( "Q is not an infinitesimal generator matrix" );
+  ( norm( sum(Q,2), "inf" ) < epsilon ) || \
+      usage( "Q must be an infinitesimal generator matrix" );
 
   ( isvector(p) && length(p) == N && all(p>=0) && abs(sum(p)-1.0)<epsilon ) || \
       usage( "p must be a probability vector" );
@@ -90,7 +90,7 @@
 
 %!test
 %! Q = [0 1 0; 1 0 1; 0 0 0 ];
-%! fail( "ctmc_mtta(Q,[1 0 0])", "not an infinitesimal");
+%! fail( "ctmc_mtta(Q,[1 0 0])", "must be an infinitesimal");
 
 %!test
 %! Q = [ 0 0.1 0 0; \

Modified: trunk/octave-forge/main/queueing/inst/ctmc_taexps.m
===================================================================
--- trunk/octave-forge/main/queueing/inst/ctmc_taexps.m	2012-03-10 19:46:27 UTC (rev 9810)
+++ trunk/octave-forge/main/queueing/inst/ctmc_taexps.m	2012-03-10 20:27:25 UTC (rev 9811)
@@ -17,15 +17,15 @@
 
 ## -*- texinfo -*-
 ##
-## @deftypefn {Function File} {@var{M} =} ctmc_taexps (@var{Q}, @var{tt}, @var{p})
+## @deftypefn {Function File} {@var{M} =} ctmc_taexps (@var{Q}, @var{t}, @var{p})
 ##
 ## @cindex Markov chain, continuous time
 ## @cindex Time-alveraged sojourn time
 ##
-## Compute the @emph{time-averaged sojourn time} @code{@var{M}(t,j)},
-## defined as the fraction of the time interval @code{[0,@var{tt}(t))} spent in
-## state @math{j}, assuming that at time 0 the state occupancy
-## probability was @var{p}.
+## Compute the @emph{time-averaged sojourn time} @code{@var{M}(i)},
+## defined as the fraction of the time interval @math{[0,t]} spent in
+## state @math{i}, assuming that the state occupancy probabilities at
+## time 0 are @var{p}.
 ##
 ## @strong{INPUTS}
 ##
@@ -35,16 +35,10 @@
 ## Infinitesimal generator matrix. @code{@var{Q}(i,j)} is the transition
 ## rate from state @math{i} to state @math{j},
 ## @math{1 @leq{} i \neq j @leq{} N}. The
-## matrix @var{Q} must also satisfy the condition @code{sum(@var{Q},2) == 0}
+## matrix @var{Q} must also satisfy the condition @math{\sum_{j=1}^N Q_{ij} = 0}
 ##
-## @item tt
-## This parameter is a vector used for numerical integration of the
-## sujourn time. The first element @code{@var{tt}(1)} must be slightly
-## larger than 0, and the
-## last element @code{@var{tt}(end)} must be the upper limit of the
-## interval @math{[0,t)} of interest (@code{@var{tt}(end) == @math{t}}).
-## This vector is used by the ODE solver to compute the solution
-## @var{M}.
+## @item t
+## Time
 ##
 ## @item p
 ## @code{@var{p}(i)} is the probability that, at time 0, the system was in
@@ -57,10 +51,9 @@
 ## @table @var
 ##
 ## @item M
-## @code{@var{M}(t,j)} is the expected fraction of time spent in state
-## @math{j} during the interval @math{[0,tt(t))} assuming that the state
-## occupancy probability at time zero was @var{p}. @code{1 @leq{}
-## @var{t} @leq{} length(@var{tt})}
+## @code{@var{M}(i)} is the expected fraction of time spent in state
+## @math{i} during the interval @math{[0,t]} assuming that the state
+## occupancy probability at time zero is @var{p}.
 ##
 ## @end table
 ##
@@ -87,11 +80,19 @@
 
   ( isvector(p) && length(p) == N && all(p>=0) && abs(sum(p)-1.0)<epsilon ) || \
       usage( "p must be a probability vector" );
-  t = t(:)'; # make t a row vector
-  p = p(:)'; # make p a row vector
-  ff = @(x,t) (((x')*(Q-eye(N)/t).+p/t)');
-  fj = @(x,t) (Q-eye(N)/t);
-  M = lsode( {ff, fj}, zeros(size(p)), t );
+  if ( isscalar(t) )
+    (t >= 0) || \
+	usage( "t must be >= 0" );
+    F = @(x) (p*expm(Q*x));
+    M = quadv(F,0,t) / t;
+  else
+    ## FIXME: deprecate this?
+    t = t(:)'; # make t a row vector
+    p = p(:)'; # make p a row vector
+    ff = @(x,t) (((x')*(Q-eye(N)/t).+p/t)');
+    fj = @(x,t) (Q-eye(N)/t);
+    M = lsode( {ff, fj}, zeros(size(p)), t );
+  endif
 endfunction
 
 %!demo
@@ -101,9 +102,12 @@
 %! death = zeros(1,N-1);
 %! Q = diag(birth,1)+diag(death,-1);
 %! Q -= diag(sum(Q,2));
-%! t = linspace(1e-3,50,500);
+%! t = linspace(1e-5,30,100);
 %! p = zeros(1,N); p(1)=1;
-%! M = ctmc_taexps(Q,t,p);
+%! M = zeros(length(t),N);
+%! for i=1:length(t)
+%!   M(i,:) = ctmc_taexps(Q,t(i),p);
+%! endfor
 %! plot(t, M(:,1), ";State 1;", "linewidth", 2, \
 %!      t, M(:,2), ";State 2;", "linewidth", 2, \
 %!      t, M(:,3), ";State 3;", "linewidth", 2, \

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[Octave-cvsupdate] SF.net SVN: octave:[9810] trunk/octave-forge/extra/control-devel/inst/@ iddata/subsref.m

From: <par...@us...> - 2012-03-10 19:46:33

Revision: 9810
          http://octave.svn.sourceforge.net/octave/?rev=9810&view=rev
Author:   paramaniac
Date:     2012-03-10 19:46:27 +0000 (Sat, 10 Mar 2012)
Log Message:
-----------
control-devel: use recursion instead of for-loop, fix subsref tsam

Modified Paths:
--------------
    trunk/octave-forge/extra/control-devel/inst/@iddata/subsref.m

Modified: trunk/octave-forge/extra/control-devel/inst/@iddata/subsref.m
===================================================================
--- trunk/octave-forge/extra/control-devel/inst/@iddata/subsref.m	2012-03-10 19:45:06 UTC (rev 9809)
+++ trunk/octave-forge/extra/control-devel/inst/@iddata/subsref.m	2012-03-10 19:46:27 UTC (rev 9810)
@@ -21,36 +21,31 @@
 
 ## Author: Lukas Reichlin <luk...@gm...>
 ## Created: February 2012
-## Version: 0.1
+## Version: 0.2
 
 function a = subsref (a, s)
 
-  if (isempty (s))
-    error ("iddata: subsref: missing index");
+  if (numel (s) == 0)
+    return;
   endif
 
-  for k = 1 : numel (s)
-    if (isa (a, "iddata"))
-      switch (s(k).type)
-        case "()"
-          idx = s(k).subs;
-          if (numel (idx) > 4)
-            error ("iddata: subsref: need four or less indices");
-          else
-            a = __dat_prune__ (a, idx{:}); 
-          endif
-        case "."
-          fld = s(k).subs;
-          a = get (a, fld);
-        otherwise
-          error ("iddata: subsref: invalid subscript type");
-      endswitch
-    else  # not an iddata set
-      a = subsref (a, s(k:end));
-      return;
-    endif
-  endfor
+  switch (s(1).type)
+    case "()"
+      idx = s(1).subs;
+      if (numel (idx) > 4)
+        error ("iddata: subsref: need four or less indices");
+      else
+        a = __dat_prune__ (a, idx{:}); 
+      endif
+    case "."
+      fld = s(1).subs;
+      a = get (a, fld);
+    otherwise
+      error ("iddata: subsref: invalid subscript type");
+  endswitch
 
+  a = subsref (a, s(2:end));
+
 endfunction
 
 
@@ -69,5 +64,6 @@
   endif
 
   dat.expname = dat.expname(exp_idx);
+  dat.tsam = dat.tsam(exp_idx);
 
-endfunction
\ No newline at end of file
+endfunction

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[Octave-cvsupdate] SF.net SVN: octave:[9809] trunk/octave-forge/main/control/inst/@lti/subsref .m

From: <par...@us...> - 2012-03-10 19:45:12

Revision: 9809
          http://octave.svn.sourceforge.net/octave/?rev=9809&view=rev
Author:   paramaniac
Date:     2012-03-10 19:45:06 +0000 (Sat, 10 Mar 2012)
Log Message:
-----------
control: use recursion instead of for-loop for subs ref

Modified Paths:
--------------
    trunk/octave-forge/main/control/inst/@lti/subsref.m

Modified: trunk/octave-forge/main/control/inst/@lti/subsref.m
===================================================================
--- trunk/octave-forge/main/control/inst/@lti/subsref.m	2012-03-10 16:03:47 UTC (rev 9808)
+++ trunk/octave-forge/main/control/inst/@lti/subsref.m	2012-03-10 19:45:06 UTC (rev 9809)
@@ -1,4 +1,4 @@
-## Copyright (C) 2009   Lukas F. Reichlin
+## Copyright (C) 2009, 2012   Lukas F. Reichlin
 ##
 ## This file is part of LTI Syncope.
 ##
@@ -21,37 +21,32 @@
 
 ## Author: Lukas Reichlin <luk...@gm...>
 ## Created: September 2009
-## Version: 0.2
+## Version: 0.3
 
 function a = subsref (a, s)
 
-  if (isempty (s))
-    error ("lti: subsref: missing index");
+  if (numel (s) == 0)
+    return;
   endif
 
-  for k = 1 : numel (s)
-    if (isa (a, "lti"))
-      switch (s(k).type)
-        case "()"
-          idx = s(k).subs;
-          if (numel (idx) == 2)
-            a = __sys_prune__ (a, idx{1}, idx{2});
-          elseif (numel (idx) == 1)
-            a = __freqresp__ (a, idx{1});  
-          else
-            error ("lti: subsref: need one or two indices");
-          endif
-        case "."
-          fld = s(k).subs;
-          a = get (a, fld);
-          ## warning ("lti: subsref: do not use subsref for development");
-        otherwise
-          error ("lti: subsref: invalid subscript type");
-      endswitch
-    else  # not an LTI model
-      a = subsref (a, s(k:end));
-      return;
-    endif
-  endfor
+  switch (s(1).type)
+    case "()"
+      idx = s(1).subs;
+      if (numel (idx) == 2)
+        a = __sys_prune__ (a, idx{1}, idx{2});
+      elseif (numel (idx) == 1)
+        a = __freqresp__ (a, idx{1});  
+      else
+        error ("lti: subsref: need one or two indices");
+      endif
+    case "."
+      fld = s(1).subs;
+      a = get (a, fld);
+      ## warning ("lti: subsref: do not use subsref for development");
+    otherwise
+      error ("lti: subsref: invalid subscript type");
+  endswitch
+  
+  a = subsref (a, s(2:end));
 
-endfunction
\ No newline at end of file
+endfunction

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[Octave-cvsupdate] SF.net SVN: octave:[9808] trunk/octave-forge/main/queueing

From: <mma...@us...> - 2012-03-10 16:03:56

Revision: 9808
          http://octave.svn.sourceforge.net/octave/?rev=9808&view=rev
Author:   mmarzolla
Date:     2012-03-10 16:03:47 +0000 (Sat, 10 Mar 2012)
Log Message:
-----------
fixed bug in texinfo documentation

Modified Paths:
--------------
    trunk/octave-forge/main/queueing/doc/queueing.html
    trunk/octave-forge/main/queueing/doc/queueing.pdf
    trunk/octave-forge/main/queueing/inst/ctmc_exps.m

Modified: trunk/octave-forge/main/queueing/doc/queueing.html
===================================================================
--- trunk/octave-forge/main/queueing/doc/queueing.html	2012-03-10 16:00:45 UTC (rev 9807)
+++ trunk/octave-forge/main/queueing/doc/queueing.html	2012-03-10 16:03:47 UTC (rev 9808)
@@ -1100,36 +1100,46 @@
    <p><a name="doc_002dctmc_005fexps"></a>
 
 <div class="defun">
-&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, tt, p</var>)<var><a name="index-ctmc_005fexps-20"></a></var><br>
+&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, tt, p </var>)<var><a name="index-ctmc_005fexps-20"></a></var><br>
+&mdash; Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fexps-21"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-21"></a><a name="index-Expected-sojourn-time-22"></a>
-Compute the expected total time <var>L</var><code>(t,j)</code> spent in state
-j during the time interval <code>[0,</code><var>tt</var><code>(t))</code>, assuming
-that at time 0 the state occupancy probability was <var>p</var>.
+        <p><a name="index-Markov-chain_002c-continuous-time-22"></a><a name="index-Expected-sojourn-time-23"></a>
+With three arguments, compute the expected time <var>L</var><code>(t,j)</code>
+spent in each state j during the time interval
+<code>[0,</code><var>tt</var><code>(t))</code>, assuming that at time 0 the state occupancy
+probability was <var>p</var>. With two arguments, compute the expected
+time <var>L</var><code>(j)</code> spent in each state j until absorption.
 
         <p><strong>INPUTS</strong>
 
           <dl>
-<dt><var>Q</var><dd>Infinitesimal generator matrix. <var>Q</var><code>(i,j)</code> is the transition
-rate from state i to state j,
-1 &le; i \neq j &le; N. The matrix <var>Q</var> must also satisfy the
-condition <code>sum(</code><var>Q</var><code>,2) == 0</code>
+<dt><var>Q</var><dd>N \times N infinitesimal generator matrix. <var>Q</var><code>(i,j)</code>
+is the transition rate from state i to state j, 1
+&le; i \neq j &le; N. The matrix <var>Q</var> must also satisfy the
+condition \sum_j=1^N Q_ij = 0.
 
           <br><dt><var>tt</var><dd>This parameter is a vector used for numerical integration. The first
 element <var>tt</var><code>(1)</code> must be 0, and the last element
 <var>tt</var><code>(end)</code> must be the upper bound of the interval
 [0,t) of interest (<var>tt</var><code>(end) == t</code>).
 
-          <br><dt><var>p</var><dd><var>p</var><code>(i)</code> is the probability that at time 0 the system was in
-state i, for all i = 1, <small class="dots">...</small>, N
+          <br><dt><var>p</var><dd>Initial occupancy probability vector; <var>p</var><code>(i)</code> is the
+probability the system is in state i at time 0, i = 1,
+<small class="dots">...</small>, N
 
         </dl>
 
         <p><strong>OUTPUTS</strong>
 
           <dl>
-<dt><var>L</var><dd><var>L</var><code>(t,j)</code> is the expected time spent in state j
-during the interval <code>[0,</code><var>tt</var><code>(t))</code>. <code>1 &le; </code><var>t</var><code> &le; length(</code><var>tt</var><code>)</code>
+<dt><var>L</var><dd>If this function is called with three arguments, <var>L</var> is a matrix
+of size <code>[length(</code><var>tt</var><code>), N]</code> where <var>L</var><code>(t,j)</code> is the
+expected time spent in state j during the interval
+<code>[0,</code><var>tt</var><code>(t)]</code>. If this function is called with two
+arguments, <var>L</var> is a vector with N elements where
+<var>L</var><code>(j)</code> is the expected time spent in state j until
+absorption, if j is a transient state. If j
+is an absorbing state, <var>L</var><code>(j) = 0</code>.
 
         </dl>
 
@@ -1175,9 +1185,9 @@
 <p><a name="doc_002dctmc_005ftaexps"></a>
 
 <div class="defun">
-&mdash; Function File: <var>M</var> = <b>ctmc_taexps</b> (<var>Q, tt, p</var>)<var><a name="index-ctmc_005ftaexps-23"></a></var><br>
+&mdash; Function File: <var>M</var> = <b>ctmc_taexps</b> (<var>Q, tt, p</var>)<var><a name="index-ctmc_005ftaexps-24"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-24"></a><a name="index-Time_002dalveraged-sojourn-time-25"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-25"></a><a name="index-Time_002dalveraged-sojourn-time-26"></a>
 Compute the <em>time-averaged sojourn time</em> <var>M</var><code>(t,j)</code>,
 defined as the fraction of the time interval <code>[0,</code><var>tt</var><code>(t))</code> spent in
 state j, assuming that at time 0 the state occupancy
@@ -1264,12 +1274,13 @@
    <p><a name="doc_002dctmc_005fmtta"></a>
 
 <div class="defun">
-&mdash; Function File: <var>t</var> = <b>ctmc_mtta</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fmtta-26"></a></var><br>
+&mdash; Function File: <var>t</var> = <b>ctmc_mtta</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fmtta-27"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-27"></a><a name="index-Mean-time-to-absorption-28"></a>
-Compute the Mean-Time to Absorption (MTTA) starting from initial
-occupancy probability <var>p</var> at time 0. If there are no absorbing
-states, this function fails with an error.
+        <p><a name="index-Markov-chain_002c-continuous-time-28"></a><a name="index-Mean-time-to-absorption-29"></a>
+Compute the Mean-Time to Absorption (MTTA) of the CTMC described by
+the infinitesimal generator matrix <var>Q</var>, starting from initial
+occupancy probability <var>p</var>. If there are no absorbing states, this
+function fails with an error.
 
         <p><strong>INPUTS</strong>
 
@@ -1326,7 +1337,7 @@
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998.
 
-   <p><a name="index-Bolch_002c-G_002e-29"></a><a name="index-Greiner_002c-S_002e-30"></a><a name="index-de-Meer_002c-H_002e-31"></a><a name="index-Trivedi_002c-K_002e-32"></a>
+   <p><a name="index-Bolch_002c-G_002e-30"></a><a name="index-Greiner_002c-S_002e-31"></a><a name="index-de-Meer_002c-H_002e-32"></a><a name="index-Trivedi_002c-K_002e-33"></a>
 <div class="node">
 <a name="CTMC-First-Passage-Times"></a>
 <p><hr>
@@ -1340,10 +1351,10 @@
 <p><a name="doc_002dctmc_005ffpt"></a>
 
 <div class="defun">
-&mdash; Function File: <var>M</var> = <b>ctmc_fpt</b> (<var>Q</var>)<var><a name="index-ctmc_005ffpt-33"></a></var><br>
-&mdash; Function File: <var>m</var> = <b>ctmc_fpt</b> (<var>Q, i, j</var>)<var><a name="index-ctmc_005ffpt-34"></a></var><br>
+&mdash; Function File: <var>M</var> = <b>ctmc_fpt</b> (<var>Q</var>)<var><a name="index-ctmc_005ffpt-34"></a></var><br>
+&mdash; Function File: <var>m</var> = <b>ctmc_fpt</b> (<var>Q, i, j</var>)<var><a name="index-ctmc_005ffpt-35"></a></var><br>
 <blockquote>
-        <p><a name="index-Markov-chain_002c-continuous-time-35"></a><a name="index-First-passage-times-36"></a>
+        <p><a name="index-Markov-chain_002c-continuous-time-36"></a><a name="index-First-passage-times-37"></a>
 If called with a single argument, computes the mean first passage
 times <var>M</var><code>(i,j)</code>, the average times before state <var>j</var> is
 reached, starting from state <var>i</var>, for all 1 \leq i, j \leq
@@ -1449,9 +1460,9 @@
    <p><a name="doc_002dqnmm1"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmm1</b> (<var>lambda, mu</var>)<var><a name="index-qnmm1-37"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmm1</b> (<var>lambda, mu</var>)<var><a name="index-qnmm1-38"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002f1_007d-system-38"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002f1_007d-system-39"></a>
 Compute utilization, response time, average number of requests
 and throughput for a M/M/1 queue.
 
@@ -1496,7 +1507,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.3.
 
-   <p><a name="index-Bolch_002c-G_002e-39"></a><a name="index-Greiner_002c-S_002e-40"></a><a name="index-de-Meer_002c-H_002e-41"></a><a name="index-Trivedi_002c-K_002e-42"></a>
+   <p><a name="index-Bolch_002c-G_002e-40"></a><a name="index-Greiner_002c-S_002e-41"></a><a name="index-de-Meer_002c-H_002e-42"></a><a name="index-Trivedi_002c-K_002e-43"></a>
 <!-- M/M/m -->
 <div class="node">
 <a name="The-M%2fM%2fm-System"></a>
@@ -1522,10 +1533,10 @@
    <p><a name="doc_002dqnmmm"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu</var>)<var><a name="index-qnmmm-43"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu, m</var>)<var><a name="index-qnmmm-44"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu</var>)<var><a name="index-qnmmm-44"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu, m</var>)<var><a name="index-qnmmm-45"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002fm_007d-system-45"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002fm_007d-system-46"></a>
 Compute utilization, response time, average number of requests in
 service and throughput for a M/M/m queue, a queueing
 system with m identical service centers connected to a single queue.
@@ -1577,7 +1588,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.5.
 
-   <p><a name="index-Bolch_002c-G_002e-46"></a><a name="index-Greiner_002c-S_002e-47"></a><a name="index-de-Meer_002c-H_002e-48"></a><a name="index-Trivedi_002c-K_002e-49"></a>
+   <p><a name="index-Bolch_002c-G_002e-47"></a><a name="index-Greiner_002c-S_002e-48"></a><a name="index-de-Meer_002c-H_002e-49"></a><a name="index-Trivedi_002c-K_002e-50"></a>
 <!-- M/M/inf -->
 <div class="node">
 <a name="The-M%2fM%2finf-System"></a>
@@ -1600,7 +1611,7 @@
    <p><a name="doc_002dqnmminf"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmminf</b> (<var>lambda, mu</var>)<var><a name="index-qnmminf-50"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmminf</b> (<var>lambda, mu</var>)<var><a name="index-qnmminf-51"></a></var><br>
 <blockquote>
         <p>Compute utilization, response time, average number of requests and
 throughput for a M/M/\infty queue. This is a system with an
@@ -1608,7 +1619,7 @@
 system is always stable, regardless the values of the arrival and
 service rates.
 
-        <p><a name="index-g_t_0040math_007bM_002fM_002f_007dinf-system-51"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002f_007dinf-system-52"></a>
 
         <p><strong>INPUTS</strong>
 
@@ -1626,7 +1637,7 @@
 different from the utilization, which in the case of M/M/\infty
 centers is always zero.
 
-          <p><a name="index-traffic-intensity-52"></a>
+          <p><a name="index-traffic-intensity-53"></a>
 <br><dt><var>R</var><dd>Service center response time.
 
           <br><dt><var>Q</var><dd>Average number of requests in the system (which is equal to the
@@ -1654,7 +1665,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.4.
 
-   <p><a name="index-Bolch_002c-G_002e-53"></a><a name="index-Greiner_002c-S_002e-54"></a><a name="index-de-Meer_002c-H_002e-55"></a><a name="index-Trivedi_002c-K_002e-56"></a>
+   <p><a name="index-Bolch_002c-G_002e-54"></a><a name="index-Greiner_002c-S_002e-55"></a><a name="index-de-Meer_002c-H_002e-56"></a><a name="index-Trivedi_002c-K_002e-57"></a>
 <!-- M/M/1/k -->
 <div class="node">
 <a name="The-M%2fM%2f1%2fK-System"></a>
@@ -1678,9 +1689,9 @@
    <p><a name="doc_002dqnmm1k"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmm1k</b> (<var>lambda, mu, K</var>)<var><a name="index-qnmm1k-57"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmm1k</b> (<var>lambda, mu, K</var>)<var><a name="index-qnmm1k-58"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002f1_002fK_007d-system-58"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002f1_002fK_007d-system-59"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/M/1/K finite capacity system. In a
 M/M/1/K queue there is a single server; the maximum number of
@@ -1747,9 +1758,9 @@
    <p><a name="doc_002dqnmmmk"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmmmk</b> (<var>lambda, mu, m, K</var>)<var><a name="index-qnmmmk-59"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmmmk</b> (<var>lambda, mu, m, K</var>)<var><a name="index-qnmmmk-60"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fM_002fm_002fK_007d-system-60"></a>
+        <p><a name="index-g_t_0040math_007bM_002fM_002fm_002fK_007d-system-61"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/M/m/K finite capacity system. In a
 M/M/m/K system there are m \geq 1 identical service
@@ -1807,7 +1818,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998, Section 6.6.
 
-   <p><a name="index-Bolch_002c-G_002e-61"></a><a name="index-Greiner_002c-S_002e-62"></a><a name="index-de-Meer_002c-H_002e-63"></a><a name="index-Trivedi_002c-K_002e-64"></a>
+   <p><a name="index-Bolch_002c-G_002e-62"></a><a name="index-Greiner_002c-S_002e-63"></a><a name="index-de-Meer_002c-H_002e-64"></a><a name="index-Trivedi_002c-K_002e-65"></a>
 
 <!-- Approximate M/M/m -->
 <div class="node">
@@ -1829,9 +1840,9 @@
    <p><a name="doc_002dqnammm"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnammm</b> (<var>lambda, mu</var>)<var><a name="index-qnammm-65"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnammm</b> (<var>lambda, mu</var>)<var><a name="index-qnammm-66"></a></var><br>
 <blockquote>
-        <p><a name="index-Asymmetric-_0040math_007bM_002fM_002fm_007d-system-66"></a>
+        <p><a name="index-Asymmetric-_0040math_007bM_002fM_002fm_007d-system-67"></a>
 Compute <em>approximate</em> utilization, response time, average number
 of requests in service and throughput for an asymmetric  M/M/m
 queue. In this system there are m different service centers
@@ -1878,7 +1889,7 @@
 and Markov Chains: Modeling and Performance Evaluation with Computer
 Science Applications</cite>, Wiley, 1998
 
-   <p><a name="index-Bolch_002c-G_002e-67"></a><a name="index-Greiner_002c-S_002e-68"></a><a name="index-de-Meer_002c-H_002e-69"></a><a name="index-Trivedi_002c-K_002e-70"></a>
+   <p><a name="index-Bolch_002c-G_002e-68"></a><a name="index-Greiner_002c-S_002e-69"></a><a name="index-de-Meer_002c-H_002e-70"></a><a name="index-Trivedi_002c-K_002e-71"></a>
 <div class="node">
 <a name="The-M%2fG%2f1-System"></a>
 <a name="The-M_002fG_002f1-System"></a>
@@ -1894,9 +1905,9 @@
 <p><a name="doc_002dqnmg1"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmg1</b> (<var>lambda, xavg, x2nd</var>)<var><a name="index-qnmg1-71"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmg1</b> (<var>lambda, xavg, x2nd</var>)<var><a name="index-qnmg1-72"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fG_002f1_007d-system-72"></a>
+        <p><a name="index-g_t_0040math_007bM_002fG_002f1_007d-system-73"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/G/1 system. The service time distribution
 is described by its mean <var>xavg</var>, and by its second moment
@@ -1953,9 +1964,9 @@
 <p><a name="doc_002dqnmh1"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmh1</b> (<var>lambda, mu, alpha</var>)<var><a name="index-qnmh1-73"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmh1</b> (<var>lambda, mu, alpha</var>)<var><a name="index-qnmh1-74"></a></var><br>
 <blockquote>
-        <p><a name="index-g_t_0040math_007bM_002fH_005fm_002f1_007d-system-74"></a>
+        <p><a name="index-g_t_0040math_007bM_002fH_005fm_002f1_007d-system-75"></a>
 Compute utilization, response time, average number of requests and
 throughput for a M/H_m/1 system. In this system, the customer
 service times have hyper-exponential distribution:
@@ -2037,7 +2048,7 @@
 <li><a accesskey="6" href="#Utility-functions">Utility functions</a>:                    Utility functions to compute miscellaneous quantities
 </ul>
 
-<p><a name="index-queueing-networks-75"></a>
+<p><a name="index-queueing-networks-76"></a>
 <!-- INTRODUCTION -->
 <div class="node">
 <a name="Introduction-to-QNs"></a>
@@ -2298,13 +2309,13 @@
    <p><a name="doc_002dqnmknode"></a>
 
 <div class="defun">
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S</var>)<var><a name="index-qnmknode-76"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S, m</var>)<var><a name="index-qnmknode-77"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/1-lcfs-pr", S</var>)<var><a name="index-qnmknode-78"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S</var>)<var><a name="index-qnmknode-79"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S, s2</var>)<var><a name="index-qnmknode-80"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S</var>)<var><a name="index-qnmknode-81"></a></var><br>
-&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S, s2</var>)<var><a name="index-qnmknode-82"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S</var>)<var><a name="index-qnmknode-77"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S, m</var>)<var><a name="index-qnmknode-78"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/1-lcfs-pr", S</var>)<var><a name="index-qnmknode-79"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S</var>)<var><a name="index-qnmknode-80"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S, s2</var>)<var><a name="index-qnmknode-81"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S</var>)<var><a name="index-qnmknode-82"></a></var><br>
+&mdash; Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S, s2</var>)<var><a name="index-qnmknode-83"></a></var><br>
 <blockquote>
         <p>Creates a node; this function can be used together with
 <code>qnsolve</code>. It is possible to create either single-class nodes
@@ -2373,10 +2384,10 @@
    <p><a name="doc_002dqnsolve"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V</var>)<var><a name="index-qnsolve-83"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V, Z</var>)<var><a name="index-qnsolve-84"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"open", lambda, QQ, V</var>)<var><a name="index-qnsolve-85"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"mixed", lambda, N, QQ, V</var>)<var><a name="index-qnsolve-86"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V</var>)<var><a name="index-qnsolve-84"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V, Z</var>)<var><a name="index-qnsolve-85"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"open", lambda, QQ, V</var>)<var><a name="index-qnsolve-86"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"mixed", lambda, N, QQ, V</var>)<var><a name="index-qnsolve-87"></a></var><br>
 <blockquote>
         <p>General evaluator of QN models. Networks can be open,
 closed or mixed; single as well as multiclass networks are supported.
@@ -2554,11 +2565,11 @@
    <p><a name="doc_002dqnjackson"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P </var>)<var><a name="index-qnjackson-87"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P, m </var>)<var><a name="index-qnjackson-88"></a></var><br>
-&mdash; Function File: <var>pr</var> = <b>qnjackson</b> (<var>lambda, S, P, m, k</var>)<var><a name="index-qnjackson-89"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P </var>)<var><a name="index-qnjackson-88"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P, m </var>)<var><a name="index-qnjackson-89"></a></var><br>
+&mdash; Function File: <var>pr</var> = <b>qnjackson</b> (<var>lambda, S, P, m, k</var>)<var><a name="index-qnjackson-90"></a></var><br>
 <blockquote>
-        <p><a name="index-open-network_002c-single-class-90"></a><a name="index-Jackson-network-91"></a>
+        <p><a name="index-open-network_002c-single-class-91"></a><a name="index-Jackson-network-92"></a>
 With three or four input parameters, this function computes the
 steady-state occupancy probabilities for a Jackson network. With five
 input parameters, this function computes the steady-state probability
@@ -2640,7 +2651,7 @@
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998, pp. 284&ndash;287.
 
-   <p><a name="index-Bolch_002c-G_002e-92"></a><a name="index-Greiner_002c-S_002e-93"></a><a name="index-de-Meer_002c-H_002e-94"></a><a name="index-Trivedi_002c-K_002e-95"></a>
+   <p><a name="index-Bolch_002c-G_002e-93"></a><a name="index-Greiner_002c-S_002e-94"></a><a name="index-de-Meer_002c-H_002e-95"></a><a name="index-Trivedi_002c-K_002e-96"></a>
 
 <h4 class="subsection">6.3.2 The Convolution Algorithm</h4>
 
@@ -2674,10 +2685,10 @@
    <p><a name="doc_002dqnconvolution"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V</var>)<var><a name="index-qnconvolution-96"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V, m</var>)<var><a name="index-qnconvolution-97"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V</var>)<var><a name="index-qnconvolution-97"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V, m</var>)<var><a name="index-qnconvolution-98"></a></var><br>
 <blockquote>
-        <p><a name="index-closed-network-98"></a><a name="index-normalization-constant-99"></a><a name="index-convolution-algorithm-100"></a>
+        <p><a name="index-closed-network-99"></a><a name="index-normalization-constant-100"></a><a name="index-convolution-algorithm-101"></a>
 This function implements the <em>convolution algorithm</em> for
 computing steady-state performance measures of product-form,
 single-class closed queueing networks. Load-independent service
@@ -2768,20 +2779,20 @@
 16, number 9, september 1973,
 pp. 527&ndash;531. <a href="http://doi.acm.org/10.1145/362342.362345">http://doi.acm.org/10.1145/362342.362345</a>
 
-   <p><a name="index-Buzen_002c-J_002e-P_002e-101"></a>
+   <p><a name="index-Buzen_002c-J_002e-P_002e-102"></a>
 This implementation is based on G. Bolch, S. Greiner, H. de Meer and
 K. Trivedi, <cite>Queueing Networks and Markov Chains: Modeling and
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998, pp. 313&ndash;317.
 
-   <p><a name="index-Bolch_002c-G_002e-102"></a><a name="index-Greiner_002c-S_002e-103"></a><a name="index-de-Meer_002c-H_002e-104"></a><a name="index-Trivedi_002c-K_002e-105"></a>
+   <p><a name="index-Bolch_002c-G_002e-103"></a><a name="index-Greiner_002c-S_002e-104"></a><a name="index-de-Meer_002c-H_002e-105"></a><a name="index-Trivedi_002c-K_002e-106"></a>
 <!-- Convolution for load-dependent service centers -->
 <a name="doc_002dqnconvolutionld"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolutionld</b> (<var>N, S, V</var>)<var><a name="index-qnconvolutionld-106"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolutionld</b> (<var>N, S, V</var>)<var><a name="index-qnconvolutionld-107"></a></var><br>
 <blockquote>
-        <p><a name="index-closed-network-107"></a><a name="index-normalization-constant-108"></a><a name="index-convolution-algorithm-109"></a><a name="index-load_002ddependent-service-center-110"></a>
+        <p><a name="index-closed-network-108"></a><a name="index-normalization-constant-109"></a><a name="index-convolution-algorithm-110"></a><a name="index-load_002ddependent-service-center-111"></a>
 This function implements the <em>convolution algorithm</em> for
 product-form, single-class closed queueing networks with general
 load-dependent service centers.
@@ -2841,7 +2852,7 @@
 Purdue University, feb, 1981 (revised). 
 <a href="http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-354.pdf">http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-354.pdf</a>
 
-   <p><a name="index-Schwetman_002c-H_002e-111"></a>
+   <p><a name="index-Schwetman_002c-H_002e-112"></a>
 M. Reiser, H. Kobayashi, <cite>On The Convolution Algorithm for
 Separable Queueing Networks</cite>, In Proceedings of the 1976 ACM
 SIGMETRICS Conference on Computer Performance Modeling Measurement and
@@ -2849,7 +2860,7 @@
 1976). SIGMETRICS '76. ACM, New York, NY,
 pp. 109&ndash;117. <a href="http://doi.acm.org/10.1145/800200.806187">http://doi.acm.org/10.1145/800200.806187</a>
 
-   <p><a name="index-Reiser_002c-M_002e-112"></a><a name="index-Kobayashi_002c-H_002e-113"></a>
+   <p><a name="index-Reiser_002c-M_002e-113"></a><a name="index-Kobayashi_002c-H_002e-114"></a>
 This implementation is based on G. Bolch, S. Greiner, H. de Meer and
 K. Trivedi, <cite>Queueing Networks and Markov Chains: Modeling and
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
@@ -2861,7 +2872,7 @@
 function f_i defined in Schwetman, <code>Some Computational
 Aspects of Queueing Network Models</code>.
 
-   <p><a name="index-Bolch_002c-G_002e-114"></a><a name="index-Greiner_002c-S_002e-115"></a><a name="index-de-Meer_002c-H_002e-116"></a><a name="index-Trivedi_002c-K_002e-117"></a>
+   <p><a name="index-Bolch_002c-G_002e-115"></a><a name="index-Greiner_002c-S_002e-116"></a><a name="index-de-Meer_002c-H_002e-117"></a><a name="index-Trivedi_002c-K_002e-118"></a>
 
 <h4 class="subsection">6.3.3 Open networks</h4>
 
@@ -2869,10 +2880,10 @@
 <p><a name="doc_002dqnopensingle"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V</var>)<var><a name="index-qnopensingle-118"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopensingle-119"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V</var>)<var><a name="index-qnopensingle-119"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopensingle-120"></a></var><br>
 <blockquote>
-        <p><a name="index-open-network_002c-single-class-120"></a><a name="index-BCMP-network-121"></a>
+        <p><a name="index-open-network_002c-single-class-121"></a><a name="index-BCMP-network-122"></a>
 Analyze open, single class BCMP queueing networks.
 
         <p>This function works for a subset of BCMP single-class open networks
@@ -2965,16 +2976,16 @@
 Networks and Markov Chains: Modeling and Performance Evaluation with
 Computer Science Applications</cite>, Wiley, 1998.
 
-   <p><a name="index-Bolch_002c-G_002e-122"></a><a name="index-Greiner_002c-S_002e-123"></a><a name="index-de-Meer_002c-H_002e-124"></a><a name="index-Trivedi_002c-K_002e-125"></a>
+   <p><a name="index-Bolch_002c-G_002e-123"></a><a name="index-Greiner_002c-S_002e-124"></a><a name="index-de-Meer_002c-H_002e-125"></a><a name="index-Trivedi_002c-K_002e-126"></a>
 
 <!-- Open network with multiple classes -->
    <p><a name="doc_002dqnopenmulti"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V</var>)<var><a name="index-qnopenmulti-126"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopenmulti-127"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V</var>)<var><a name="index-qnopenmulti-127"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopenmulti-128"></a></var><br>
 <blockquote>
-        <p><a name="index-open-network_002c-multiple-classes-128"></a>
+        <p><a name="index-open-network_002c-multiple-classes-129"></a>
 Exact analysis of open, multiple-class BCMP networks. The network can
 be made of <em>single-server</em> queueing centers (FCFS, LCFS-PR or
 PS) or delay centers (IS). This function assumes a network with
@@ -3039,7 +3050,7 @@
 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In
 particular, see section 7.4.1 ("Open Model Solution Techniques").
 
-   <p><a name="index-Lazowska_002c-E_002e-D_002e-129"></a><a name="index-Zahorjan_002c-J_002e-130"></a><a name="index-Graham_002c-G_002e-S_002e-131"></a><a name="index-Sevcik_002c-K_002e-C_002e-132"></a>
+   <p><a name="index-Lazowska_002c-E_002e-D_002e-130"></a><a name="index-Zahorjan_002c-J_002e-131"></a><a name="index-Graham_002c-G_002e-S_002e-132"></a><a name="index-Sevcik_002c-K_002e-C_002e-133"></a>
 
 <h4 class="subsection">6.3.4 Closed Networks</h4>
 
@@ -3047,11 +3058,11 @@
 <p><a name="doc_002dqnclosedsinglemva"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemva-133"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemva-134"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemva-135"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemva-134"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemva-135"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemva-136"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-136"></a><a name="index-closed-network_002c-single-class-137"></a><a name="index-normalization-constant-138"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-137"></a><a name="index-closed-network_002c-single-class-138"></a><a name="index-normalization-constant-139"></a>
 Analyze closed, single class queueing networks using the exact Mean
 Value Analysis (MVA) algorithm. The following queueing disciplines
 are supported: FCFS, LCFS-PR, PS and IS (Infinite Server). This
@@ -3097,8 +3108,11 @@
 <var>X</var><code>(k)*</code><var>S</var><code>(k)</code>.
 
           <br><dt><var>R</var><dd><var>R</var><code>(k)</code> is the response time at center k. 
+The <em>Residence Time</em> at center k is
+<var>R</var><code>(k) * </code><var>V</var><code>(k)</code>. 
 The system response time <var>Rsys</var>
-can be computed as <var>Rsys</var><code> = </code><var>N</var><code>/</code><var>Xsys</var><code> - Z</code>
+can be computed either as <var>Rsys</var><code> = </code><var>N</var><code>/</code><var>Xsys</var><code> - Z</code>
+or as <var>Rsys</var><code> = dot(</code><var>R</var><code>,</code><var>V</var><code>)</code>
 
           <br><dt><var>Q</var><dd><var>Q</var><code>(k)</code> is the average number of requests at center
 k. The number of requests in the system can be computed
@@ -3149,7 +3163,7 @@
 Multichain Queuing Networks</cite>, Journal of the ACM, vol. 27, n. 2, April
 1980, pp. 313&ndash;322. <a href="http://doi.acm.org/10.1145/322186.322195">http://doi.acm.org/10.1145/322186.322195</a>
 
-   <p><a name="index-Reiser_002c-M_002e-139"></a><a name="index-Lavenberg_002c-S_002e-S_002e-140"></a>
+   <p><a name="index-Reiser_002c-M_002e-140"></a><a name="index-Lavenberg_002c-S_002e-S_002e-141"></a>
 This implementation is described in R. Jain , <cite>The Art of Computer
 Systems Performance Analysis</cite>, Wiley, 1991, p. 577.  Multi-server nodes
 <!-- and the computation of @math{G(N)}, -->
@@ -3158,15 +3172,15 @@
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
 1998, Section 8.2.1, "Single Class Queueing Networks".
 
-   <p><a name="index-Jain_002c-R_002e-141"></a><a name="index-Bolch_002c-G_002e-142"></a><a name="index-Greiner_002c-S_002e-143"></a><a name="index-de-Meer_002c-H_002e-144"></a><a name="index-Trivedi_002c-K_002e-145"></a>
+   <p><a name="index-Jain_002c-R_002e-142"></a><a name="index-Bolch_002c-G_002e-143"></a><a name="index-Greiner_002c-S_002e-144"></a><a name="index-de-Meer_002c-H_002e-145"></a><a name="index-Trivedi_002c-K_002e-146"></a>
 <!-- MVA for single class, closed networks with load dependent servers -->
 <a name="doc_002dqnclosedsinglemvald"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvald-146"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V, Z</var>)<var><a name="index-qnclosedsinglemvald-147"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvald-147"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V, Z</var>)<var><a name="index-qnclosedsinglemvald-148"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-148"></a><a name="index-closed-network_002c-single-class-149"></a><a name="index-load_002ddependent-service-center-150"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-149"></a><a name="index-closed-network_002c-single-class-150"></a><a name="index-load_002ddependent-service-center-151"></a>
 Exact MVA algorithm for closed, single class queueing networks
 with load-dependent service centers. This function supports
 FCFS, LCFS-PR, PS and IS nodes. For networks with only fixed-rate
@@ -3224,15 +3238,15 @@
 1998, Section 8.2.4.1, &ldquo;Networks with Load-Deèpendent Service: Closed
 Networks&rdquo;.
 
-   <p><a name="index-Bolch_002c-G_002e-151"></a><a name="index-Greiner_002c-S_002e-152"></a><a name="index-de-Meer_002c-H_002e-153"></a><a name="index-Trivedi_002c-K_002e-154"></a>
+   <p><a name="index-Bolch_002c-G_002e-152"></a><a name="index-Greiner_002c-S_002e-153"></a><a name="index-de-Meer_002c-H_002e-154"></a><a name="index-Trivedi_002c-K_002e-155"></a>
 <!-- CMVA for single class, closed networks with a single load dependent servers -->
 <a name="doc_002dqncmva"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V</var>)<var><a name="index-qncmva-155"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V, Z</var>)<var><a name="index-qncmva-156"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V</var>)<var><a name="index-qncmva-156"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V, Z</var>)<var><a name="index-qncmva-157"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-157"></a><a name="index-CMVA-158"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-158"></a><a name="index-CMVA-159"></a>
 Implementation of the Conditional MVA (CMVA) algorithm, a numerically
 stable variant of MVA for load-dependent servers. CMVA is described
 in G. Casale, <cite>A Note on Stable Flow-Equivalent Aggregation in
@@ -3286,19 +3300,19 @@
 closed networks</cite>. Queueing Syst. Theory Appl., 60:193–202, December
 2008.
 
-   <p><a name="index-Casale_002c-G_002e-159"></a>
+   <p><a name="index-Casale_002c-G_002e-160"></a>
 <!-- Approximate MVA for single class, closed networks -->
 
    <p><a name="doc_002dqnclosedsinglemvaapprox"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvaapprox-160"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemvaapprox-161"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemvaapprox-162"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedsinglemvaapprox-163"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedsinglemvaapprox-164"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvaapprox-161"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemvaapprox-162"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemvaapprox-163"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedsinglemvaapprox-164"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedsinglemvaapprox-165"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-165"></a><a name="index-Approximate-MVA-166"></a><a name="index-Closed-network_002c-single-class-167"></a><a name="index-Closed-network_002c-approximate-analysis-168"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-166"></a><a name="index-Approximate-MVA-167"></a><a name="index-Closed-network_002c-single-class-168"></a><a name="index-Closed-network_002c-approximate-analysis-169"></a>
 Analyze closed, single class queueing networks using the Approximate
 Mean Value Analysis (MVA) algorithm. This function is based on
 approximating the number of customers seen at center k when a
@@ -3377,20 +3391,20 @@
 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In
 particular, see section 6.4.2.2 ("Approximate Solution Techniques").
 
-   <p><a name="index-Lazowska_002c-E_002e-D_002e-169"></a><a name="index-Zahorjan_002c-J_002e-170"></a><a name="index-Graham_002c-G_002e-S_002e-171"></a><a name="index-Sevcik_002c-K_002e-C_002e-172"></a>
+   <p><a name="index-Lazowska_002c-E_002e-D_002e-170"></a><a name="index-Zahorjan_002c-J_002e-171"></a><a name="index-Graham_002c-G_002e-S_002e-172"></a><a name="index-Sevcik_002c-K_002e-C_002e-173"></a>
 
 <!-- MVA for multiple class, closed networks -->
    <p><a name="doc_002dqnclosedmultimva"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S </var>)<var><a name="index-qnclosedmultimva-173"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimva-174"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimva-175"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimva-176"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P</var>)<var><a name="index-qnclosedmultimva-177"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P, m</var>)<var><a name="index-qnclosedmultimva-178"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S </var>)<var><a name="index-qnclosedmultimva-174"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimva-175"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimva-176"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimva-177"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P</var>)<var><a name="index-qnclosedmultimva-178"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P, m</var>)<var><a name="index-qnclosedmultimva-179"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-179"></a><a name="index-closed-network_002c-multiple-classes-180"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-180"></a><a name="index-closed-network_002c-multiple-classes-181"></a>
 Analyze closed, multiclass queueing networks with K service
 centers and C independent customer classes (chains) using the
 Mean Value Analysys (MVA) algorithm.
@@ -3477,8 +3491,10 @@
 defined as <var>U</var><code>(c,k) = </code><var>X</var><code>(c,k)*</code><var>S</var><code>(c,k)</code>.
 
           <br><dt><var>R</var><dd><var>R</var><code>(c,k)</code> is the class c response time at
-center k. The total class c system response time
-can be computed as <code>dot(</code><var>R</var><code>, </code><var>V</var><code>, 2)</code>.
+center k. The class c <em>residence time</em>
+at center k is <var>R</var><code>(c,k) * </code><var>C</var><code>(c,k)</code>. 
+The total class c system response time
+is <code>dot(</code><var>R</var><code>, </code><var>V</var><code>, 2)</code>.
 
           <br><dt><var>Q</var><dd><var>Q</var><code>(c,k)</code> is the average number of
 class c requests at center k. The total number of
@@ -3518,7 +3534,7 @@
 Multichain Queuing Networks</cite>, Journal of the ACM, vol. 27, n. 2, April
 1980, pp. 313&ndash;322. <a href="http://doi.acm.org/10.1145/322186.322195">http://doi.acm.org/10.1145/322186.322195</a>
 
-   <p><a name="index-Reiser_002c-M_002e-181"></a><a name="index-Lavenberg_002c-S_002e-S_002e-182"></a>
+   <p><a name="index-Reiser_002c-M_002e-182"></a><a name="index-Lavenberg_002c-S_002e-S_002e-183"></a>
 This implementation is based on G. Bolch, S. Greiner, H. de Meer and
 K. Trivedi, <cite>Queueing Networks and Markov Chains: Modeling and
 Performance Evaluation with Computer Science Applications</cite>, Wiley,
@@ -3528,18 +3544,18 @@
 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In
 particular, see section 7.4.2.1 ("Exact Solution Techniques").
 
-   <p><a name="index-Bolch_002c-G_002e-183"></a><a name="index-Greiner_002c-S_002e-184"></a><a name="index-de-Meer_002c-H_002e-185"></a><a name="index-Trivedi_002c-K_002e-186"></a><a name="index-Lazowska_002c-E_002e-D_002e-187"></a><a name="index-Zahorjan_002c-J_002e-188"></a><a name="index-Graham_002c-G_002e-S_002e-189"></a><a name="index-Sevcik_002c-K_002e-C_002e-190"></a>
+   <p><a name="index-Bolch_002c-G_002e-184"></a><a name="index-Greiner_002c-S_002e-185"></a><a name="index-de-Meer_002c-H_002e-186"></a><a name="index-Trivedi_002c-K_002e-187"></a><a name="index-Lazowska_002c-E_002e-D_002e-188"></a><a name="index-Zahorjan_002c-J_002e-189"></a><a name="index-Graham_002c-G_002e-S_002e-190"></a><a name="index-Sevcik_002c-K_002e-C_002e-191"></a>
 <!-- Approximate MVA, with Bard-Schweitzer approximation -->
 <a name="doc_002dqnclosedmultimvaapprox"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimvaapprox-191"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimvaapprox-192"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimvaapprox-193"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedmultimvaapprox-194"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedmultimvaapprox-195"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimvaapprox-192"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimvaapprox-193"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimvaapprox-194"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedmultimvaapprox-195"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedmultimvaapprox-196"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-196"></a><a name="index-Approximate-MVA-197"></a><a name="index-Closed-network_002c-multiple-classes-198"></a><a name="index-Closed-network_002c-approximate-analysis-199"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-197"></a><a name="index-Approximate-MVA-198"></a><a name="index-Closed-network_002c-multiple-classes-199"></a><a name="index-Closed-network_002c-approximate-analysis-200"></a>
 Analyze closed, multiclass queueing networks with K service
 centers and C customer classes using the approximate Mean
 Value Analysys (MVA) algorithm.
@@ -3624,12 +3640,12 @@
 proc. 4th Int. Symp. on Modelling and Performance Evaluation of
 Computer Systems, feb. 1979, pp. 51&ndash;62.
 
-   <p><a name="index-Bard_002c-Y_002e-200"></a>
+   <p><a name="index-Bard_002c-Y_002e-201"></a>
 P. Schweitzer, <cite>Approximate Analysis of Multiclass Closed
 Networks of Queues</cite>, Proc. Int. Conf. on Stochastic Control and
 Optimization, jun 1979, pp. 25&ndash;29.
 
-   <p><a name="index-Schweitzer_002c-P_002e-201"></a>
+   <p><a name="index-Schweitzer_002c-P_002e-202"></a>
 This implementation is based on Edward D. Lazowska, John Zahorjan, G. 
 Scott Graham, and Kenneth C. Sevcik, <cite>Quantitative System
 Performance: Computer System Analysis Using Queueing Network Models</cite>,
@@ -3640,7 +3656,7 @@
 described above, as it computes the average response times R
 instead of the residence times.
 
-   <p><a name="index-Lazowska_002c-E_002e-D_002e-202"></a><a name="index-Zahorjan_002c-J_002e-203"></a><a name="index-Graham_002c-G_002e-S_002e-204"></a><a name="index-Sevcik_002c-K_002e-C_002e-205"></a>
+   <p><a name="index-Lazowska_002c-E_002e-D_002e-203"></a><a name="index-Zahorjan_002c-J_002e-204"></a><a name="index-Graham_002c-G_002e-S_002e-205"></a><a name="index-Sevcik_002c-K_002e-C_002e-206"></a>
 
 <h4 class="subsection">6.3.5 Mixed Networks</h4>
 
@@ -3648,9 +3664,9 @@
 <p><a name="doc_002dqnmix"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmix</b> (<var>lambda, N, S, V, m</var>)<var><a name="index-qnmix-206"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmix</b> (<var>lambda, N, S, V, m</var>)<var><a name="index-qnmix-207"></a></var><br>
 <blockquote>
-        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-207"></a><a name="index-mixed-network-208"></a>
+        <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-208"></a><a name="index-mixed-network-209"></a>
 Solution of mixed queueing networks through MVA. The network consists
 of K service centers (single-server or delay centers) and
 C independent customer chains. Both open and closed chains
@@ -3741,14 +3757,14 @@
 Note that in this function we compute the mean response time R
 instead of the mean residence time as in the reference.
 
-   <p><a name="index-Lazowska_002c-E_002e-D_002e-209"></a><a name="index-Zahorjan_002c-J_002e-210"></a><a name="index-Graham_002c-G_002e-S_002e-211"></a><a name="index-Sevcik_002c-K_002e-C_002e-212"></a>
+   <p><a name="index-Lazowska_002c-E_002e-D_002e-210"></a><a name="index-Zahorjan_002c-J_002e-211"></a><a name="index-Graham_002c-G_002e-S_002e-212"></a><a name="index-Sevcik_002c-K_002e-C_002e-213"></a>
 Herb Schwetman, <cite>Implementing the Mean Value Algorithm for the
 Solution of Queueing Network Models</cite>, Technical Report CSD-TR-355,
 Department of Computer Sciences, Purdue University, feb 15, 1982,
 available at
 <a href="http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-355.pdf">http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-355.pdf</a>
 
-   <p><a name="index-Schwetman_002c-H_002e-213"></a>
+   <p><a name="index-Schwetman_002c-H_002e-214"></a>
 
 <div class="node">
 <a name="Algorithms-for-non-Product-form-QNs"></a>
@@ -3767,9 +3783,9 @@
 <p><a name="doc_002dqnmvablo"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmvablo</b> (<var>N, S, M, P</var>)<var><a name="index-qnmvablo-214"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmvablo</b> (<var>N, S, M, P</var>)<var><a name="index-qnmvablo-215"></a></var><br>
 <blockquote>
-        <p><a name="index-queueing-network-with-blocking-215"></a><a name="index-blocking-queueing-network-216"></a><a name="index-closed-network_002c-finite-capacity-217"></a>
+        <p><a name="index-queueing-network-with-blocking-216"></a><a name="index-blocking-queueing-network-217"></a><a name="index-closed-network_002c-finite-capacity-218"></a>
 MVA algorithm for closed queueing networks with blocking. <samp><span class="command">qnmvablo</span></samp>
 computes approximate utilization, response time and mean queue length
 for closed, single class queueing networks with blocking.
@@ -3824,16 +3840,16 @@
 Networks</cite>, IEEE Transactions on Software Engineering, vol. 14, n. 2,
 april 1988, pp. 418&ndash;428.  <a href="http://dx.doi.org/10.1109/32.4663">http://dx.doi.org/10.1109/32.4663</a>
 
-   <p><a name="index-Akyildiz_002c-I_002e-F_002e-218"></a>
+   <p><a name="index-Akyildiz_002c-I_002e-F_002e-219"></a>
 <a name="doc_002dqnmarkov"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>lambda, S, C, P</var>)<var><a name="index-qnmarkov-219"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>lambda, S, C, P, m</var>)<var><a name="index-qnmarkov-220"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>N, S, C, P</var>)<var><a name="index-qnmarkov-221"></a></var><br>
-&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>N, S, C, P, m</var>)<var><a name="index-qnmarkov-222"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>lambda, S, C, P</var>)<var><a name="index-qnmarkov-220"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>lambda, S, C, P, m</var>)<var><a name="index-qnmarkov-221"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>N, S, C, P</var>)<var><a name="index-qnmarkov-222"></a></var><br>
+&mdash; Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>N, S, C, P, m</var>)<var><a name="index-qnmarkov-223"></a></var><br>
 <blockquote>
-        <p><a name="index-closed-network_002c-multiple-classes-223"></a><a name="index-closed-network_002c-finite-capacity-224"></a><a name="index-blocking-queueing-network-225"></a><a name="index-RS-blocking-226"></a>
+        <p><a name="index-closed-network_002c-multiple-classes-224"></a><a name="index-closed-network_002c-finite-capacity-225"></a><a name="index-blocking-queueing-network-226"></a><a name="index-RS-blocking-227"></a>
 Compute utilization, response time, average queue length and
 throughput for open or closed queueing networks with finite capacity. 
 Blocking type is Repetitive-Service (RS). This function explicitly
@@ -3943,9 +3959,9 @@
 <p><a name="doc_002dqnopenab"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>Xu</var>, <var>Rl</var>] = <b>qnopenab</b> (<var>lambda, D</var>)<var><a name="index-qnopenab-227"></a></var><br>
+&mdash; Function File: [<var>Xu</var>, <var>Rl</var>] = <b>qnopenab</b> (<var>lambda, D</var>)<var><a name="index-qnopenab-228"></a></var><br>
 <blockquote>
-        <p><a name="index-bounds_002c-asymptotic-228"></a><a name="index-open-network-229"></a>
+        <p><a name="index-bounds_002c-asymptotic-229"></a><a name="index-open-network-230"></a>
 Compute Asymptotic Bounds for single-class, open Queueing Networks
 with K service centers.
 
@@ -3985,14 +4001,14 @@
 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In
 particular, see section 5.2 ("Asymptotic Bounds").
 
-   <p><a name="index-Lazowska_002c-E_002e-D_002e-230"></a><a name="index-Zahorjan_002c-J_002e-231"></a><a name="index-Graham_002c-G_002e-S_002e-232"></a><a name="index-Sevcik_002c-K_002e-C_002e-233"></a>
+   <p><a name="index-Lazowska_002c-E_002e-D_002e-231"></a><a name="index-Zahorjan_002c-J_002e-232"></a><a name="index-Graham_002c-G_002e-S_002e-233"></a><a name="index-Sevcik_002c-K_002e-C_002e-234"></a>
 <a name="doc_002dqnclosedab"></a>
 
 <div class="defun">
-&mdash; Function File: [<var>Xl</var>, <var>Xu</var>, <var>Rl</var>, <var>Ru</var>] = <b>qnclosedab</b> (<var>N, D</var>)<var><a name="index-qnclosedab-234"></a></var><br>
-&mdash; Function File: [<var>Xl</var>, <var>Xu</var>, <var>Rl</var>, <var>Ru</var>] = <b>qnclosedab</b> (<var>N, D, Z</var>)<var><a name="index-qnclosedab-235"></a></var><br>
+&mdash; Function File: [<var>Xl</var>, <var>Xu</var>, <var>Rl</var>, <var>Ru</var>] = <b>qnclosedab</b> (<var>N, D</var>)<var><a name="index-qnclosedab-235"></a></var><br>
+&mdash; Function File: [<var>Xl</var>, <var>Xu</var>, <var>Rl</var>, <var>Ru</var>] = <b>qnclosedab</b> (<var>N, D, Z</var>)<var><a name="index-qnclosedab-236"></a></var><br>
 <blockquote>
-        <p><a name="index-bounds_002c-asymptotic-236"></a><a name="index-closed-network-237"></a>
+        <p><a name="index-bounds_002c-asymptotic-237"></a><a name="index-closed-network-238"></a>
 Compute Asymptotic Bounds for single-class, closed Queueing Networks
 wit...
 
[truncated message content]

[Octave-cvsupdate] SF.net SVN: octave:[9807] trunk/octave-forge/main/queueing

From: <mma...@us...> - 2012-03-10 16:00:52

Revision: 9807
          http://octave.svn.sourceforge.net/octave/?rev=9807&view=rev
Author:   mmarzolla
Date:     2012-03-10 16:00:45 +0000 (Sat, 10 Mar 2012)
Log Message:
-----------
Bug fix and enhancements in ctmc_exps()

Modified Paths:
--------------
    trunk/octave-forge/main/queueing/ChangeLog
    trunk/octave-forge/main/queueing/NEWS
    trunk/octave-forge/main/queueing/inst/ctmc_exps.m
    trunk/octave-forge/main/queueing/inst/ctmc_mtta.m

Modified: trunk/octave-forge/main/queueing/ChangeLog
===================================================================
--- trunk/octave-forge/main/queueing/ChangeLog	2012-03-10 12:44:08 UTC (rev 9806)
+++ trunk/octave-forge/main/queueing/ChangeLog	2012-03-10 16:00:45 UTC (rev 9807)
@@ -1,3 +1,13 @@
+2012-02-XX Moreno Marzolla <mar...@cs...>
+
+	* Version 1.0.X released
+	* Fixed bug in qnvisits() which made the function behave incorrectly
+	  under particular degenerate cases.
+	* Fixed bug in ctmc_exps() (wrong initial value in call to lsode)
+	* Function ctmc_exps() can now also compute the expected sojourn time
+	  until absorption for absorbing CTMCs.
+	* Miscellaneous fixes/improvements to the documentation
+
 2012-02-04 Moreno Marzolla <mar...@cs...>
 
 	* Version 1.0.0 released under the name "queueing" (initial

Modified: trunk/octave-forge/main/queueing/NEWS
===================================================================
--- trunk/octave-forge/main/queueing/NEWS	2012-03-10 12:44:08 UTC (rev 9806)
+++ trunk/octave-forge/main/queueing/NEWS	2012-03-10 16:00:45 UTC (rev 9807)
@@ -1,3 +1,8 @@
+Summary of important user-visible changes for queueing-1.0.X
+
+** Function ctmc_exps() can now compute the expected sojourn time
+   until absorption for absorming CTMC
+
 Summary of important user-visible changes for queueing-1.0.0
 ------------------------------------------------------------------------------
 

Modified: trunk/octave-forge/main/queueing/inst/ctmc_exps.m
===================================================================
--- trunk/octave-forge/main/queueing/inst/ctmc_exps.m	2012-03-10 12:44:08 UTC (rev 9806)
+++ trunk/octave-forge/main/queueing/inst/ctmc_exps.m	2012-03-10 16:00:45 UTC (rev 9807)
@@ -17,24 +17,27 @@
 
 ## -*- texinfo -*-
 ##
-## @deftypefn {Function File} {@var{L} =} ctmc_exps (@var{Q}, @var{tt}, @var{p})
+## @deftypefn {Function File} {@var{L} =} ctmc_exps (@var{Q}, @var{tt}, @var{p} )
+## @deftypefnx {Function File} {@var{L} =} ctmc_exps (@var{Q}, @var{p})
 ##
 ## @cindex Markov chain, continuous time
 ## @cindex Expected sojourn time
 ##
-## Compute the expected total time @code{@var{L}(t,j)} spent in state
-## @math{j} during the time interval @code{[0,@var{tt}(t))}, assuming
-## that at time 0 the state occupancy probability was @var{p}.
+## With three arguments, compute the expected time @code{@var{L}(t,j)}
+## spent in each state @math{j} during the time interval
+## @code{[0,@var{tt}(t))}, assuming that at time 0 the state occupancy
+## probability was @var{p}. With two arguments, compute the expected
+## time @code{@var{L}(j}} spent in each state @math{j} until absorption.
 ##
 ## @strong{INPUTS}
 ##
 ## @table @var
 ##
 ## @item Q
-## Infinitesimal generator matrix. @code{@var{Q}(i,j)} is the transition
-## rate from state @math{i} to state @math{j},
-## @math{1 @leq{} i \neq j @leq{} N}. The matrix @var{Q} must also satisfy the
-## condition @code{sum(@var{Q},2) == 0}
+## @math{N \times N} infinitesimal generator matrix. @code{@var{Q}(i,j)}
+## is the transition rate from state @math{i} to state @math{j}, @math{1
+## @leq{} i \neq j @leq{} N}. The matrix @var{Q} must also satisfy the
+## condition @math{\sum_{j=1}^N Q_{ij} = 0}.
 ##
 ## @item tt
 ## This parameter is a vector used for numerical integration. The first
@@ -43,8 +46,9 @@
 ## @math{[0,t)} of interest (@code{@var{tt}(end) == @math{t}}).
 ##
 ## @item p
-## @code{@var{p}(i)} is the probability that at time 0 the system was in
-## state @math{i}, for all @math{i = 1, @dots{}, N}
+## Initial occupancy probability vector; @code{@var{p}(i)} is the
+## probability the system is in state @math{i} at time 0, @math{i = 1,
+## @dots{}, N}
 ##
 ## @end table
 ##
@@ -53,8 +57,14 @@
 ## @table @var
 ##
 ## @item L
-## @code{@var{L}(t,j)} is the expected time spent in state @math{j}
-## during the interval @code{[0,@var{tt}(t))}. @code{1 @leq{} @var{t} @leq{} length(@var{tt})}
+## If this function is called with three arguments, @var{L} is a matrix
+## of size @code{[length(@var{tt}), N]} where @code{@var{L}(t,j)} is the
+## expected time spent in state @math{j} during the interval
+## @code{[0,@var{tt}(t)]}. If this function is called with two
+## arguments, @var{L} is a vector with @math{N} elements where
+## @code{@var{L}(j)} is the expected time spent in state @math{j} until
+## absorption, if @math{j} is a transient state. If @math{j}
+## is an absorbing state, @code{@var{L}(j) = 0}.
 ##
 ## @end table
 ##
@@ -63,11 +73,11 @@
 ## Author: Moreno Marzolla <marzolla(at)cs.unibo.it>
 ## Web: http://www.moreno.marzolla.name/
 
-function L = ctmc_exps( Q, tt, p )
+function L = ctmc_exps( Q, varargin )
 
   persistent epsilon = 10*eps;
 
-  if ( nargin != 3 )
+  if ( nargin < 2 || nargin > 3 )
     print_usage();
   endif
 
@@ -77,16 +87,56 @@
   ( norm( sum(Q,2), "inf" ) < epsilon ) || \
       error( "Q is not an infinitesimal generator matrix" );
 
+  if ( nargin == 2 )
+    p = varargin{1};
+  else
+    tt = varargin{1};
+    p = varargin{2};
+  endif
+
   ( isvector(p) && length(p) == size(Q,1) && all(p>=0) && abs(sum(p)-1.0)<epsilon ) || \
       usage( "p must be a probability vector" );
 
-  ( isvector(tt) && abs(tt(1)) < epsilon ) || \
-      usage( "tt must be a vector, and tt(1) must be 0.0" );
-  tt = tt(:)'; # make tt a row vector
-  p = p(:)'; # make p a row vector
-  ff = @(x,t) (x(:)'*Q+p);
-  fj = @(x,t) (Q);
-  L = lsode( {ff, fj}, p, tt );
+  if ( nargin == 3 ) 
+    ( isvector(tt) && abs(tt(1)) < epsilon ) || \
+	usage( "tt must be a vector, and tt(1) must be 0.0" );
+    tt = tt(:)'; # make tt a row vector
+    p = p(:)'; # make p a row vector
+    ff = @(x,t) (x(:)'*Q+p);
+    fj = @(x,t) (Q);
+    L = lsode( {ff, fj}, zeros(size(p)), tt );
+  else
+#{
+    ## F(t) are the transient state occupancy probabilities at time t.
+    ## It is known that F(t) = p*expm(Q*t) (see function ctmc()).
+    ## The expected times spent in each state until absorption can
+    ## be computed as the integral of F(t) from t=0 to t=inf
+    F = @(t) (p*expm(Q*t)); ## FIXME: this must be restricted to transient states ONLY!!!!
+
+    ## Since function quadv does not support infinite integration
+    ## limits, we define a new function G(u) = F(tan(pi/2*u)) such that
+    ## the integral of G(u) on [0,1] is the integral of F(t) on [0,
+    ## +inf].
+    G = @(u) (F(tan(pi/2*u))*pi/2*(1+tan(pi/2*u)**2));
+
+    L = quadv(G,0,1);
+#}
+    ## Find nonzero rows. Nonzero rows correspond to transient states,
+    ## while zero rows are absorbing states. If there are no zero rows,
+    ## then the Markov chain does not contain absorbing states and we
+    ## raise an error
+    N = rows(Q);
+    nzrows = find( any( abs(Q) > epsilon, 2 ) );
+    if ( length( nzrows ) == N )
+      error( "There are no absorbing states" );
+    endif
+    
+    QN = Q(nzrows,nzrows);
+    pN = p(nzrows);
+    LN = -pN*inv(QN);
+    L = zeros(1,N);
+    L(nzrows) = LN;
+  endif
 endfunction
 
 %!demo
@@ -99,10 +149,25 @@
 %! tt = linspace(0,10,100);
 %! p0 = zeros(1,N); p0(1)=1;
 %! L = ctmc_exps(Q,tt,p0);
+%! #L2 = 0*L;
+%! #for i=1:length(tt)
+%! #  L2(i,:) = quadv( @(t) (p0*expm(Q*t)) , 0, tt(i) );
+%! #endfor
 %! plot( tt, L(:,1), ";State 1;", "linewidth", 2, \
+%! #      tt, L2(:,1), "+;State 1 (quadv);", "markersize", 8, \
 %!       tt, L(:,2), ";State 2;", "linewidth", 2, \
 %!       tt, L(:,3), ";State 3;", "linewidth", 2, \
 %!       tt, L(:,4), ";State 4 (absorbing);", "linewidth", 2);
 %! legend("location","northwest");
 %! xlabel("Time");
 %! ylabel("Expected sojourn time");
+
+%!demo
+%! lambda = 0.5;
+%! N = 4;
+%! birth = lambda*linspace(1,N-1,N-1);
+%! death = 0*birth;
+%! Q = diag(birth,1)+diag(death,-1);
+%! Q -= diag(sum(Q,2));
+%! p0 = zeros(1,N); p0(1)=1;
+%! L = ctmc_exps(Q,p0)

Modified: trunk/octave-forge/main/queueing/inst/ctmc_mtta.m
===================================================================
--- trunk/octave-forge/main/queueing/inst/ctmc_mtta.m	2012-03-10 12:44:08 UTC (rev 9806)
+++ trunk/octave-forge/main/queueing/inst/ctmc_mtta.m	2012-03-10 16:00:45 UTC (rev 9807)
@@ -22,9 +22,10 @@
 ## @cindex Markov chain, continuous time
 ## @cindex Mean time to absorption
 ##
-## Compute the Mean-Time to Absorption (MTTA) starting from initial
-## occupancy probability @var{p} at time 0. If there are no absorbing
-## states, this function fails with an error.
+## Compute the Mean-Time to Absorption (MTTA) of the CTMC described by
+## the infinitesimal generator matrix @var{Q}, starting from initial
+## occupancy probability @var{p}. If there are no absorbing states, this
+## function fails with an error.
 ##
 ## @strong{INPUTS}
 ##
@@ -76,18 +77,7 @@
   ( isvector(p) && length(p) == N && all(p>=0) && abs(sum(p)-1.0)<epsilon ) || \
       usage( "p must be a probability vector" );
 
-  ## Find nonzero rows. Nonzero rows correspond to transient states,
-  ## while zero rows are absorbing states. If there are no zero rows,
-  ## then the Markov chain does not contain absorbing states and we
-  ## raise an error
-  nzrows = find( any( abs(Q) > epsilon, 2 ) );
-  if ( length( nzrows ) == N )
-    error( "There are no absorbing states" );
-  endif
-
-  QN = Q(nzrows,nzrows);
-  pN = p(nzrows);
-  L = -pN*inv(QN);
+  L = ctmc_exps(Q,p);
   t = sum(L);
 endfunction
 %!test
@@ -122,7 +112,7 @@
 %! death = [ 3 4 5 ] * mu;
 %! Q = diag(death,-1);
 %! Q -= diag(sum(Q,2));
-%! t = ctmc_mtta(Q,[0 0 0 1])
+%! [t L] = ctmc_mtta(Q,[0 0 0 1])
 
 %!demo
 %! N = 100;

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[Octave-cvsupdate] SF.net SVN: octave:[9806] trunk/octave-forge/main/signal/inst/rceps.m

From: <jpi...@us...> - 2012-03-10 12:44:14

Revision: 9806
          http://octave.svn.sourceforge.net/octave/?rev=9806&view=rev
Author:   jpicarbajal
Date:     2012-03-10 12:44:08 +0000 (Sat, 10 Mar 2012)
Log Message:
-----------
signal: adding tolerance to test of transposed. Potntially a bug.

Modified Paths:
--------------
    trunk/octave-forge/main/signal/inst/rceps.m

Modified: trunk/octave-forge/main/signal/inst/rceps.m
===================================================================
--- trunk/octave-forge/main/signal/inst/rceps.m	2012-03-10 12:40:15 UTC (rev 9805)
+++ trunk/octave-forge/main/signal/inst/rceps.m	2012-03-10 12:44:08 UTC (rev 9806)
@@ -73,8 +73,9 @@
 %! x=randn(256,1);
 %! [y, xm] = rceps(x);
 %! [yt, xmt] = rceps(x.');
-%! assert(yt.', y); 
-%! assert(xmt.', xm);
+%! tol = 1e-14;
+%! assert(yt.', y, tol);
+%! assert(xmt.', xm, tol);
 
 %!demo
 %! f0=70; Fs=10000;           # 100 Hz fundamental, 10kHz sampling rate
@@ -87,7 +88,7 @@
 %! figure(1);
 %! subplot(311);
 %!    auplot(x,Fs,'b',';signal;');
-%!    hold on; auplot(xm,Fs,'g',';reconstruction;'); 
+%!    hold on; auplot(xm,Fs,'g',';reconstruction;');
 %!    hold off;
 %! subplot(312);
 %!    axis("ticy");

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[Octave-cvsupdate] SF.net SVN: octave:[9805] trunk/octave-forge/main/signal/inst

From: <jpi...@us...> - 2012-03-10 12:40:23

Revision: 9805
          http://octave.svn.sourceforge.net/octave/?rev=9805&view=rev
Author:   jpicarbajal
Date:     2012-03-10 12:40:15 +0000 (Sat, 10 Mar 2012)
Log Message:
-----------
signal: Applying patches from devian packaging group. Generator Rafael Laboissiere ra...@la...

Modified Paths:
--------------
    trunk/octave-forge/main/signal/inst/filtfilt.m
    trunk/octave-forge/main/signal/inst/fir1.m
    trunk/octave-forge/main/signal/inst/fir2.m
    trunk/octave-forge/main/signal/inst/impinvar.m
    trunk/octave-forge/main/signal/inst/invimpinvar.m
    trunk/octave-forge/main/signal/inst/residued.m

Modified: trunk/octave-forge/main/signal/inst/filtfilt.m
===================================================================
--- trunk/octave-forge/main/signal/inst/filtfilt.m	2012-03-10 04:18:08 UTC (rev 9804)
+++ trunk/octave-forge/main/signal/inst/filtfilt.m	2012-03-10 12:40:15 UTC (rev 9805)
@@ -105,11 +105,11 @@
 %! y = filtfilt(b, a, r+s);
 %! assert (size(r), size(y));
 %! assert (mean(abs(y)) < 1e3);
-%! assert (corrcoef(s(250:750), y(250:750)) > .95)
+%! assert (corr(s(250:750), y(250:750)) > .95)
 %! [b,a] = butter(2, [4e-4 8e-2]);
 %! yb = filtfilt(b, a, r+s);
 %! assert (mean(abs(yb)) < 1e3);
-%! assert (corrcoef(y, yb) > .99)
+%! assert (corr(y, yb) > .99)
 
 %!test
 %! randn('state',0);

Modified: trunk/octave-forge/main/signal/inst/fir1.m
===================================================================
--- trunk/octave-forge/main/signal/inst/fir1.m	2012-03-10 04:18:08 UTC (rev 9804)
+++ trunk/octave-forge/main/signal/inst/fir1.m	2012-03-10 12:40:15 UTC (rev 9805)
@@ -92,7 +92,7 @@
   if rem(n,2)==1 && m(2*bands)==1, 
     warning("n must be even for highpass and bandstop filters. Incrementing.");
     n = n+1;
-    if isvector(window) && isreal(window)
+    if isvector(window) && isreal(window) && !ischar(window)
       ## Extend the window using interpolation
       M = length(window);
       if M == 1,

Modified: trunk/octave-forge/main/signal/inst/fir2.m
===================================================================
--- trunk/octave-forge/main/signal/inst/fir2.m	2012-03-10 04:18:08 UTC (rev 9804)
+++ trunk/octave-forge/main/signal/inst/fir2.m	2012-03-10 12:40:15 UTC (rev 9805)
@@ -72,7 +72,7 @@
   if length(ramp_n)>1, w=ramp_n; ramp_n=grid_n/20; endif
   if nargin < 6, window=w; endif
   if isempty(window), window=hamming(n+1); endif
-  if !isreal(window), window=feval(window, n+1); endif
+  if !isreal(window) || ischar(window), window=feval(window, n+1); endif
   if length(window) != n+1, usage("window must be of length n+1"); endif
 
   ## make sure grid is big enough for the window

Modified: trunk/octave-forge/main/signal/inst/impinvar.m
===================================================================
--- trunk/octave-forge/main/signal/inst/impinvar.m	2012-03-10 04:18:08 UTC (rev 9804)
+++ trunk/octave-forge/main/signal/inst/impinvar.m	2012-03-10 12:40:15 UTC (rev 9805)
@@ -123,7 +123,7 @@
 %!
 %!  % calculate impulse response of continuous time system
 %!  % at discrete time intervals 1/fs
-%!  ys=impulse(s,1,(n-1)/fs,n);
+%!  ys=impulse(s,(n-1)/fs,1/fs)';
 %!
 %!  % impulse response of discrete time system
 %!  yz=filter(bz,az,[1 zeros(1,n-1)]);

Modified: trunk/octave-forge/main/signal/inst/invimpinvar.m
===================================================================
--- trunk/octave-forge/main/signal/inst/invimpinvar.m	2012-03-10 04:18:08 UTC (rev 9804)
+++ trunk/octave-forge/main/signal/inst/invimpinvar.m	2012-03-10 12:40:15 UTC (rev 9805)
@@ -126,7 +126,7 @@
 %!
 %!  % calculate impulse response of continuous time system
 %!  % at discrete time intervals 1/fs
-%!  ys=impulse(s,1,(n-1)/fs,n);
+%!  ys=impulse(s,(n-1)/fs,1/fs)';
 %!
 %!  % impulse response of discrete time system
 %!  yz=filter(bz,az,[1 zeros(1,n-1)]);

Modified: trunk/octave-forge/main/signal/inst/residued.m
===================================================================
--- trunk/octave-forge/main/signal/inst/residued.m	2012-03-10 04:18:08 UTC (rev 9804)
+++ trunk/octave-forge/main/signal/inst/residued.m	2012-03-10 12:40:15 UTC (rev 9805)
@@ -15,9 +15,9 @@
 
 %% -*- texinfo -*-
 %% @deftypefn {Function File} {[@var{r}, @var{p}, @var{f}, @var{m}] =} residued (@var{B}, @var{A})
-%% Compute the partial fraction expansion (PFE) of filter 
+%% Compute the partial fraction expansion (PFE) of filter
 %% @math{H(z) = B(z)/A(z)}.
-%% In the usual PFE function @code{residuez}, 
+%% In the usual PFE function @code{residuez},
 %% the IIR part (poles @var{p} and residues
 %% @var{r}) is driven @emph{in parallel} with the FIR part (@var{f}).
 %% In this variant (@code{residued}) the IIR part is driven
@@ -26,7 +26,7 @@
 %%
 %% INPUTS:
 %% @var{B} and @var{A} are vectors specifying the digital filter @math{H(z) = B(z)/A(z)}.
-%% Say @code{help filter} for documentation of the @var{B} and @var{A} 
+%% Say @code{help filter} for documentation of the @var{B} and @var{A}
 %% filter coefficients.
 %%
 %% RETURNED:
@@ -42,9 +42,9 @@
 %%   Say @code{test residued verbose} to see a number of examples.
 %% @end example
 %%
-%% For the theory of operation, see 
+%% For the theory of operation, see
 %% @indicateurl{http://ccrma.stanford.edu/~jos/filters/residued.html}
-%% 
+%%
 %% @seealso{residue residued}
 %% @end deftypefn
 
@@ -60,21 +60,21 @@
   %
   % This is the same result as returned by RESIDUEZ.
   % Otherwise, the FIR part f will be nonempty,
-  % and the returned filter is 
+  % and the returned filter is
   %
   % H(z) = f(1) + f(2)/z + f(3)/z^2 + ... + f(nf)/z^M + R(z)/z^M
   %
   % where R(z) is the parallel one-pole filter bank defined above,
   % and M is the order of F(z) = length(f)-1 = nb-na.
-  % 
+  %
   % Note, in particular, that the impulse-response of the parallel
   % (complex) one-pole filter bank starts AFTER that of the the FIR part.
   % In the result returned by RESIDUEZ, R(z) is not divided by z^M,
   % so its impulse response starts at time 0 in parallel with f(n).
   %
   % J.O. Smith, 9/19/05
-    
-  if nargin==3, 
+
+  if nargin==3,
     warning("tolerance ignored");
   end
   NUM = b(:)';
@@ -91,7 +91,7 @@
   if f2, error('f2 not empty as expected'); end
 end
 
-%!test 
+%!test
 %! B=1; A=[1 -1];
 %! [r,p,f,m] = residued(B,A);
 %! assert({r,p,f,m},{1,1,[],1},100*eps);
@@ -99,38 +99,38 @@
 %! assert({r,p,f,m},{r2,p2,f2,m2},100*eps);
 % residuez and residued should be identical when length(B)<length(A)
 
-%!test 
+%!test
 %! B=[1 -2 1]; A=[1 -1];
 %! [r,p,f,m] = residued(B,A);
 %! assert({r,p,f,m},{0,1,[1 -1],1},100*eps);
 
-%!test 
+%!test
 %! B=[1 -2 1]; A=[1 -0.5];
 %! [r,p,f,m] = residued(B,A);
 %! assert({r,p,f,m},{0.25,0.5,[1 -1.5],1},100*eps);
 
-%!test 
+%!test
 %! B=1; A=[1 -0.75 0.125];
 %! [r,p,f,m] = residued(B,A);
 %! [r2,p2,f2,m2] = residuez(B,A);
 %! assert({r,p,f,m},{r2,p2,f2,m2},100*eps);
 % residuez and residued should be identical when length(B)<length(A)
 
-%!test 
+%!test
 %! B=1; A=[1 -2 1];
 %! [r,p,f,m] = residued(B,A);
 %! [r2,p2,f2,m2] = residuez(B,A);
 %! assert({r,p,f,m},{r2,p2,f2,m2},100*eps);
 % residuez and residued should be identical when length(B)<length(A)
 
-%!test 
+%!test
 %! B=[6,2]; A=[1 -2 1];
 %! [r,p,f,m] = residued(B,A);
 %! [r2,p2,f2,m2] = residuez(B,A);
 %! assert({r,p,f,m},{r2,p2,f2,m2},100*eps);
 % residuez and residued should be identical when length(B)<length(A)
 
-%!test 
+%!test
 %! B=[1 1 1]; A=[1 -2 1];
 %! [r,p,f,m] = residued(B,A);
 %! assert(r,[0;3],1e-7);
@@ -138,7 +138,7 @@
 %! assert(f,1,100*eps);
 %! assert(m,[1;2],100*eps);
 
-%!test 
+%!test
 %! B=[2 6 6 2]; A=[1 -2 1];
 %! [r,p,f,m] = residued(B,A);
 %! assert(r,[8;16],3e-7);
@@ -146,7 +146,7 @@
 %! assert(f,[2,10],100*eps);
 %! assert(m,[1;2],100*eps);
 
-%!test 
+%!test
 %! B=[1,6,2]; A=[1 -2 1];
 %! [r,p,f,m] = residued(B,A);
 %! assert(r,[-1;9],3e-7);
@@ -154,8 +154,8 @@
 %! assert(f,1,100*eps);
 %! assert(m,[1;2],100*eps);
 
-%!test 
+%!test
 %! B=[1 0 0 0 1]; A=[1 0 0 0 -1];
 %! [r,p,f,m] = residued(B,A);
-%! assert({r,p,f,m},{[-1/2;1/2;-j/2;j/2],[-1;1;-j;j],1,[1;1;1;1]},100*eps);
+%! assert({r,p,f,m},{[-j/2;j/2;1/2;-1/2],[-j;j;1;-1],1,[1;1;1;1]},100*eps);
 %  Verified in maxima: ratsimp(%I/2/(1-%I * d) - %I/2/(1+%I * d)); etc.

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[Octave-cvsupdate] SF.net SVN: octave:[9804] trunk/octave-forge/main/geometry/inst/io/private/ pointGeo.m

From: <jpi...@us...> - 2012-03-10 04:18:15

Revision: 9804
          http://octave.svn.sourceforge.net/octave/?rev=9804&view=rev
Author:   jpicarbajal
Date:     2012-03-10 04:18:08 +0000 (Sat, 10 Mar 2012)
Log Message:
-----------
geometry: write points in mesh file with higher resolution

Modified Paths:
--------------
    trunk/octave-forge/main/geometry/inst/io/private/pointGeo.m

Modified: trunk/octave-forge/main/geometry/inst/io/private/pointGeo.m
===================================================================
--- trunk/octave-forge/main/geometry/inst/io/private/pointGeo.m	2012-03-09 20:03:49 UTC (rev 9803)
+++ trunk/octave-forge/main/geometry/inst/io/private/pointGeo.m	2012-03-10 04:18:08 UTC (rev 9804)
@@ -1,5 +1,5 @@
 %% Copyright (c) 2010 Juan Pablo Carbajal <car...@if...>
-%% 
+%%
 %%    This program is free software: you can redistribute it and/or modify
 %%    it under the terms of the GNU General Public License as published by
 %%    the Free Software Foundation, either version 3 of the License, or
@@ -17,9 +17,9 @@
 %% @deftypefn {Function File} @var{str} =  poointGeo (@var{n}, @var{xyz}, @var{l})
 %% Generates a string for Gmsh Point format.
 %%
-%% Gmsh's simplest `elementary entity', a `Point'. A Point is defined by a list 
-%% of five numbers: @var{n} the identificator, @var{xyz} three coordinates (X, Y 
-%% and Z), and a characteristic length @var{l} that sets the target element size 
+%% Gmsh's simplest `elementary entity', a `Point'. A Point is defined by a list
+%% of five numbers: @var{n} the identificator, @var{xyz} three coordinates (X, Y
+%% and Z), and a characteristic length @var{l} that sets the target element size
 %% at the point:
 %% The distribution of the mesh element sizes is then obtained by
 %% interpolation of these characteristic lengths throughout the
@@ -28,5 +28,5 @@
 %% @end deftypefn
 
 function str = pointGeo(n,xyz,l)
-    str = sprintf('Point(%d) = {%f,%f,%f,%f};\n',n,xyz,l);
+    str = sprintf('Point(%d) = {%.16g,%.16g,%.16g,%.16g};\n',n,xyz,l);
 end

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[Octave-cvsupdate] SF.net SVN: octave:[9803] trunk/octave-forge/extra/NaN/inst/cov.m

From: <sch...@us...> - 2012-03-09 20:03:56

Revision: 9803
          http://octave.svn.sourceforge.net/octave/?rev=9803&view=rev
Author:   schloegl
Date:     2012-03-09 20:03:49 +0000 (Fri, 09 Mar 2012)
Log Message:
-----------
explain relationship to corrcoef in help text

Modified Paths:
--------------
    trunk/octave-forge/extra/NaN/inst/cov.m

Property Changed:
----------------
    trunk/octave-forge/extra/NaN/inst/cov.m

Modified: trunk/octave-forge/extra/NaN/inst/cov.m
===================================================================
--- trunk/octave-forge/extra/NaN/inst/cov.m	2012-03-09 16:13:10 UTC (rev 9802)
+++ trunk/octave-forge/extra/NaN/inst/cov.m	2012-03-09 20:03:49 UTC (rev 9803)
@@ -4,6 +4,14 @@
 % NaN's are skipped, NaN do not result in a NaN output. 
 % The output gives NaN only if there are insufficient input data
 % The mean is removed from the data. 
+% 
+% Remark: for data contains missing values, the resulting 
+% matrix might not be positiv definite, and its elements have magnitudes
+% larger than one. This ill-behavior is more likely for small sample 
+% sizes, but there is no garantee that the result "behaves well" for larger
+% sample sizes. If you want the a "well behaved" result (i.e. positive 
+% definiteness and magnitude of elements not larger than 1), use CORRCOEF. 
+% However, COV is faster than CORRCOEF and might be good enough in some cases.
 %
 % C = COV(X [,Mode]);
 %      calculates the (auto-)correlation matrix of X
@@ -26,7 +34,7 @@
 % http://mathworld.wolfram.com/Covariance.html
 
 %	$Id$
-%	Copyright (C) 2000-2003,2005,2009 by Alois Schloegl <alo...@gm...>	
+%	Copyright (C) 2000-2003,2005,2009,2011,2012 by Alois Schloegl <alo...@is...>	
 %       This function is part of the NaN-toolbox 
 %       http://pub.ist.ac.at/~schloegl/matlab/NaN/
 


Property changes on: trunk/octave-forge/extra/NaN/inst/cov.m
___________________________________________________________________
Modified: svn:keywords
   - Id Revision
   + Id

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[Octave-cvsupdate] SF.net SVN: octave:[9802] trunk/octave-forge/extra/quaternion_oo/inst/@ quaternion/subsref.m

From: <par...@us...> - 2012-03-09 16:13:16

Revision: 9802
          http://octave.svn.sourceforge.net/octave/?rev=9802&view=rev
Author:   paramaniac
Date:     2012-03-09 16:13:10 +0000 (Fri, 09 Mar 2012)
Log Message:
-----------
quaternion_oo: enable subsref stuff like q(1:2,2).w(2)

Modified Paths:
--------------
    trunk/octave-forge/extra/quaternion_oo/inst/@quaternion/subsref.m

Modified: trunk/octave-forge/extra/quaternion_oo/inst/@quaternion/subsref.m
===================================================================
--- trunk/octave-forge/extra/quaternion_oo/inst/@quaternion/subsref.m	2012-03-09 11:51:33 UTC (rev 9801)
+++ trunk/octave-forge/extra/quaternion_oo/inst/@quaternion/subsref.m	2012-03-09 16:13:10 UTC (rev 9802)
@@ -1,4 +1,4 @@
-## Copyright (C) 2010, 2011   Lukas F. Reichlin
+## Copyright (C) 2010, 2011, 2012   Lukas F. Reichlin
 ##
 ## This program is free software: you can redistribute it and/or modify
 ## it under the terms of the GNU General Public License as published by
@@ -18,10 +18,15 @@
 
 ## Author: Lukas Reichlin <luk...@gm...>
 ## Created: May 2010
-## Version: 0.3
+## Version: 0.4
 
 function ret = subsref (q, s)
 
+  if (numel (s) == 0)
+    ret = q;
+    return;
+  endif
+
   switch (s(1).type)
     case "."                                # q.w
       switch (tolower (s(1).subs))
@@ -41,11 +46,12 @@
       endswitch
 
     case "()"                               # q(...)
-      w = subsref (q.w, s);
-      x = subsref (q.x, s);
-      y = subsref (q.y, s);
-      z = subsref (q.z, s);
-      ret = quaternion (w, x, y, z);
+      w = subsref (q.w, s(1));
+      x = subsref (q.x, s(1));
+      y = subsref (q.y, s(1));
+      z = subsref (q.z, s(1));
+      tmp = quaternion (w, x, y, z);
+      ret = subsref (tmp, s(2:end));
       
     otherwise
       error ("quaternion: invalid subscript type '%s'", s(1).type);

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[Octave-cvsupdate] SF.net SVN: octave:[9801] trunk/octave-forge/main/miscellaneous/inst/map.m

From: <jpi...@us...> - 2012-03-09 11:51:44

Revision: 9801
          http://octave.svn.sourceforge.net/octave/?rev=9801&view=rev
Author:   jpicarbajal
Date:     2012-03-09 11:51:33 +0000 (Fri, 09 Mar 2012)
Log Message:
-----------
miscellaneous: Ready for release...i guess. Added note on coypright and removed old code

Modified Paths:
--------------
    trunk/octave-forge/main/miscellaneous/inst/map.m

Modified: trunk/octave-forge/main/miscellaneous/inst/map.m
===================================================================
--- trunk/octave-forge/main/miscellaneous/inst/map.m	2012-03-09 11:21:27 UTC (rev 9800)
+++ trunk/octave-forge/main/miscellaneous/inst/map.m	2012-03-09 11:51:33 UTC (rev 9801)
@@ -1,6 +1,7 @@
 ## Copyright (C) 2003 Tomer Altman <ta...@lb...>
 ## Copyright (C) 2007 Muthiah Annamalai <mut...@ma...>
 ## Copyright (C) 2012 Carnë Draug <car...@gm...>
+## Copyright (C) 2012 Juan Pablo Carbajal <car...@if...>
 ##
 ## This program is free software; you can redistribute it and/or modify it under
 ## the terms of the GNU General Public License as published by the Free Software
@@ -75,59 +76,10 @@
     error ("fun_handle must either be a function handle or the name of a function");
   endif
 
-#  nRows = rows    (data_struct);
-#  nCols = columns (data_struct);
-
-#  otherdata = length (varargin);
-#  val       = cell (1, otherdata+1);
-#  val (:)   = 0;
-
   if (iscell (data_struct))
-# KaKiLa Fri 09 Mar 2012 09:47:52 AM CET
-# Works even if varargin is empty
     return_type = cellfun (fun_handle, data_struct,varargin{:});
-#    return_type = cell (nRows, nCols);
-#    if (otherdata >= 1)
-#      return_type = cellfun (fun_handle, data_struct,varargin{:});
-#      for i = 1:nRows
-#        for j = 1:nCols
-#         val {1} = data_struct {i, j};
-#          for idx = 2:otherdata+1
-#            val {idx} = varargin {idx-1}{i,j};
-#          endfor
-#            return_type {i,j} = apply (fun_handle, val);
-#        endfor
-#      endfor
-#    else
-#       return_type = cellfun (fun_handle, data_struct);
-#      for i = 1:nRows
-#        for j = 1:nCols
-#          return_type {i,j} = fun_handle (data_struct {i,j});
-#        endfor
-#      endfor
-#    endif
   else
-# KaKiLa Fri 09 Mar 2012 09:47:52 AM CET
-# Works even if varargin is empty
     return_type = arrayfun (fun_handle, data_struct,varargin{:});
-#    return_type = zeros (nRows, nCols);
-#    if (otherdata >= 1)
-#      for i = 1:nRows
-#        for j = 1:nCols
-#          val {1} = data_struct (i,j);
-#          for idx = 2:otherdata+1
-#            val {idx} = varargin {idx-1}(i,j);
-#          endfor
-#            return_type (i, j) = apply (fun_handle, val);
-#        endfor
-#      endfor
-#    else
-#      for i = 1:nRows
-#        for j = 1:nCols
-#          return_type (i, j) = fun_handle (data_struct (i, j));
-#        endfor
-#      endfor
-#    endif
   endif
 
 endfunction

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[Octave-cvsupdate] SF.net SVN: octave:[9800] trunk/octave-forge/main/sparsersb/src

From: <mic...@us...> - 2012-03-09 11:21:34

Revision: 9800
          http://octave.svn.sourceforge.net/octave/?rev=9800&view=rev
Author:   michelemartone
Date:     2012-03-09 11:21:27 +0000 (Fri, 09 Mar 2012)
Log Message:
-----------
sparsersb: update to the octave-sparsersb (same matrix) benchmarking script; added a comment in the .cc file.  

Modified Paths:
--------------
    trunk/octave-forge/main/sparsersb/src/octavebench.m
    trunk/octave-forge/main/sparsersb/src/sparsersb.cc

Modified: trunk/octave-forge/main/sparsersb/src/octavebench.m
===================================================================
--- trunk/octave-forge/main/sparsersb/src/octavebench.m	2012-03-09 09:03:26 UTC (rev 9799)
+++ trunk/octave-forge/main/sparsersb/src/octavebench.m	2012-03-09 11:21:27 UTC (rev 9800)
@@ -1,7 +1,16 @@
 #!/usr/bin/octave -q
 # a benchmark program for octave/matlab
+# TODO: fix output format 
+# TODO: correct symmetric / hermitian matrices handling
+# TODO: sound, time-and-runs-based benchmarking criteria 
+
 n=10;
 
+function printbenchline(matrixname,opname,sw,times,nnz,tottime,mxxops,bpnz,msstr)
+	printf("FIXME (temporary format)\n");
+	printf("%s %s %s %d %d %.4f %10.2f %.4f %s\n",matrixname,opname,sw,times,nnz,tottime,mxxops,bpnz,msstr);
+end
+
 if nargin <= 0
 # DGEMV benchmark
 for o=1024:1024
@@ -27,36 +36,67 @@
 
 #matrices=ls("*.mtx")';
 f=1;
+uc=2;
 while f<=nargin
 	MB=1024*1024;
 	mmn=cell2mat(argv()(f))';
 	mn=strtrim(mmn');
 	tic();
-	nm=mmread(mn);
+	#nm=mmread(mn);
+	[nm,nrows,ncols,entries,rep,field,symm]=mmread(mn);
+	#if(symm=="symmetric")uc+=2;endif
+	if(strcmp(symm,"symmetric"))uc+=1;endif
 	fsz=stat(mn).size;
-	rnz=nnz(nm);
 	rt=toc();
 	[ia,ja,va]=find(nm);
-	printf("%s: %.2f MBytes read in  %.4f s (%10.2f MB/s)\n",mn',fsz/MB,rt,fsz/(rt*MB));
+	printf("%s: %.2f MBytes read by mmread in  %.4f s (%10.2f MB/s)\n",mn',fsz/MB,rt,fsz/(rt*MB));
 	#ia=ia'; ja=ja'; va=va';
-for ski=1:2
+for ski=1:uc
+	oppnz=1;
 	# FIXME: what about symmetry ?
 	sparsekw="sparse";
 	if(ski==2)sparsekw="sparsersb";endif
+	if(ski==3);
+		oppnz=2;
+		sparsekw="sparsersb";
+		tic(); [nm]=sparsersb(mn); rt=toc();
+		sparsersb(nm,"info")
+		printf("%s: %.2f MBytes read by librsb in  %.4f s (%10.2f MB/s)\n",mn',fsz/MB,rt,fsz/(rt*MB));
+	endif
+	if(ski==4);
+		nm=tril(nm);
+	endif
+	[ia,ja,va]=find(nm);
+	rnz=nnz(nm);
+	printf("benchmarking %s\n",sparsekw);
+	#printf("symmetry ? %s\n",issymmetric(sparse(nm)));
 	mrc=rows(nm); mcc=columns(nm);
+
+
+	if(ski!=3);
 	tic();
 	eval(["for i=1:n;  om=",sparsekw,"(ia,ja,va,mrc,mcc,\"summation\"); end"]);
+	printf("benchmarking %s\n",sparsekw);
 	at=toc();
 	mnz=nnz(om);
 	amflops=n*2.0*mnz/(10^6 * at);
 	printf("%s (%s) %d spBLD for %d nnz in  %.4f secs, so %10.2f Mflops\n",mn',sparsekw,n,rnz,at,amflops);
+	else
+	mnz=rnz;
+	end
+
 	#rm=sparsersb(ia,ja,va);# UNFINISHED
 	r=v=linspace(1,1,size(om,1))';
 	tic(); for i=1:n; r+=om  *v; end; umt=toc();
-	UMflops=n*2.0*mnz/(10^6 * umt);
+	UMflops=oppnz*n*2.0*mnz/(10^6 * umt);
 	printf("%s (%s) %d spMV  for %d nnz in  %.4f secs, so %10.2f Mflops\n",mn',sparsekw,n,mnz,umt, UMflops);
+	bpnz=-1;  # FIXME: bytes per nonzero!
+	msstr="?";# FIXME: matrix structure string!
+	# FIXME: finish the following!
+	#printbenchline(mn',"spMV",sparsekw,n,mnz,umt, UMflops,bpnz,msstr);
+	#
 	tic(); for i=1:n; r+=om.'*v; end; tmt=toc();
-	TMflops=n*2.0*mnz/(10^6 * tmt);
+	TMflops=oppnz*n*2.0*mnz/(10^6 * tmt);
 	printf("%s (%s) %d spMVT for %d nnz in  %.4f secs, so %10.2f Mflops\n",mn',sparsekw,n,mnz,tmt, TMflops);
 end 
 	++f;

Modified: trunk/octave-forge/main/sparsersb/src/sparsersb.cc
===================================================================
--- trunk/octave-forge/main/sparsersb/src/sparsersb.cc	2012-03-09 09:03:26 UTC (rev 9799)
+++ trunk/octave-forge/main/sparsersb/src/sparsersb.cc	2012-03-09 11:21:27 UTC (rev 9800)
@@ -45,6 +45,7 @@
  * error reporting is insufficient
  * elemental division support for complex matrices is incomplete
  * shall update to symmetric be forbidden or rather trigger a conversion ?
+ * after file read, shall return various structural info
  *
  * Developer notes:
  /usr/share/doc/octave3.2-htmldoc//interpreter/Getting-Started-with-Oct_002dFiles.html#Getting-Started-with-Oct_002dFiles

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[Octave-cvsupdate] SF.net SVN: octave:[9799] trunk/octave-forge/main/miscellaneous/inst/map.m

From: <jpi...@us...> - 2012-03-09 09:03:32

Revision: 9799
          http://octave.svn.sourceforge.net/octave/?rev=9799&view=rev
Author:   jpicarbajal
Date:     2012-03-09 09:03:26 +0000 (Fri, 09 Mar 2012)
Log Message:
-----------
miscellaneous: removed apply from @seealso in doc

Modified Paths:
--------------
    trunk/octave-forge/main/miscellaneous/inst/map.m

Modified: trunk/octave-forge/main/miscellaneous/inst/map.m
===================================================================
--- trunk/octave-forge/main/miscellaneous/inst/map.m	2012-03-09 09:02:26 UTC (rev 9798)
+++ trunk/octave-forge/main/miscellaneous/inst/map.m	2012-03-09 09:03:26 UTC (rev 9799)
@@ -56,7 +56,7 @@
 ##   [2,2] = 0.84645
 ## @}
 ## @end example
-## @seealso{reduce, match, apply}
+## @seealso{reduce, match}
 ## @end deftypefn
 
 function return_type = map (fun_handle, data_struct, varargin)

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[Octave-cvsupdate] SF.net SVN: octave:[9798] trunk/octave-forge/main/miscellaneous/inst/map.m

From: <jpi...@us...> - 2012-03-09 09:02:37

Revision: 9798
          http://octave.svn.sourceforge.net/octave/?rev=9798&view=rev
Author:   jpicarbajal
Date:     2012-03-09 09:02:26 +0000 (Fri, 09 Mar 2012)
Log Message:
-----------
miscellaneous: commenting details

Modified Paths:
--------------
    trunk/octave-forge/main/miscellaneous/inst/map.m

Modified: trunk/octave-forge/main/miscellaneous/inst/map.m
===================================================================
--- trunk/octave-forge/main/miscellaneous/inst/map.m	2012-03-09 08:55:13 UTC (rev 9797)
+++ trunk/octave-forge/main/miscellaneous/inst/map.m	2012-03-09 09:02:26 UTC (rev 9798)
@@ -75,12 +75,12 @@
     error ("fun_handle must either be a function handle or the name of a function");
   endif
 
-  nRows = rows    (data_struct);
-  nCols = columns (data_struct);
+#  nRows = rows    (data_struct);
+#  nCols = columns (data_struct);
 
-  otherdata = length (varargin);
-  val       = cell (1, otherdata+1);
-  val (:)   = 0;
+#  otherdata = length (varargin);
+#  val       = cell (1, otherdata+1);
+#  val (:)   = 0;
 
   if (iscell (data_struct))
 # KaKiLa Fri 09 Mar 2012 09:47:52 AM CET

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