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[Octave-cvsupdate] SF.net SVN: octave:[10173] trunk/octave-forge/main/queueing/doc
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From: <mma...@us...> - 2012-04-08 20:02:53
|
Revision: 10173
http://octave.svn.sourceforge.net/octave/?rev=10173&view=rev
Author: mmarzolla
Date: 2012-04-08 20:02:44 +0000 (Sun, 08 Apr 2012)
Log Message:
-----------
refactored documentation
Modified Paths:
--------------
trunk/octave-forge/main/queueing/doc/Makefile
trunk/octave-forge/main/queueing/doc/queueing.html
trunk/octave-forge/main/queueing/doc/queueing.pdf
trunk/octave-forge/main/queueing/doc/queueing.texi
Added Paths:
-----------
trunk/octave-forge/main/queueing/doc/gettingstarted.txi
trunk/octave-forge/main/queueing/doc/gpl.txi
trunk/octave-forge/main/queueing/doc/installation.txi
trunk/octave-forge/main/queueing/doc/markovchains.txi
trunk/octave-forge/main/queueing/doc/munge-texi.m
trunk/octave-forge/main/queueing/doc/queueingnetworks.txi
trunk/octave-forge/main/queueing/doc/references.txi
trunk/octave-forge/main/queueing/doc/singlestation.txi
trunk/octave-forge/main/queueing/doc/summary.txi
Removed Paths:
-------------
trunk/octave-forge/main/queueing/doc/ack.texi
trunk/octave-forge/main/queueing/doc/contributing.texi
trunk/octave-forge/main/queueing/doc/demos/Makefile
trunk/octave-forge/main/queueing/doc/gettingstarted.texi
trunk/octave-forge/main/queueing/doc/gpl.texi
trunk/octave-forge/main/queueing/doc/help/Makefile
trunk/octave-forge/main/queueing/doc/installation.texi
trunk/octave-forge/main/queueing/doc/markovchains.texi
trunk/octave-forge/main/queueing/doc/queueingnetworks.texi
trunk/octave-forge/main/queueing/doc/references.texi
trunk/octave-forge/main/queueing/doc/singlestation.texi
trunk/octave-forge/main/queueing/doc/summary.texi
Modified: trunk/octave-forge/main/queueing/doc/Makefile
===================================================================
--- trunk/octave-forge/main/queueing/doc/Makefile 2012-04-06 19:07:39 UTC (rev 10172)
+++ trunk/octave-forge/main/queueing/doc/Makefile 2012-04-08 20:02:44 UTC (rev 10173)
@@ -1,7 +1,6 @@
DOC=queueing
-CHAPTERS=$(wildcard *.texi)
+CHAPTERS=$(patsubst %.txi, %.texi, $(wildcard *.txi))
DISTFILES=README INSTALL $(DOC).pdf $(DOC).html $(DOC).texi $(CHAPTERS)
-SUBDIRS=demos help
.PHONY: clean dist
@@ -17,32 +16,23 @@
-$(MAKEINFO) -D INSTALLONLY \
--no-validate --no-headers --no-split --output INSTALL $<
-$(DOC).html: $(DOC).texi $(CHAPTERS) demos/DONE help/DONE
+$(DOC).html: $(DOC).texi $(CHAPTERS)
-$(MAKEINFO) --html --no-split $(DOC).texi
-$(DOC).pdf: $(DOC).texi $(CHAPTERS) demos/DONE help/DONE
+$(DOC).pdf: $(DOC).texi $(CHAPTERS)
texi2pdf -o $(DOC).pdf $(DOC).texi
-$(DOC).info: $(DOC).texi $(CHAPTERS) demos/DONE help/DONE
+$(DOC).info: $(DOC).texi $(CHAPTERS)
-$(MAKEINFO) $(DOC).texi
-demos/DONE:
- $(MAKE) -C demos
+%.texi: %.txi
+ octave -p../inst/ -q munge-texi.m $< ../inst/ > $@
-help/DONE:
- $(MAKE) -C help
-
dist:
ln $(DISTFILES) ../`cat ../fname`/doc/
clean:
- for d in $(SUBDIRS); do \
- $(MAKE) -C $$d $(MAKECMDGOALS); \
- done
- \rm -f *.fns *.pdf *.aux *.log *.dvi *.out *.info *.html *.ky *.tp *.toc *.vr *.cp *.fn *.pg *.op *.au *.aus *.cps x.log *~ DOCSTRINGS DEMOS HELP INSTALL
+ \rm -f *.fns *.pdf *.aux *.log *.dvi *.out *.info *.html *.ky *.tp *.toc *.vr *.cp *.fn *.pg *.op *.au *.aus *.cps x.log *~ DOCSTRINGS INSTALL $(CHAPTERS)
distclean: clean
- for d in $(SUBDIRS); do \
- $(MAKE) -C $$d $(MAKECMDGOALS); \
- done
Deleted: trunk/octave-forge/main/queueing/doc/ack.texi
===================================================================
--- trunk/octave-forge/main/queueing/doc/ack.texi 2012-04-06 19:07:39 UTC (rev 10172)
+++ trunk/octave-forge/main/queueing/doc/ack.texi 2012-04-08 20:02:44 UTC (rev 10173)
@@ -1,28 +0,0 @@
-@c -*- texinfo -*-
-
-@c Copyright (C) 2008, 2009, 2010, 2011, 2012 Moreno Marzolla
-@c
-@c This file is part of the queueing toolbox, a Queueing Networks
-@c analysis package for GNU Octave.
-@c
-@c The queueing toolbox is free software; you can redistribute it
-@c and/or modify it under the terms of the GNU General Public License
-@c as published by the Free Software Foundation; either version 3 of
-@c the License, or (at your option) any later version.
-@c
-@c The queueing toolbox is distributed in the hope that it will be
-@c useful, but WITHOUT ANY WARRANTY; without even the implied warranty
-@c of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-@c GNU General Public License for more details.
-@c
-@c You should have received a copy of the GNU General Public License
-@c along with the queueing toolbox; see the file COPYING. If not, see
-@c <http://www.gnu.org/licenses/>.
-
-@node Acknowledgements
-@appendix Acknowledgements
-
-The following people (listed in alphabetical order) contributed to the
-@code{queueing} package, either by providing feedback, reporting bugs
-or contributing code: Philip Carinhas, Phil Colbourn, Yves Durand,
-Marco Guazzone, Dmitry Kolesnikov.
Deleted: trunk/octave-forge/main/queueing/doc/contributing.texi
===================================================================
--- trunk/octave-forge/main/queueing/doc/contributing.texi 2012-04-06 19:07:39 UTC (rev 10172)
+++ trunk/octave-forge/main/queueing/doc/contributing.texi 2012-04-08 20:02:44 UTC (rev 10173)
@@ -1,57 +0,0 @@
-@c -*- texinfo -*-
-
-@c Copyright (C) 2008, 2009, 2010, 2011, 2012 Moreno Marzolla
-@c
-@c This file is part of the queueing toolbox, a Queueing Networks
-@c analysis package for GNU Octave.
-@c
-@c The queueing toolbox is free software; you can redistribute it
-@c and/or modify it under the terms of the GNU General Public License
-@c as published by the Free Software Foundation; either version 3 of
-@c the License, or (at your option) any later version.
-@c
-@c The queueing toolbox is distributed in the hope that it will be
-@c useful, but WITHOUT ANY WARRANTY; without even the implied warranty
-@c of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-@c GNU General Public License for more details.
-@c
-@c You should have received a copy of the GNU General Public License
-@c along with the queueing toolbox; see the file COPYING. If not, see
-@c <http://www.gnu.org/licenses/>.
-
-@node Contributing Guidelines
-@appendix Contributing Guidelines
-
-Contributions and bug reports are @emph{always} welcome. If you want
-to contribute to the @code{queueing} package, here are some
-guidelines:
-
-@itemize
-
-@item If you are contributing a new function, please embed proper
-documentation within the function itself. The documentation must be in
-@code{texinfo} format, so that it can be extracted and formatted into
-the printable manual. See the existing functions of the
-@code{queueing} package for the documentation style.
-
-@item Make sure that each new function
-properly checks the validity of its input parameters. For example,
-each function accepting vectors should check whether the dimensions
-match.
-
-@item Provide bibliographic references for each new algorithm you
-contribute. If your implementation differs in some way from the
-reference you give, please describe how and why your implementation
-differs. Add references to the @file{doc/references.txi} file.
-
-@item Include test and demo blocks with your code.
-Test blocks are particularly important, since most algorithms tend to
-be quite tricky to implement correctly. If appropriate, test blocks
-should also verify that the function fails on incorrect input
-parameters.
-
-@end itemize
-
-Send your contribution to Moreno Marzolla
-(@email{marzolla@@cs.unibo.it}). If you are just a user of this
-package and find it useful, let me know by dropping me a line. Thanks.
Deleted: trunk/octave-forge/main/queueing/doc/demos/Makefile
===================================================================
--- trunk/octave-forge/main/queueing/doc/demos/Makefile 2012-04-06 19:07:39 UTC (rev 10172)
+++ trunk/octave-forge/main/queueing/doc/demos/Makefile 2012-04-08 20:02:44 UTC (rev 10173)
@@ -1,13 +0,0 @@
-DISTFILES=$(wildcard *.texi)
-
-ALL:
- octave -p ../../inst/ -q ../grabdemo.m ../../inst/ && touch DONE
-
-dist:
- ln $(DISTFILES) ../../`cat ../../fname`/doc/demos
-
-clean:
- \rm -f *.texi *~ DONE
-
-distclean: clean
-
Deleted: trunk/octave-forge/main/queueing/doc/gettingstarted.texi
===================================================================
--- trunk/octave-forge/main/queueing/doc/gettingstarted.texi 2012-04-06 19:07:39 UTC (rev 10172)
+++ trunk/octave-forge/main/queueing/doc/gettingstarted.texi 2012-04-08 20:02:44 UTC (rev 10173)
@@ -1,316 +0,0 @@
-@c -*- texinfo -*-
-
-@c Copyright (C) 2008, 2009, 2010, 2011, 2012 Moreno Marzolla
-@c
-@c This file is part of the queueing toolbox, a Queueing Networks
-@c analysis package for GNU Octave.
-@c
-@c The queueing toolbox is free software; you can redistribute it
-@c and/or modify it under the terms of the GNU General Public License
-@c as published by the Free Software Foundation; either version 3 of
-@c the License, or (at your option) any later version.
-@c
-@c The queueing toolbox is distributed in the hope that it will be
-@c useful, but WITHOUT ANY WARRANTY; without even the implied warranty
-@c of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-@c GNU General Public License for more details.
-@c
-@c You should have received a copy of the GNU General Public License
-@c along with the queueing toolbox; see the file COPYING. If not, see
-@c <http://www.gnu.org/licenses/>.
-
-@node Getting Started
-@chapter Introduction and Getting Started
-
-@menu
-* Analysis of Closed Networks::
-* Analysis of Open Networks::
-@end menu
-
-In this chapter we give some usage examples of the @code{queueing}
-package. The reader is assumed to be familiar with Queueing Networks
-(although some basic terminology and notation will be given
-here). Additional usage examples are embedded in most of the function
-files; to display and execute the demos associated with function
-@emph{fname} you can type @command{demo @emph{fname}} at the Octave
-prompt. For example
-
-@example
-@kbd{demo qnclosed}
-@end example
-
-@noindent executes all demos (if any) for the @command{qnclosed} function.
-
-@node Analysis of Closed Networks
-@section Analysis of Closed Networks
-
-Let us consider a simple closed network with @math{K=3} service
-centers. Each center is of type @math{M/M/1}--FCFS. We denote with
-@math{S_i} the average service time at center @math{i}, @math{i=1, 2,
-3}. Let @math{S_1 = 1.0}, @math{S_2 = 2.0} and @math{S_3 = 0.8}. The
-routing of jobs within the network is described with a @emph{routing
-probability matrix} @math{P}. Specifically, a request completing
-service at center @math{i} is enqueued at center @math{j} with
-probability @math{P_{i, j}}. Let us assume the following routing
-probability matrix:
-
-@iftex
-@tex
-$$
-P = \pmatrix{ 0 & 0.3 & 0.7 \cr
- 1 & 0 & 0 \cr
- 1 & 0 & 0 }
-$$
-@end tex
-@end iftex
-@ifnottex
-@example
- [ 0 0.3 0.7 ]
-P = [ 1 0 0 ]
- [ 1 0 0 ]
-@end example
-@end ifnottex
-
-For example, according to matric @math{P} a job completing service at
-center 1 is routed to center 2 with probability 0.3, and is routed to
-center 3 with probability 0.7.
-
-The network above can be analyzed with the @command{qnclosed}
-function; if there is just a single class of requests, as in the
-example above, @command{qnclosed} calls @command{qnclosedsinglemva}
-which implements the Mean Value Analysys (MVA) algorithm for
-single-class, product-form network.
-
-@command{qnclosed} requires the following parameters:
-
-@table @var
-
-@item N
-Number of requests in the network (since we are considering a closed
-network, the number of requests is fixed)
-
-@item S
-Array of average service times at the centers: @code{@var{S}(k)} is
-the average service time at center @math{k}.
-
-@item V
-Array of visit ratios: @code{@var{V}(k)} is the average number of
-visits to center @math{k}.
-
-@end table
-
-As can be seen, we must compute the @emph{visit ratios} (or visit
-counts) @math{V_k} for each center @math{k}. The visit counts satisfy
-the following equations:
-
-@iftex
-@tex
-$$
-V_j = \sum_{i=1}^K V_i P_{i, j}
-$$
-@end tex
-@end iftex
-@ifnottex
-@example
-V_j = sum_i V_i P_ij
-@end example
-@end ifnottex
-
-We can compute @math{V_k} from the routing probability matrix
-@math{P_{i, j}} using the @command{qnvisits} function:
-
-@example
-@group
-@kbd{P = [0 0.3 0.7; 1 0 0; 1 0 0];}
-@kbd{V = qnvisits(P)}
- @result{} V = 1.00000 0.30000 0.70000
-@end group
-@end example
-
-We can check that the computed values satisfy the above equation by
-evaluating the following expression:
-
-@example
-@kbd{V*P}
- @result{} ans = 1.00000 0.30000 0.70000
-@end example
-
-@noindent which is equal to @math{V}.
-Hence, we can analyze the network for a given population size @math{N}
-(for example, @math{N=10}) as follows:
-
-@example
-@group
-@kbd{N = 10;}
-@kbd{S = [1 2 0.8];}
-@kbd{P = [0 0.3 0.7; 1 0 0; 1 0 0];}
-@kbd{V = qnvisits(P);}
-@kbd{[U R Q X] = qnclosed( N, S, V )}
- @result{} U = 0.99139 0.59483 0.55518
- @result{} R = 7.4360 4.7531 1.7500
- @result{} Q = 7.3719 1.4136 1.2144
- @result{} X = 0.99139 0.29742 0.69397
-@end group
-@end example
-
-The output of @command{qnclosed} includes the vector of utilizations
-@math{U_k} at center @math{k}, response time @math{R_k}, average
-number of customers @math{Q_k} and throughput @math{X_k}. In our
-example, the throughput of center 1 is @math{X_1 = 0.99139}, and the
-average number of requests in center 3 is @math{Q_3 = 1.2144}. The
-utilization of center 1 is @math{U_1 = 0.99139}, which is the higher
-value among the service centers. Tus, center 1 is the @emph{bottleneck
-device}.
-
-This network can also be analyzed with the @command{qnsolve}
-function. @command{qnsolve} can handle open, closed or mixed networks,
-and allows the network to be described in a very flexible way. First,
-let @var{Q1}, @var{Q2} and @var{Q3} be the variables describing the
-service centers. Each variable is instantiated with the
-@command{qnmknode} function.
-
-@example
-@group
-@kbd{Q1 = qnmknode( "m/m/m-fcfs", 1 );}
-@kbd{Q2 = qnmknode( "m/m/m-fcfs", 2 );}
-@kbd{Q3 = qnmknode( "m/m/m-fcfs", 0.8 );}
-@end group
-@end example
-
-The first parameter of @command{qnmknode} is a string describing the
-type of the node. Here we use @code{"m/m/m-fcfs"} to denote a
-@math{M/M/m}--FCFS center. The second parameter gives the average
-service time. An optional third parameter can be used to specify the
-number @math{m} of service centers. If omitted, it is assumed
-@math{m=1} (single-server node).
-
-Now, the network can be analyzed as follows:
-
-@example
-@group
-@kbd{N = 10;}
-@kbd{V = [1 0.3 0.7];}
-@kbd{[U R Q X] = qnsolve( "closed", N, @{ Q1, Q2, Q3 @}, V )}
- @result{} U = 0.99139 0.59483 0.55518
- @result{} R = 7.4360 4.7531 1.7500
- @result{} Q = 7.3719 1.4136 1.2144
- @result{} X = 0.99139 0.29742 0.69397
-@end group
-@end example
-
-Of course, we get exactly the same results. Other functions can be used
-for closed networks, @pxref{Algorithms for Product-Form QNs}.
-
-@node Analysis of Open Networks
-@section Analysis of Open Networks
-
-Open networks can be analyzed in a similar way. Let us consider
-an open network with @math{K=3} service centers, and routing
-probability matrix as follows:
-
-@iftex
-@tex
-$$
-P = \pmatrix{ 0 & 0.3 & 0.5 \cr
- 1 & 0 & 0 \cr
- 1 & 0 & 0 }
-$$
-@end tex
-@end iftex
-@ifnottex
-@example
- [ 0 0.3 0.5 ]
-P = [ 1 0 0 ]
- [ 1 0 0 ]
-@end example
-@end ifnottex
-
-In this network, requests can leave the system from center 1 with
-probability @math{(1-(0.3+0.5) = 0.2}. We suppose that external jobs
-arrive at center 1 with rate @math{\lambda_1 = 0.15}; there are no
-arrivals at centers 2 and 3.
-
-Similarly to closed networks, we first need to compute the visit
-counts @math{V_k} to center @math{k}. Again, we use the
-@command{qnvisits} function as follows:
-
-@example
-@group
-@kbd{P = [0 0.3 0.5; 1 0 0; 1 0 0];}
-@kbd{lambda = [0.15 0 0];}
-@kbd{V = qnvisits(P, lambda)}
- @result{} V = 5.00000 1.50000 2.50000
-@end group
-@end example
-
-@noindent where @code{@var{lambda}(k)} is the arrival rate at center @math{k},
-and @var{P} is the routing matrix. The visit counts @math{V_k} for
-open networks satisfy the following equation:
-
-@iftex
-@tex
-$$
-V_j = P_{0, j} + \sum_{i=1}^K V_i P_{i, j}
-$$
-@end tex
-@end iftex
-@ifnottex
-@example
-V_j = sum_i V_i P_ij
-@end example
-@end ifnottex
-
-where @math{P_{0, j}} is the probability of an external arrival to
-center @math{j}. This can be computed as:
-
-@tex
-$$
-P_{0, j} = {\lambda_j \over \sum_{i=1}^K \lambda_i }
-$$
-@end tex
-
-Assuming the same service times as in the previous example, the
-network can be analyzed with the @command{qnopen} function, as
-follows:
-
-@example
-@group
-@kbd{S = [1 2 0.8];}
-@kbd{[U R Q X] = qnopen( sum(lambda), S, V )}
- @result{} U = 0.75000 0.45000 0.30000
- @result{} R = 4.0000 3.6364 1.1429
- @result{} Q = 3.00000 0.81818 0.42857
- @result{} X = 0.75000 0.22500 0.37500
-@end group
-@end example
-
-The first parameter of the @command{qnopen} function is the (scalar)
-aggregate arrival rate.
-
-Again, it is possible to use the @command{qnsolve} high-level function:
-
-@example
-@group
-@kbd{Q1 = qnmknode( "m/m/m-fcfs", 1 );}
-@kbd{Q2 = qnmknode( "m/m/m-fcfs", 2 );}
-@kbd{Q3 = qnmknode( "m/m/m-fcfs", 0.8 );}
-@kbd{lambda = [0.15 0 0];}
-@kbd{[U R Q X] = qnsolve( "open", sum(lambda), @{ Q1, Q2, Q3 @}, V )}
- @result{} U = 0.75000 0.45000 0.30000
- @result{} R = 4.0000 3.6364 1.1429
- @result{} Q = 3.00000 0.81818 0.42857
- @result{} X = 0.75000 0.22500 0.37500
-@end group
-@end example
-
-@c @node Markov Chains Analysis
-@c @section Markov Chains Analysis
-
-@c @subsection Discrete-Time Markov Chains
-
-@c (TODO)
-
-@c @subsection Continuous-Time Markov Chains
-
-@c (TODO)
-
Copied: trunk/octave-forge/main/queueing/doc/gettingstarted.txi (from rev 10172, trunk/octave-forge/main/queueing/doc/gettingstarted.texi)
===================================================================
--- trunk/octave-forge/main/queueing/doc/gettingstarted.txi (rev 0)
+++ trunk/octave-forge/main/queueing/doc/gettingstarted.txi 2012-04-08 20:02:44 UTC (rev 10173)
@@ -0,0 +1,316 @@
+@c -*- texinfo -*-
+
+@c Copyright (C) 2008, 2009, 2010, 2011, 2012 Moreno Marzolla
+@c
+@c This file is part of the queueing toolbox, a Queueing Networks
+@c analysis package for GNU Octave.
+@c
+@c The queueing toolbox is free software; you can redistribute it
+@c and/or modify it under the terms of the GNU General Public License
+@c as published by the Free Software Foundation; either version 3 of
+@c the License, or (at your option) any later version.
+@c
+@c The queueing toolbox is distributed in the hope that it will be
+@c useful, but WITHOUT ANY WARRANTY; without even the implied warranty
+@c of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+@c GNU General Public License for more details.
+@c
+@c You should have received a copy of the GNU General Public License
+@c along with the queueing toolbox; see the file COPYING. If not, see
+@c <http://www.gnu.org/licenses/>.
+
+@node Getting Started
+@chapter Introduction and Getting Started
+
+@menu
+* Analysis of Closed Networks::
+* Analysis of Open Networks::
+@end menu
+
+In this chapter we give some usage examples of the @code{queueing}
+package. The reader is assumed to be familiar with Queueing Networks
+(although some basic terminology and notation will be given
+here). Additional usage examples are embedded in most of the function
+files; to display and execute the demos associated with function
+@emph{fname} you can type @command{demo @emph{fname}} at the Octave
+prompt. For example
+
+@example
+@kbd{demo qnclosed}
+@end example
+
+@noindent executes all demos (if any) for the @command{qnclosed} function.
+
+@node Analysis of Closed Networks
+@section Analysis of Closed Networks
+
+Let us consider a simple closed network with @math{K=3} service
+centers. Each center is of type @math{M/M/1}--FCFS. We denote with
+@math{S_i} the average service time at center @math{i}, @math{i=1, 2,
+3}. Let @math{S_1 = 1.0}, @math{S_2 = 2.0} and @math{S_3 = 0.8}. The
+routing of jobs within the network is described with a @emph{routing
+probability matrix} @math{P}. Specifically, a request completing
+service at center @math{i} is enqueued at center @math{j} with
+probability @math{P_{i, j}}. Let us assume the following routing
+probability matrix:
+
+@iftex
+@tex
+$$
+P = \pmatrix{ 0 & 0.3 & 0.7 \cr
+ 1 & 0 & 0 \cr
+ 1 & 0 & 0 }
+$$
+@end tex
+@end iftex
+@ifnottex
+@example
+ [ 0 0.3 0.7 ]
+P = [ 1 0 0 ]
+ [ 1 0 0 ]
+@end example
+@end ifnottex
+
+For example, according to matric @math{P} a job completing service at
+center 1 is routed to center 2 with probability 0.3, and is routed to
+center 3 with probability 0.7.
+
+The network above can be analyzed with the @command{qnclosed}
+function; if there is just a single class of requests, as in the
+example above, @command{qnclosed} calls @command{qnclosedsinglemva}
+which implements the Mean Value Analysys (MVA) algorithm for
+single-class, product-form network.
+
+@command{qnclosed} requires the following parameters:
+
+@table @var
+
+@item N
+Number of requests in the network (since we are considering a closed
+network, the number of requests is fixed)
+
+@item S
+Array of average service times at the centers: @code{@var{S}(k)} is
+the average service time at center @math{k}.
+
+@item V
+Array of visit ratios: @code{@var{V}(k)} is the average number of
+visits to center @math{k}.
+
+@end table
+
+As can be seen, we must compute the @emph{visit ratios} (or visit
+counts) @math{V_k} for each center @math{k}. The visit counts satisfy
+the following equations:
+
+@iftex
+@tex
+$$
+V_j = \sum_{i=1}^K V_i P_{i, j}
+$$
+@end tex
+@end iftex
+@ifnottex
+@example
+V_j = sum_i V_i P_ij
+@end example
+@end ifnottex
+
+We can compute @math{V_k} from the routing probability matrix
+@math{P_{i, j}} using the @command{qnvisits} function:
+
+@example
+@group
+@kbd{P = [0 0.3 0.7; 1 0 0; 1 0 0];}
+@kbd{V = qnvisits(P)}
+ @result{} V = 1.00000 0.30000 0.70000
+@end group
+@end example
+
+We can check that the computed values satisfy the above equation by
+evaluating the following expression:
+
+@example
+@kbd{V*P}
+ @result{} ans = 1.00000 0.30000 0.70000
+@end example
+
+@noindent which is equal to @math{V}.
+Hence, we can analyze the network for a given population size @math{N}
+(for example, @math{N=10}) as follows:
+
+@example
+@group
+@kbd{N = 10;}
+@kbd{S = [1 2 0.8];}
+@kbd{P = [0 0.3 0.7; 1 0 0; 1 0 0];}
+@kbd{V = qnvisits(P);}
+@kbd{[U R Q X] = qnclosed( N, S, V )}
+ @result{} U = 0.99139 0.59483 0.55518
+ @result{} R = 7.4360 4.7531 1.7500
+ @result{} Q = 7.3719 1.4136 1.2144
+ @result{} X = 0.99139 0.29742 0.69397
+@end group
+@end example
+
+The output of @command{qnclosed} includes the vector of utilizations
+@math{U_k} at center @math{k}, response time @math{R_k}, average
+number of customers @math{Q_k} and throughput @math{X_k}. In our
+example, the throughput of center 1 is @math{X_1 = 0.99139}, and the
+average number of requests in center 3 is @math{Q_3 = 1.2144}. The
+utilization of center 1 is @math{U_1 = 0.99139}, which is the higher
+value among the service centers. Tus, center 1 is the @emph{bottleneck
+device}.
+
+This network can also be analyzed with the @command{qnsolve}
+function. @command{qnsolve} can handle open, closed or mixed networks,
+and allows the network to be described in a very flexible way. First,
+let @var{Q1}, @var{Q2} and @var{Q3} be the variables describing the
+service centers. Each variable is instantiated with the
+@command{qnmknode} function.
+
+@example
+@group
+@kbd{Q1 = qnmknode( "m/m/m-fcfs", 1 );}
+@kbd{Q2 = qnmknode( "m/m/m-fcfs", 2 );}
+@kbd{Q3 = qnmknode( "m/m/m-fcfs", 0.8 );}
+@end group
+@end example
+
+The first parameter of @command{qnmknode} is a string describing the
+type of the node. Here we use @code{"m/m/m-fcfs"} to denote a
+@math{M/M/m}--FCFS center. The second parameter gives the average
+service time. An optional third parameter can be used to specify the
+number @math{m} of service centers. If omitted, it is assumed
+@math{m=1} (single-server node).
+
+Now, the network can be analyzed as follows:
+
+@example
+@group
+@kbd{N = 10;}
+@kbd{V = [1 0.3 0.7];}
+@kbd{[U R Q X] = qnsolve( "closed", N, @{ Q1, Q2, Q3 @}, V )}
+ @result{} U = 0.99139 0.59483 0.55518
+ @result{} R = 7.4360 4.7531 1.7500
+ @result{} Q = 7.3719 1.4136 1.2144
+ @result{} X = 0.99139 0.29742 0.69397
+@end group
+@end example
+
+Of course, we get exactly the same results. Other functions can be used
+for closed networks, @pxref{Algorithms for Product-Form QNs}.
+
+@node Analysis of Open Networks
+@section Analysis of Open Networks
+
+Open networks can be analyzed in a similar way. Let us consider
+an open network with @math{K=3} service centers, and routing
+probability matrix as follows:
+
+@iftex
+@tex
+$$
+P = \pmatrix{ 0 & 0.3 & 0.5 \cr
+ 1 & 0 & 0 \cr
+ 1 & 0 & 0 }
+$$
+@end tex
+@end iftex
+@ifnottex
+@example
+ [ 0 0.3 0.5 ]
+P = [ 1 0 0 ]
+ [ 1 0 0 ]
+@end example
+@end ifnottex
+
+In this network, requests can leave the system from center 1 with
+probability @math{(1-(0.3+0.5) = 0.2}. We suppose that external jobs
+arrive at center 1 with rate @math{\lambda_1 = 0.15}; there are no
+arrivals at centers 2 and 3.
+
+Similarly to closed networks, we first need to compute the visit
+counts @math{V_k} to center @math{k}. Again, we use the
+@command{qnvisits} function as follows:
+
+@example
+@group
+@kbd{P = [0 0.3 0.5; 1 0 0; 1 0 0];}
+@kbd{lambda = [0.15 0 0];}
+@kbd{V = qnvisits(P, lambda)}
+ @result{} V = 5.00000 1.50000 2.50000
+@end group
+@end example
+
+@noindent where @code{@var{lambda}(k)} is the arrival rate at center @math{k},
+and @var{P} is the routing matrix. The visit counts @math{V_k} for
+open networks satisfy the following equation:
+
+@iftex
+@tex
+$$
+V_j = P_{0, j} + \sum_{i=1}^K V_i P_{i, j}
+$$
+@end tex
+@end iftex
+@ifnottex
+@example
+V_j = sum_i V_i P_ij
+@end example
+@end ifnottex
+
+where @math{P_{0, j}} is the probability of an external arrival to
+center @math{j}. This can be computed as:
+
+@tex
+$$
+P_{0, j} = {\lambda_j \over \sum_{i=1}^K \lambda_i }
+$$
+@end tex
+
+Assuming the same service times as in the previous example, the
+network can be analyzed with the @command{qnopen} function, as
+follows:
+
+@example
+@group
+@kbd{S = [1 2 0.8];}
+@kbd{[U R Q X] = qnopen( sum(lambda), S, V )}
+ @result{} U = 0.75000 0.45000 0.30000
+ @result{} R = 4.0000 3.6364 1.1429
+ @result{} Q = 3.00000 0.81818 0.42857
+ @result{} X = 0.75000 0.22500 0.37500
+@end group
+@end example
+
+The first parameter of the @command{qnopen} function is the (scalar)
+aggregate arrival rate.
+
+Again, it is possible to use the @command{qnsolve} high-level function:
+
+@example
+@group
+@kbd{Q1 = qnmknode( "m/m/m-fcfs", 1 );}
+@kbd{Q2 = qnmknode( "m/m/m-fcfs", 2 );}
+@kbd{Q3 = qnmknode( "m/m/m-fcfs", 0.8 );}
+@kbd{lambda = [0.15 0 0];}
+@kbd{[U R Q X] = qnsolve( "open", sum(lambda), @{ Q1, Q2, Q3 @}, V )}
+ @result{} U = 0.75000 0.45000 0.30000
+ @result{} R = 4.0000 3.6364 1.1429
+ @result{} Q = 3.00000 0.81818 0.42857
+ @result{} X = 0.75000 0.22500 0.37500
+@end group
+@end example
+
+@c @node Markov Chains Analysis
+@c @section Markov Chains Analysis
+
+@c @subsection Discrete-Time Markov Chains
+
+@c (TODO)
+
+@c @subsection Continuous-Time Markov Chains
+
+@c (TODO)
+
Deleted: trunk/octave-forge/main/queueing/doc/gpl.texi
===================================================================
--- trunk/octave-forge/main/queueing/doc/gpl.texi 2012-04-06 19:07:39 UTC (rev 10172)
+++ trunk/octave-forge/main/queueing/doc/gpl.texi 2012-04-08 20:02:44 UTC (rev 10173)
@@ -1,718 +0,0 @@
-@node Copying
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-Additional terms, permissive or non-permissive, may be stated in the
-form of a separately written license, or stated as exceptions; the
-above requirements apply either way.
-
-@item Termination.
-
-You may not propagate or modify a covered work except as expressly
-provided under this License. Any attempt otherwise to propagate or
-modify it is void, and will automatically terminate your rights under
-this License (including any patent licenses granted under the third
-paragraph of section 11).
-
-However, if you cease all violation of this License, then your license
-from a particular copyright holder is reinstated (a) provisionally,
-unless and until the copyright holder explicitly and finally
-terminates your license, and (b) permanently, if the copyright holder
-fails to notify you of the violation by some reasonable means prior to
-60 days after the cessation.
-
-Moreover, your license from a particular copyright holder is
-reinstated permanently if the copyright holder notifies you of the
-violation by some reasonable means, this is the first time you have
-received notice of violation of this License (for any work) from that
-copyright holder, and you cure the violation prior to 30 days after
-your receipt of the notice.
-
-Termination of your rights under this section does not terminate the
-licenses of parties who have received copies or rights from you under
-this License. If your rights have been terminated and not permanently
-reinstated, you do not qualify to receive new licenses for the same
-material under section 10.
-
-@item Acceptance Not Required for Having Copies.
-
-You are not required to accept this License in order to receive or run
-a copy of the Program. Ancillary propagation of a covered work
-occurring solely as a consequence of using peer-to-peer transmission
-to receive a copy likewise does not require acceptance. However,
-nothing other than this License grants you permission to propagate or
-modify any covered work. These actions infringe copyright if you do
-not accept this License. Therefore, by modifying or propagating a
-covered work, you indicate your acceptance of this License to do so.
-
-@item Automatic Licensing of Downstream Recipients.
-
-Each time you convey a covered work, the recipient automatically
-receives a license from the original licensors, to run, modify and
-propagate that work, subject to this License. You are not responsible
-for enforcing compliance by third parties with this License.
-
-An ``entity transaction'' is a transaction transferring control of an
-organization, or substantially all assets of one, or subdividing an
-organization, or merging organizations. If propagation of a covered
-work results from an entity transaction, each party to that
-transaction who receives a copy of the work also receives whatever
-licenses to the work the party's predecessor in interest had or could
-give under the previous paragraph, plus a right to possession of the
-Corresponding Source of the work from the predecessor in interest, if
-the predecessor has it or can get it with reasonable efforts.
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-You may not impose any further restrictions on the exercise of the
-rights granted or affirmed under this License. For example, you may
-not impose a license fee, royalty, or other charge for exercise of
-rights granted under this License, and you may not initiate litigation
-(including a cross-claim or counterclaim in a lawsuit) alleging that
-any patent claim is infringed by making, using, selling, offering for
-sale, or importing the Program or any portion of it.
-
-@item Patents.
-
-A ``contributor'' is a copyright holder who authorizes use under this
-License of the Program or a work on which the Program is based. The
-work thus licensed is called the contributor's ``contributor version''.
-
-A contributor's ``essential patent claims'' are all patent claims owned
-or controlled by the contributor, whether already acquired or
-hereafter acquired, that would be infringed by some manner, permitted
-by this License, of making, using, or selling its contributor version,
-but do not include claims that would be infringed only as a
-consequence of further modification of the contributor version. For
-purposes of this definition, ``control'' includes the right to grant
-patent sublicenses in a manner consistent with the requirements of
-this License.
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-Each contributor grants you a non-exclusive, worldwide, royalty-free
-patent license under the contributor's essential patent claims, to
-make, use, sell, offer for sale, import and otherwise run, modify and
-propagate the contents of its contributor version.
-
-In the following three paragraphs, a ``patent license'' is any express
-agreement or commitment, however denominated, not to enforce a patent
-(such as an express permission to practice a patent or covenant not to
-sue for patent infringement). To ``grant'' such a patent license to a
-party means to make such an agreement or commitment not to enforce a
-patent against the party.
-
-If you convey a covered work, knowingly relying on a patent license,
-and the Corresponding Source of the work is not available for anyone
-to copy, free of charge and under the terms of this License, through a
-publicly available network server or other readily accessible means,
-then you must either (1) cause the Corresponding Source to be so
-available, or (2) arrange to deprive yourself of the benefit of the
-patent license for this particular work, or (3) arrange, in a manner
-consistent with the requirements of this License, to extend the patent
-license to downstream recipients. ``Knowingly relying'' means you have
-actual knowledge that, but for the patent license, your conveying the
-covered work in a country, or your recipient's use of the covered work
-in a country, would infringe one or more identifiable patents in that
-country that you have reason to believe are valid.
-
-If, pursuant to or in connection with a single transaction or
-arrangement, you convey, or propagate by procuring conveyance of, a
-covered work, and grant a patent license to some of the parties
-receiving the covered work authorizing them to use, propagate, modify
-or convey a specific copy of the covered work, then the patent license
-you grant is automatically extended to all recipients of the covered
-work and works based on it.
-
-A patent license is ``discriminatory'' if it does not include within the
-scope of its coverage, prohibits the exercise of, or is conditioned on
-the non-exercise of one or more of the rights that are specifically
-granted under this License. You may not convey a covered work if you
-are a party to an arrangement with a third party that is in the
-business of distributing software, under which you make payment to the
-third party based on the extent of your activity of conveying the
-work, and under which the third party grants, to any of the parties
-who would receive the covered work from you, a discriminatory patent
-license (a) in connection with copies of the covered work conveyed by
-you (or copies made from those copies), or (b) primarily for and in
-connection with specific products or compilations that contain the
-covered work, unless you entered into that arrangement, or that patent
-license was granted, prior to 28 March 2007.
-
-Nothing in this License shall be construed as excluding or limiting
-any implied license or other defenses to infringement that may
-otherwise be available to you under applicable patent law.
-
-@item No Surrender of Others' Freedom.
-
-If conditions are imposed on you (whether by court order, agreement or
-otherwise) that contradict the conditions of this License, they do not
-excuse you from the conditions of this License. If you cannot convey
-a covered work so as to satisfy simultaneously your obligations under
-this License and any other pertinent obligations, then as a
-consequence you may not convey it at all. For example, if you agree
-to terms that obligate you to collect a royalty for further conveying
-from those to whom you convey the Program, the only way you could
-satisfy both those terms and this License would be to refrain entirely
-from conveying the Program.
-
-@item Use with the GNU Affero General Public License.
-
-Notwithstanding any other provision of this License, you have
-permission to link or combine any covered work with a work licensed
-under version 3 of the GNU Affero General Public License into a single
-combined work, and to convey the resulting work. The terms of this
-License will continue to apply to the part which is the covered work,
-but the special requirements of the GNU Affero General Public License,
-section 13, concerning interaction through a network will apply to the
-combination as such.
-
-@item Revised Versions of this License.
-
-The Free Software Foundation may publish revised and/or new versions
-of the GNU General Public License from time to time. Such new
-versions will be similar in spirit to the present version, but may
-differ in detail to address new problems or concerns.
-
-Each version is given a distinguishing version number. If the Program
-specifies that a certain numbered version of the GNU General Public
-License ``or any later version'' applies to it, you have the option of
-following the terms and conditions either of that numbered version or
-of any later version published by the Free Software Foundation. If
-the Program does not specify a version number of the GNU General
-Public License, you may choose any version ever published by the Free
-Software Foundation.
-
-If the Program specifies that a proxy can decide which future versions
-of the GNU General Public License can be used, that proxy's public
-statement of acceptance of a version permanently authorizes you to
-choose that version for the Program.
-
-Later license versions may give you additional or different
-permissions. However, no additional obligations are imposed on any
-author or copyright holder as a result of your choosing to follow a
-later version.
-
-@item Disclaimer of Warranty.
-
-THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
-APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
-HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM ``AS IS'' WITHOUT
-WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT
-LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
-A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND
-PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE
-DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR
-CORRECTION.
-
-@item Limitation of Liability.
-
-IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
-WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR
-CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
-INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES
-ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT
-NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR
-LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM
-TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER
-PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.
-
-@item Interpretation of Sections...
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