Mercurial > forge
changeset 9913:c29eb2c09a71 octave-forge
small fixes to the documentation
author | mmarzolla |
---|---|
date | Thu, 29 Mar 2012 20:57:24 +0000 |
parents | 6d530850180c |
children | 8cbcbddc86f1 |
files | main/queueing/doc/markovchains.txi main/queueing/doc/queueing.html main/queueing/doc/queueing.pdf main/queueing/doc/queueingnetworks.txi |
diffstat | 4 files changed, 48 insertions(+), 57 deletions(-) [+] |
line wrap: on
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--- a/main/queueing/doc/markovchains.txi Thu Mar 29 15:45:27 2012 +0000 +++ b/main/queueing/doc/markovchains.txi Thu Mar 29 20:57:24 2012 +0000 @@ -250,7 +250,7 @@ occupancy probability after @math{i} transitions. If @math{\bf P} is absorbing, i.e., the stochastic process eventually -reaches with probability 1 a state with no outgoing transitions, then +reaches a state with no outgoing transitions with probability 1, then we can compute the expected number of visits until absorption @math{\bf L}. To do so, we first rearrange the states to rewrite matrix @math{\bf P} as:
--- a/main/queueing/doc/queueing.html Thu Mar 29 15:45:27 2012 +0000 +++ b/main/queueing/doc/queueing.html Thu Mar 29 20:57:24 2012 +0000 @@ -130,7 +130,7 @@ <h2 class="unnumbered">queueing</h2> <p>This manual documents how to install and run the Queueing Toolbox. -It corresponds to version 1.X.0 of the package. +It corresponds to version 1.1.0 of the package. <!-- --> <ul class="menu"> @@ -218,14 +218,13 @@ <li>M/H_m/1 (Hyperexponential service time distribution) </ul> - <p>Functions for Markov chain analysis are also provided, for discrete-time -chains (DTMC) or continuous-time chains (CTMC): + <p>Functions for Markov chain analysis are also provided: <ul> <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>Expected sojourn times and time-averaged sojourn times; <li>Mean first passage times; </ul> @@ -317,7 +316,7 @@ <h3 class="section">2.1 Installation through Octave package management system</h3> -<p>The most recent version of <code>queueing</code> is 1.X.0 and can +<p>The most recent version of <code>queueing</code> is 1.1.0 and can be downloaded from Octave-Forge <p><a href="http://octave.sourceforge.net/queueing/">http://octave.sourceforge.net/queueing/</a> @@ -339,13 +338,13 @@ <pre class="example"> octave:1><kbd>pkg list queueing</kbd> Package Name | Version | Installation directory --------------+---------+----------------------- - queueing *| 1.X.0 | /home/moreno/octave/queueing-1.X.0 + queueing *| 1.1.0 | /home/moreno/octave/queueing-1.1.0 </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> <kbd>pkg install </kbd><em>queueing-1.X.0.tar.gz</em> +<pre class="example"> octave:1> <kbd>pkg install </kbd><em>queueing-1.1.0.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, @@ -354,7 +353,7 @@ <p>If you do not have root access, you can do a local install using: -<pre class="example"> octave:1> <kbd>pkg install -local queueing-1.X.0.tar.gz</kbd> +<pre class="example"> octave:1> <kbd>pkg install -local queueing-1.1.0.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 @@ -380,8 +379,8 @@ <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.X.0.tar.gz</kbd> - <kbd>cd queueing-1.X.0/queueing/</kbd> +<pre class="example"> <kbd>tar xvfz queueing-1.1.0.tar.gz</kbd> + <kbd>cd queueing-1.1.0/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 @@ -1049,8 +1048,11 @@ <p class="noindent">where \bf \pi(i) = \bf \pi(0)\bf P^i is the state occupancy probability after i transitions. - <p>If \bf P has absorbing states, that is, states with no out -transitions, we can rearrange the states to rewrite \bf P as: + <p>If \bf P is absorbing, i.e., the stochastic process eventually +reaches a state with no outgoing transitions with probability 1, then +we can compute the expected number of visits until absorption +\bf L. To do so, we first rearrange the states to rewrite +matrix \bf P as: <pre class="example"> / Q | R \ P = |---+---| @@ -1059,12 +1061,11 @@ <p class="noindent">where the first t states are transient and the last r states are absorbing (t+r = N). The matrix \bf N = (\bf I - \bf Q)^-1 is called the -<em>fundamental matrix</em>; N(i,j) represents the expected -number of times that the process is in the j-th transient state -if it is started in the i-th transient state. If we reshape -\bf N to the size of \bf P (filling missing entries with -zeros), we have that, for absorbing chains \bf L = \bf -\pi(0)\bf N. +<em>fundamental matrix</em>; N_i,j is the expected number of +times that the process is in the j-th transient state if it +started in the i-th transient state. If we reshape \bf N +to the size of \bf P (filling missing entries with zeros), we +have that, for absorbing chains \bf L = \bf \pi(0)\bf N. <p><a name="doc_002ddtmc_005fexps"></a> @@ -1176,19 +1177,19 @@ <p>The <em>mean time to absorption</em> is defined as the average number of transitions which are required to reach an absorbing state, starting from a transient state (or given an initial state occupancy -probability vector \bf \pi(0) ). - - <p>Let \bf t_i be the expected number of steps before being -absorbed in any absorbing state, starting from state i. Vector -\bf t can be easiliy computed from the fundamental matrix +probability vector \bf \pi(0)). + + <p>Let \bf t_i be the expected number of transitions before +being absorbed in any absorbing state, starting from state i. +Vector \bf t can be computed from the fundamental matrix \bf N (see <a href="#Expected-number-of-visits-_0028DTMC_0029">Expected number of visits (DTMC)</a>) as <pre class="example"> t = 1 N </pre> - <p>We can define a matrix \bf B = [ B_i, j ] such that -B_i, j is the probability of being absorbed in state -j, starting from transient state i. Again, using -the fundamental matrix \bf N and \bf R, we have + <p>Let \bf B = [ B_i, j ] be a matrix where B_i, j is +the probability of being absorbed in state j, starting from +transient state i. Again, using matrices \bf N and +\bf R (see <a href="#Expected-number-of-visits-_0028DTMC_0029">Expected number of visits (DTMC)</a>) we can write <pre class="example"> B = N R </pre> @@ -1260,9 +1261,9 @@ <h4 class="subsection">4.1.6 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 +<p>The First Passage Time M_i, j is 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 <pre class="example"> ___ @@ -1275,7 +1276,7 @@ used. Let \bf W be the N \times N matrix having each row equal to the steady-state probability vector \bf \pi for \bf P; let \bf I be the N \times N identity -matrix. Define matrix \bf Z as follows: +matrix. Define \bf Z as follows: <pre class="example"> -1 Z = (I - P + W) @@ -1287,18 +1288,14 @@ \pi_j </pre> <p>According to the definition above, M_i,i = 0. We arbitrarily -redefine M_i,i to be the <em>mean recurrence time</em> -r_i for state i, that is the average number of -transitions needed to return to state i starting from -it. r_i is defined as: +let M_i,i to be the <em>mean recurrence time</em> r_i +for state i, that is the average number of transitions needed +to return to state i starting from it. r_i is: <pre class="example"> 1 r_i = ----- \pi_i </pre> - <p class="noindent">where \pi_i is the stationary probability of visiting state -i. - <p><a name="doc_002ddtmc_005ffpt"></a> <div class="defun"> @@ -2652,7 +2649,6 @@ /___ i=1 - V(1) == 1 && V == V*P; </pre> <h4 class="subsection">6.1.2 Multiple class models</h4> @@ -5159,35 +5155,31 @@ <ul> <li>If you are contributing a new function, please embed proper documentation within the function itself. The documentation must be in -<code>texinfo</code> format, so that it will be extracted and formatted into +<code>texinfo</code> format, so that it can be extracted and formatted into the printable manual. See the existing functions of the <code>queueing</code> package for the documentation style. - <li>The documentation should be as precise as possible. In particular, -always state what the valid ranges of the parameters are. - - <li>If you are contributing a new function, ensure that the function + <li>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. - <li>Always provide bibliographic references for each algorithm you + <li>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. - - <li>Include Octave test and demo blocks with your code. -Test blocks are particularly important, because Queueing Network -algorithms tend to be quite complex to implement correctly, and we -must ensure that the implementations provided with the -<code>queueing</code> package are (mostly) correct. +differs. Add references to the <samp><span class="file">doc/references.txi</span></samp> file. + + <li>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. </ul> <p>Send your contribution to Moreno Marzolla -(<a href="mailto:marzolla@cs.unibo.it">marzolla@cs.unibo.it</a>). Even if you are just a user of -<code>queueing</code>, and find this package useful, let me know by -dropping me a line. Thanks. +(<a href="mailto:marzolla@cs.unibo.it">marzolla@cs.unibo.it</a>). If you are just a user of this +package and find it useful, let me know by dropping me a line. Thanks. <!-- DO NOT EDIT! Generated automatically by munge-texi. --> <!-- *- texinfo -*- -->