petrinettoolboxatafirstglance.htm
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<a href="PNToolbox-toc.htm" target="left">Contents</a>
<a href="PNToolbox-index.htm" target="left">Index</a>
<a href="i1overview.htm">Next</a>
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<p class=heading-1>Petri Net Toolbox at a First Glance</p>
<p class=heading-1-p> </p>
<p align="justify" class=normal> </p>
<p align="justify" class=normal> <b><u>Expected Background</u></b><b><u>.</u></b>
To derive a full benefit from reading this guide, you should be familiar with:</p>
<p class=normal> </p>
<p class=normal style="margin-left: 18pt;">•</p><p class=normal style="margin-left: 36pt; margin-top: -12pt;">the formal and graphical exploitation of PNs as a highly effective tool for modeling discrete event dynamical systems;</p>
<p class=normal style="margin-left: 18pt;">•</p><p class=normal style="margin-left: 36pt; margin-top: -12pt;">the concepts and use of MATLAB programming language.</p>
<p class=normal> </p>
<p align="justify" class=normal><b><u>Types of Petri Nets</u></b><b><u>.</u></b>
In the current version of the <b><i>Petri Net Toolbox (PN Toolbox)</i></b>,
five types of classic Petri Net (PN) models are accepted, namely: untimed, transition
timed, place-timed, stochastic and generalized<i> </i>stochastic. The timed
nets can be deterministic or stochastic, and the stochastic case allows using
the appropriate distribution function.</p>
<p align="justify" class=normal> </p>
<p align="justify" class=normal>Unlike other PN software, where places are meant
as having finite capacity (because of the arithmetic representation used by
the computational environment), our toolbox is able to operate with infinite-capacity
places, since MATLAB includes the built-in function <b>Inf</b>, which returns
the IEEE arithmetic representation for positive infinity.</p>
<p align="justify" class=normal> </p>
<p align="justify" class=normal><b><u>Main Features</u></b><b><u>.</u></b><b>
</b>The <b><i>PN Toolbox</i></b> has an easy to exploit <b><i><a href="i1overview.htm">Graphical
User Interface</a></i></b> (GUI - see <a href="petrinettoolboxatafirstglance.htm#Fig1">fig. I.1.</a>), whose purpose is twofold. First, it gives
the user the possibility to draw PNs in a natural fashion, to store, retrieve
and resize (by Zoom-In and Zoom-Out features) such drawings. Second, it permits
the simulation, analysis and design of the PNs, by exploiting all the computational
resources of the environment, via the global variables stored in the MATLAB’s
Workspace. All the net nodes and arcs are handled as MATLAB objects so as changes
in their parameters can be approached through the standard functions <b>set</b>
and <b>get</b>.</p>
<p align="justify" class=normal> </p>
<p align="justify" class=normal> When starting to build a new PN model, the user
must define its type by appropriate checking in a dialogue box. The properties
of the net-objects (places, transitions, arcs) depend on the selected type of
model.</p>
<p class=normal> </p>
<p class=normal> After drawing a PN model, the user can:</p>
<p class=normal style="margin-left: 18pt;">•</p>
<p align="justify" class=normal style="margin-left: 36pt; margin-top: -12pt;">visualize
the <b><i><a href="ii21overview.htm#incidence">Incidence Matrix</a></i></b>, which
is automatically built from the net topology;</p>
<p align="justify" class=normal style="margin-left: 18pt;">•</p>
<p align="justify" class=normal style="margin-left: 36pt; margin-top: -12pt;">explore
the<i> </i><b><i><a href="ii23behavioralproperties.htm">Behavioral Properties</a></i></b>
(such as liveness, boundedness, reversibility etc.) by consulting the <b><i>Coverability</i></b><b>
</b><b><i>Tree</i></b>, which is automatically built from the net topology and
initial marking;</p>
<p align="justify" class=normal style="margin-left: 18pt;">•</p>
<p align="justify" class=normal style="margin-left: 36pt; margin-top: -12pt;">explore
the <b><i><a href="ii24structuralproperties.htm">Structural Properties</a></i></b>
(such as structural boundedness, repetitiveness, conservativeness and consistency):</p>
<p align="justify" class=normal style="margin-left: 18pt;">•</p>
<p align="justify" class=normal style="margin-left: 36pt; margin-top: -12pt;">calculate
<b><i><a href="ii24structuralproperties.htm#invariants">P-Invariants</a></i></b> and <b><i><a href="ii24structuralproperties.htm#invariants">T-Invariants</a></i></b>;</p>
<p align="justify" class=normal style="margin-left: 18pt;">•</p>
<p align="justify" class=normal style="margin-left: 36pt; margin-top: -12pt;">run
a <b><i><a href="ii31overview.htm">Simulation</a></i></b> experiment;</p>
<p align="justify" class=normal style="margin-left: 18pt;">•</p>
<p align="justify" class=normal style="margin-left: 36pt; margin-top: -12pt;">display
current results of the simulation using the <b><i><a href="ii38scope.htm">Scope</a></i>
</b>and <b><i><a href="ii37diary.htm">Diary</a></i></b><i> </i>facilities;</p>
<p align="justify" class=normal style="margin-left: 18pt;">•</p>
<p align="justify" class=normal style="margin-left: 36pt; margin-top: -12pt;">evaluate
the global <b><i><a href="ii4analyzingsimulationresults.htm">Performance Indices</a></i></b>
(such as average marking of places, average firing delay of transitions, etc.);</p>
<p align="justify" class=normal style="margin-left: 18pt;">•</p>
<p align="justify" class=normal style="margin-left: 36pt; margin-top: -12pt;">perform
a <b><i><a href="ii5maxplusmodels.htm">Max-Plus Analysis</a></i></b> (restricted
to event-graphs);</p>
<p align="justify" class=normal style="margin-left: 18pt;">•</p>
<p align="justify" class=normal style="margin-left: 36pt; margin-top: -12pt;"><b><i><a href="ii6design.htm">Design</a></i></b>
a configuration with suitable dynamics (via automated iterative simulations).</p>
<p class=normal> </p>
<p class=normal> </p>
<p align="justify" class=normal>The <b><i>PN Toolbox</i></b> uses the <i>XML</i>
format for saving a model. A short description of the file<i> </i>format and
the specific commands is given in <a href="appendixaxmlfileformatofafilecontainingapnmodel.htm">Appendix
A</a> of this documentation.</p>
<p align="justify" class=normal> </p>
<p align="justify" class=normal> To ensure flexibility, the set of all default
values manipulated by the <b><i>PN Toolbox</i></b> are accessible to the user
by means of a configuration file presented in <a href="appendixbconfigurationfileforthepetrinettoolbox.htm">Appendix
B</a>.</p>
<p align="justify" class=normal> </p>
<p ID="Fig1" align="center" class=normal><img border=0 src="_PNToolbox-1.jpg"></p>
<p align="center" class=normal>(a)</p>
<p ID="Fig2" align="center" class=normal><img border=0 src="_PNToolbox-2.jpg"></p>
<p align="center" class=normal>(b)</p>
<p class=spatiu> </p>
<p align="center" class=figura>Fig. I.1. <i>The main </i><b><i>PN Toolbox</i></b><i>
window</i> </p>
<p align="center" class=figura>(a) <i>Draw Mode ,</i> (b) <i>Explore Mode.</i></p>
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