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<p class=heading-1>II.5. Max-Plus Models</p>
<p class=heading-1-p> </p>
<p align="justify" class=normal>For place-timed event graphs, the <b><i>PN Toolbox</i></b>
is able to directly derive the max-plus state-space representation from the
topology and initial marking of a marked graph, in an implicit form:</p>
<br>
<p align="center" class=normal><img src="_PNToolbox-17.png" border=0 align="absmiddle">,
<img src="_PNToolbox-18.png" border=0 align="absmiddle"></p>
<br>
<p align="justify" class=normal>where <i>M</i> denotes the maximal number of tokens
in the initial marking and <i>N</i> stands for the number of simulated iterations.
The components of the input vector <img src="_PNToolbox-19.png" border=0 align="absmiddle" >
and those of the output vector <img src="_PNToolbox-20.png" border=0 align="absmiddle">
represent the <i>k</i>-th firing moments of the <i>m </i>source transitions
and of the <i>p</i> sink transitions, respectively. In a similar manner, the
state vector <img src="_PNToolbox-21.png" border=0 align="absmiddle"> corresponds
to the <i>n</i> transitions in the net that have both input and output places
(i.e. those transitions which are neither sources nor sinks). </p>
<br>
<p align="center" class=normal><img ID="FigII13" border=0 src="_PNToolbox-22.jpg"></p>
<p align="center" class=figura>Fig. II.13. <i>Facilities</i><i> available</i><i>
in the</i> <b><i>PN Toolbox</i></b><i> </i><i>for max-plus analysis</i>.</p>
<br>
<p class=normal> The max-plus model is automatically constructed by the <b><i>PN
Toolbox</i></b> by using the <b><i><a href="i27maxplusmenu.htm">Max-</a></i></b><a href="i27maxplusmenu.htm"><b><i>Plus</i></b></a><b><i>
</i></b>menu. This command opens the <b><i>Max-Plus </i></b>window (denoted
by (1) in <a href="#FigII13">fig. II.13</a>) providing access to the following
features available for max-plus analysis:</p>
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