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We analyze a timed Petri net model of an emergency call center whichprocesses calls with different levels of priority. The counter variables of thePetri net represent the cumulated number of events as a function of time. Weshow that these variables are determined by a piecewise linear dynamicalsystem. We also prove that computing the stationary regimes of the associatedfluid dynamics reduces to solving a polynomial system over a tropical(min-plus) semifield of germs. This leads to explicit formul{\ae} expressingthe throughput of the fluid system as a piecewise linear function of theresources, revealing the existence of different congestion phases. Numericalexperiments show that the analysis of the fluid dynamics yields a goodapproximation of the real throughput.

Performance evaluation of an emergency call center: tropical polynomial systems applied to timed Petri nets