Piecewise Affine Dynamical Models of Petri Nets – Application to Emergency Call Centers*

We study timed Petri nets, with preselection and priority routing. represent the behavior of these systems by piecewise affine dynamical systems. use tools from theory nonexpansive mappings to analyze establishan equivalence theorem between priority-free fluid nets semi-Markov decision processes, which we derive convergence a periodic regime polynomial-time computability throughput. More generally, develop an approach inspired tropical geometry, characterizing congestion phases as cells polyhedral complex. illustrate results current application performance evaluation emergency call centers in Paris area. show that priorities can lead paradoxical behavior: certain regimes, throughput most prioritary task may not be increasing function resources.