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Journal Articles Fundamenta Informaticae Year : 2021

Piecewise Affine Dynamical Models of Timed Petri Nets -- Application to Emergency Call Centers

Xavier Allamigeon
Marin Boyet
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Stéphane Gaubert

Abstract

We study timed Petri nets, with preselection and priority routing. We represent the behavior of these systems by piecewise affine dynamical systems. We use tools from the theory of nonexpansive mappings to analyze these systems. We establishan equivalence theorem between priority-free fluid timed Petri nets and semi-Markov decision processes, from which we derive the convergence to a periodic regime and the polynomial-time computability of the throughput. More generally, we develop an approach inspired by tropical geometry, characterizing the congestion phases as the cells of a polyhedral complex. We illustrate these results by a current application to the performance evaluation of emergency call centers in the Paris area.

Dates and versions

hal-02550006 , version 1 (21-04-2020)

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Xavier Allamigeon, Marin Boyet, Stéphane Gaubert. Piecewise Affine Dynamical Models of Timed Petri Nets -- Application to Emergency Call Centers. Fundamenta Informaticae, 2021, 183 (3-4), pp.169-201. ⟨10.3233/FI-2021-2086⟩. ⟨hal-02550006⟩
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