Xavier Allamigeon ; Marin Boyet ; Stéphane Gaubert - Piecewise Affine Dynamical Models of Timed Petri Nets -- Application to Emergency Call Centers

fi:7629 - Fundamenta Informaticae, December 23, 2021, Volume 183, Issues 3-4: Petri Nets 2020
Piecewise Affine Dynamical Models of Timed Petri Nets -- Application to Emergency Call Centers

Authors: Xavier Allamigeon ; Marin Boyet ; Stéphane Gaubert

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. We show that priorities can lead to a paradoxical behavior: in certain regimes, the throughput of the most prioritary task may not be an increasing function of the resources.


Volume: Volume 183, Issues 3-4: Petri Nets 2020
Published on: December 23, 2021
Accepted on: October 28, 2021
Submitted on: June 29, 2021
Keywords: Mathematics - Optimization and Control


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