scholarly journals Performance Evaluation of an Emergency Call Center: Tropical Polynomial Systems Applied to Timed Petri Nets

2015 ◽  
pp. 10-26 ◽  
Author(s):  
Xavier Allamigeon ◽  
Vianney Bœuf ◽  
Stéphane Gaubert
Keyword(s):  
Performance Evaluation ◽  
Petri Nets ◽  
Call Center ◽  
Polynomial Systems ◽  
Emergency Call ◽  
Timed Petri Nets

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

2022 ◽  
Vol 183 (3-4) ◽  
pp. 169-201
Author(s):  
Xavier Allamigeon ◽  
Marin Boyet ◽  
Stéphane Gaubert
Keyword(s):  
Petri Nets ◽  
Call Centers ◽  
Nonexpansive Mappings ◽  
Emergency Call ◽  
Free Fluid ◽  
Periodic Regime ◽  
Timed Petri Nets ◽  
Polyhedral Complex ◽  
Piecewise Affine ◽  
Paris Area

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 establish an 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.

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