@inproceedings{9a90f0e684da43589cc834163001e70b,
title = "Piecewise Affine Dynamical Models of Timed Petri Nets {\textendash} Application to Emergency Call Centers",
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 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.",
keywords = "Emergency call center, Markov decision process, Performance evaluation, Timed Petri net, Tropical geometry",
author = "Xavier Allamigeon and Marin Boyet and St{\'e}phane Gaubert",
note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.; 41st International Conference on Application and Theory of Petri Nets and Concurrency, PETRI NETS 2020 ; Conference date: 24-06-2020 Through 25-06-2020",
year = "2020",
month = jan,
day = "1",
doi = "10.1007/978-3-030-51831-8\_13",
language = "English",
isbn = "9783030518301",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer",
pages = "260--279",
editor = "Ryszard Janicki and Natalia Sidorova and Thomas Chatain",
booktitle = "Application and Theory of Petri Nets and Concurrency - 41st International Conference, PETRI NETS 2020, Proceedings",
}