@inproceedings{a1e13d90872646f4865c4e765116370e,
title = "Computing Transience Bounds of Emergency Call Centers: A Hierarchical Timed Petri Net Approach",
abstract = "A fundamental issue in the analysis of emergency call centers is to estimate the time needed to return to a congestion-free regime after an unusual event with a massive arrival of calls. Call centers can generally be represented by timed Petri nets with a hierarchical structure, in which several layers describe the successive steps of treatments of calls. We study a continuous approximation of the Petri net dynamics (with infinitesimal tokens). Then, we show that a counter function, measuring the deviation to the stationary regime, coincides with the value function of a semi-Markov decision problem. We establish a finite time convergence result, exploiting the hierarchical structure of the Petri net. We obtain an explicit bound for the transience time, as a function of the initial marking and sojourn times. This is based on methods from the theory of stochastic shortest paths and non-linear Perron–Frobenius theory. We illustrate the bound on a case study of a medical emergency call center.",
keywords = "Continuous Petri Nets, Emergency Call Centers, Semi-Markov Decision Processes, Stationary Regimes, Stochastic Shortest Path, Timed Petri Nets, Transience bound",
author = "Xavier Allamigeon and Marin Boyet and St{\'e}phane Gaubert",
note = "Publisher Copyright: {\textcopyright} 2022, Springer Nature Switzerland AG.; 43rd International Conference on Application and Theory of Petri Nets and Concurrency, PETRI NETS 2022 ; Conference date: 19-06-2022 Through 24-06-2022",
year = "2022",
month = jan,
day = "1",
doi = "10.1007/978-3-031-06653-5\_5",
language = "English",
isbn = "9783031066528",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "90--112",
editor = "Luca Bernardinello and Laure Petrucci",
booktitle = "Application and Theory of Petri Nets and Concurrency - 43rd International Conference, PETRI NETS 2022, Proceedings",
}