TY - GEN
T1 - Computing Transience Bounds of Emergency Call Centers
T2 - 43rd International Conference on Application and Theory of Petri Nets and Concurrency, PETRI NETS 2022
AU - Allamigeon, Xavier
AU - Boyet, Marin
AU - Gaubert, Stéphane
N1 - Publisher Copyright:
© 2022, Springer Nature Switzerland AG.
PY - 2022/1/1
Y1 - 2022/1/1
N2 - 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.
AB - 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.
KW - Continuous Petri Nets
KW - Emergency Call Centers
KW - Semi-Markov Decision Processes
KW - Stationary Regimes
KW - Stochastic Shortest Path
KW - Timed Petri Nets
KW - Transience bound
UR - https://www.scopus.com/pages/publications/85132996070
U2 - 10.1007/978-3-031-06653-5_5
DO - 10.1007/978-3-031-06653-5_5
M3 - Conference contribution
AN - SCOPUS:85132996070
SN - 9783031066528
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 90
EP - 112
BT - Application and Theory of Petri Nets and Concurrency - 43rd International Conference, PETRI NETS 2022, Proceedings
A2 - Bernardinello, Luca
A2 - Petrucci, Laure
PB - Springer Science and Business Media Deutschland GmbH
Y2 - 19 June 2022 through 24 June 2022
ER -