TY - GEN
T1 - Piecewise Affine Dynamical Models of Timed Petri Nets – Application to Emergency Call Centers
AU - Allamigeon, Xavier
AU - Boyet, Marin
AU - Gaubert, Stéphane
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - 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.
AB - 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.
KW - Emergency call center
KW - Markov decision process
KW - Performance evaluation
KW - Timed Petri net
KW - Tropical geometry
UR - https://www.scopus.com/pages/publications/85088246855
U2 - 10.1007/978-3-030-51831-8_13
DO - 10.1007/978-3-030-51831-8_13
M3 - Conference contribution
AN - SCOPUS:85088246855
SN - 9783030518301
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 260
EP - 279
BT - Application and Theory of Petri Nets and Concurrency - 41st International Conference, PETRI NETS 2020, Proceedings
A2 - Janicki, Ryszard
A2 - Sidorova, Natalia
A2 - Chatain, Thomas
PB - Springer
T2 - 41st International Conference on Application and Theory of Petri Nets and Concurrency, PETRI NETS 2020
Y2 - 24 June 2020 through 25 June 2020
ER -