@inproceedings{e5578150be174330acd714b5d40ee97c,
title = "Performance evaluation of an emergency call center: Tropical polynomial systems applied to timed petri nets",
abstract = "We analyze a timed Petri net model of an emergency call center which processes calls with different levels of priority. The counter variables of the Petri net represent the cumulated number of events as a function of time. We show that these variables are determined by a piecewise linear dynamical system. We also prove that computing the stationary regimes of the associated fluid dynamics reduces to solving a polynomial system over a tropical (min-plus) semifield of germs. This leads to explicit formula expressing the throughput of the fluid system as a piecewise linear function of the resources, revealing the existence of different congestion phases. Numerical experiments show that the analysis of the fluid dynamics yields a good approximation of the real throughput.",
author = "Xavier Allamigeon and Vianney Boeuf and St{\'e}phane Gaubert",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.; 13th International Conference on Formal Modeling and Analysis of Timed Systems, FORMATS 2015 ; Conference date: 02-09-2015 Through 04-09-2015",
year = "2015",
month = jan,
day = "1",
doi = "10.1007/978-3-319-22975-1\_2",
language = "English",
isbn = "9783319229744",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "10--26",
editor = "Sriram Sankaranarayanan and Enrico Vicario",
booktitle = "Formal Modeling and Analysis of Timed Systems - 13th International Conference, FORMATS 2015, Proceedings",
}