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 formulæ 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.
The three authors were partially supported by the programme “Concepts, Systèmes et Outils pour la Sécurité Globale” of the French National Agency of Research (ANR), project “DEMOCRITE”, number ANR-13-SECU-0007-01. The first and last authors were partially supported by the programme “Ingènierie Numérique & Sécurité” of ANR, project “MALTHY”, number ANR-13-INSE-0003.
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Allamigeon, X., Bœuf, V., Gaubert, S. (2015). Performance Evaluation of an Emergency Call Center: Tropical Polynomial Systems Applied to Timed Petri Nets. In: Sankaranarayanan, S., Vicario, E. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2015. Lecture Notes in Computer Science(), vol 9268. Springer, Cham. https://doi.org/10.1007/978-3-319-22975-1_2
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