Performance evaluation of an emergency call center: tropical polynomial systems applied to timed Petri nets

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 formul{\ae} 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.Comment: 21 pages, 4 figures. A shorter version can be found in the proceedings of the conference FORMATS 201

Parametric timed model checking for guaranteeing timed opacity

Information leakage can have dramatic consequences on systems security. Among harmful information leaks, the timing information leakage is the ability for an attacker to deduce internal information depending on the system execution time. We address the following problem: given a timed system, synthesize the execution times for which one cannot deduce whether the system performed some secret behavior. We solve this problem in the setting of timed automata (TAs). We first provide a general solution, and then extend the problem to parametric TAs, by synthesizing internal timings making the TA secure. We study decidability, devise algorithms, and show that our method can also apply to program analysis.Comment: This is the author (and extended) version of the manuscript of the same name published in the proceedings of ATVA 2019. This work is partially supported by the ANR national research program PACS (ANR-14-CE28-0002), the ANR-NRF research program (ProMiS) and by ERATO HASUO Metamathematics for Systems Design Project (No. JPMJER1603), JS

Computing Branching Distances Using Quantitative Games

We lay out a general method for computing branching distances between labeled transition systems. We translate the quantitative games used for defining these distances to other, path-building games which are amenable to methods from the theory of quantitative games. We then show for all common types of branching distances how the resulting path-building games can be solved. In the end, we achieve a method which can be used to compute all branching distances in the linear-time--branching-time spectrum

Non-interference control synthesis for security timed automata

AbstractIn this paper, the problem of synthesizing controllers that ensures non interference for multilevel security dense timed discrete event systems modeled by an extension of Timed Automata, is addressed for the first time. We first discuss a notion of non interference for dense real-time systems that refines notions existing in the literature and investigate decidability issues raised by the verification problem for dense time properties. We then prove the decidability of the problem of synthesis of the timed controller for some of these timed non interference properties, providing so a symbolic method to synthesize a controller that ensures them

A chemical sensor array based system for protecting wastewater treatment plants

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