Modeling of timed Petri nets using deterministic (max,+) automata

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Max-plus algebra in the history of discrete event systems

This paper is a survey of the history of max-plus algebra and its role in the field of discrete event systems during the last three decades. It is based on the perspective of the authors but it covers a large variety of topics, where max-plus algebra plays a key role

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

Effective representation of RT-LOTOS terms by finite time petri nets

The paper describes a transformational approach for the specification and formal verification of concurrent and real-time systems. At upper level, one system is specified using the timed process algebra RT-LOTOS. The output of the proposed transformation is a Time Petri net (TPN). The paper particularly shows how a TPN can be automatically constructed from an RT-LOTOS specification using a compositionally defined mapping. The proof of the translation consistency is sketched in the paper and developed in [1]. The RT-LOTOS to TPN translation patterns formalized in the paper are being implemented. in a prototype tool. This enables reusing TPNs verification techniques and tools for the profit of RT-LOTOS

Dependability checking with StoCharts: Is train radio reliable enough for trains?

Performance, dependability and quality of service (QoS) are prime aspects of the UML modelling domain. To capture these aspects effectively in the design phase, we have recently proposed STOCHARTS, a conservative extension of UML statechart diagrams. In this paper, we apply the STOCHART formalism to a safety critical design problem. We model a part of the European Train Control System specification, focusing on the risks of wireless communication failures in future high-speed cross-European trains. Stochastic model checking with the model checker PROVER enables us to derive constraints under which the central quality requirements are satisfied by the STOCHART model. The paper illustrates the flexibility and maturity of STOCHARTS to model real problems in safety critical system design

Modeling and Analysis of Hybrid Dynamic Systems Using Hybrid Petri Nets

International audienceWe consider in this paper the extensions of the PN formalism in the direction of hybrid modeling. We briefly presents hybrid dynamic systems. Then the hybrid automata model. Is introduced and we discuss continuous Petri nets. These models are obtained from discrete PNs by the fluidification of the markings. They constitute the first steps in the extension of PNs toward hybrid modeling. Two hybrid PN models, which differ in the class of HDS they can deal with, are studied. The first one is used for deterministic HDS modeling, whereas the second one can deal with HDS with nondeterministic behavior. The general control structure based on hybrid PNs is briefly described

MeGARA: Menu-based Game Abstraction and Abstraction Refinement of Markov Automata

Markov automata combine continuous time, probabilistic transitions, and nondeterminism in a single model. They represent an important and powerful way to model a wide range of complex real-life systems. However, such models tend to be large and difficult to handle, making abstraction and abstraction refinement necessary. In this paper we present an abstraction and abstraction refinement technique for Markov automata, based on the game-based and menu-based abstraction of probabilistic automata. First experiments show that a significant reduction in size is possible using abstraction.Comment: In Proceedings QAPL 2014, arXiv:1406.156