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Networked conflicting timed event graphs representation in (Max,+) algebra

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Abstract

Timed Event Graphs (TEGs) are a specific class of Petri nets that have been thoroughly studied given their useful linear state representation in (Max,+) algebra. Unfortunately, TEGs are generally not suitable for modeling systems displaying resources sharing (or conflicts). In this paper, we show that if a system with conflicts is modeled using a NCTEG (Networked Conflicting Timed Event Graphs), it is quite possible to obtain an equivalent (Max,+) representation. More precisely, we prove that the evolution of a NCTEG satisfies linear time-varying (Max,+) equations. In case of cyclic NCTEGs, which are a natural model of many repetitive systems, we provide a standard time-invariant (Max,+) representation. As an application of the proposed approach to exhibit its interest, we consider the case of Jobshops. We first propose a generic NCTEG-based model of these systems and subsequently apply the corresponding (Max,+) representation to evaluate some of their performances.

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Authors and Affiliations

  1. Automated Production Research Laboratory (LURPA), 61 av du President Wilson, Cachan, 94235, France

    Boussad Addad, Saïd Amari & Jean-Jacques Lesage

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  1. Boussad Addad
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  2. Saïd Amari
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  3. Jean-Jacques Lesage
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Correspondence to Boussad Addad.

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Addad, B., Amari, S. & Lesage, JJ. Networked conflicting timed event graphs representation in (Max,+) algebra. Discrete Event Dyn Syst 22, 429–449 (2012). https://doi.org/10.1007/s10626-012-0136-0

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  • DOI: https://doi.org/10.1007/s10626-012-0136-0

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