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Discrete Event Dynamic Systems

, Volume 22, Issue 4, pp 429–449 | Cite as

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

  • Boussad AddadEmail author
  • Saïd Amari
  • Jean-Jacques Lesage
Article

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.

Keywords

Timed event graph (Max,+) algebra Conflict Linear-time varying systems Repetitive systems 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Boussad Addad
    • 1
    Email author
  • Saïd Amari
    • 1
  • Jean-Jacques Lesage
    • 1
  1. 1.Automated Production Research Laboratory (LURPA)CachanFrance

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