Networked Conflicting Timed Event Graphs Representation in (Max,+) Algebra

Boussad Addad (1) , Saïd Amari (1) , Jean-Jacques Lesage (1)

1 LURPA - Laboratoire Universitaire de Recherche en Production Automatisée

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.

Mots clés: Timed Event Graph; (Max; +) algebra; Conflict; Linear-Time Varying Systems; Repetitive Systems.; Repetitive Systems

Domaines: Automatique / Robotique

Boussad Addad, Saïd Amari, Jean-Jacques Lesage. Networked Conflicting Timed Event Graphs Representation in (Max,+) Algebra. Discrete Event Dynamic Systems, 2012, 22 (4), pp.429-449. ⟨hal-00782849⟩