Linear Time-Varying (Max,+) Representation of Conflicting Timed Event Graphs

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 an extended class of TEGs: Conflicting Timed Event Graphs (CTEGs), then it is quite possible to obtain an equivalent (Max,+) representation. More precisely, we prove that the evolution of a CTEG satisfies linear time-varying (Max,+) equations. In case of cyclic CTEGs, which are a natural model of many repetitive systems, we provide a standard time-invariant (Max,+) representation. Finally, a practical example (a Jobshop) is used for illustration to exhibit the interest of this investigation.

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

Domaines: Automatique

Boussad Addad, Saïd Amari, Jean-Jacques Lesage. Linear Time-Varying (Max,+) Representation of Conflicting Timed Event Graphs. 10th Int Workshop on Discrete Event Systems, Aug 2010, Berlin, Germany. pp.310-315. ⟨hal-00514901⟩