Analysis of deadlocks and circular waits using a matrix model for discrete event systems

Abstract

A new matrix rule-based model of discrete-part discrete event systems is given that, together with the well-known Petri net marking transition equation, yields a complete matrix-based dynamical description of these systems. In this application to deadlock analysis, the exact relations between circular blockings and deadlocks are given for a large class of reentrant flow lines. Explicit matrix equations are given for online dynamic deadlock analysis in terms of circular blockings, and certain 'critical siphons' and 'critical subsystems'. This allows efficient dispatching with deadlock avoidance using a generalized kanban scheme. For the class of flow lines considered, the existence of matrix formulae shows that deadlock analysis is not NP-complete, but of polynomial complexity.