Self-liveness of a class of Petri net models for flexible manufacturing systems

As a highly undesirable situation, deadlocks usually occur in flexible manufacturing systems because of the limited resources. To develop a deadlock control policy, Petri nets (PN) are widely used to model these systems. For a class of PN, WS³PR-weighted systems of simple sequential processes with resources, this study reveals the relationship between its siphons and deadlocks and explores the conditions under which it is live. The concept of self-max´-controlled siphons is proposed and a sufficient condition for self-max´-controllability of siphons is developed. The authors conclude that a WS³PR is live if each strict minimal siphon is self-max´-controlled. Examples are used to demonstrate the proposed concepts and methods.