Extracting all minimal siphons from maximal unmarked siphons in manufacturing-oriented Petri nets

Deadlock control is an important research issue in automated manufacturing systems that have a high degree of resource sharing and concurrency. Since minimal siphons are closely tied with deadlocks in Petri net models, their efficient extraction is fundamentally important. The existing methods can rapidly extract one minimal siphon given a maximal unmarked siphon that is obtained by using a mixed integer programming approach. This paper for the first time presents an extraction algorithm that can efficiently extract all minimal ones. The idea is based on the generation and use of a subnet tree structure given the places in a maximal unmarked siphon. Several Petri net models of automated manufacturing systems are used to illustrate the proposed concepts and methods.