A Quick Heuristic Algorithm for Enforcing the Liveness of S3PR Petri Nets

The optimal deadlock avoiding, deadlock recovery, as well as deadlock detection in Petri nets are the NP-hard problems. For this reason, heuristic algorithms for finding the approximate solutions of such problems are of a great interest. In the paper a heuristic method of deadlock recovery for the S3PR nets, which are often used for modelling of manufacturing systems, is proposed. The method is based on the idea of resetting the process instances in the S3PR nets and a heuristic for breaking the cycles in the wait-for graphs. The method does not require any time consuming operations such as construction of the reachability graph, explicit detecting of all reachable deadlocks or all elementary cycles in a wait-for graph, hence it is quick. The simple recovery transitions are added to the net providing recovery from both global and local deadlocks.