Analysis of the Petri net model of parallel manufacturing processes with shared resources

A method of analysis for a class of Petri nets (PNs) called parallel process net with resources (PPNRs) is presented in this paper. The proposed analysis method is based on reduced reachability graph (RRG) of PPNRs to verify the correspondence between required specification of manufacturing system and its PN representation. In order to reduce the reachability graph (RG), a new technique is proposed which incorporates the transition vectors (TVs) to determine all the enabled transitions at a given state of system and to recognize them as dependent or independent. An algorithm, based on the idea of simultaneous execution of concurrently enabled independent transitions, is developed to reduce the RG and its analysis is also performed. Moreover, relationship between the reduction of RG and parallel structure in the PN model is discovered. The proposed technique replaces the RG by a structure which directly depicts concurrent execution and does not show the irrelevant states by presenting the concurrent behavior of system in the reduced state space. The analysis of PPNRs based on RRG generated by proposed method is also presented and demonstrated by a practical example.