A reachability-decidable petri net modeling method and its application to flexible manufacturing systems

Petri nets (PNs) are graphical and mathematical tools used to model various discrete event systems and analyze their properties. Reachability is their fundamental property. When we use a state equation to determine a state’s (marking’s) reachability, the existence of legal firing sequences (LFSs) corresponding to nonnegative integer solutions (NISs) of the state equation needs to be determined. Our previous work has proposed an algorithm to determine the LFSs’ existence in polynomial time. However, when a state equation has an infinite number of NISs, we cannot check all NISs to determine a marking’s reachability. Hence, this work studies the relationship between the structure of an ordinary PN and the number of NISs of its state equation. Then, a method is proposed to modify the structure of the PN such that the state equation has no more than one NIS. The modified PN is used as the final model of the system, which maintains the functions of its modeled system. Its reachability can be determined in polynomial time. This work shows the application of the proposed method to a flexible manufacturing system’s modeling and analysis.