Partial Reachability Graph Analysis of Petri Nets for Flexible Manufacturing Systems

Petri nets are an important and popular tool to model and analyze deadlocks in flexible manufacturing systems. The state space of a Petri net model can be divided into two disjoint parts: a live-zone and a dead-zone. Reachability graph analysis plays an important role in the modeling and control of Petri nets. Most existing studies have to fully enumerate the reachable markings of a Petri net to obtain the first-met bad markings (FBMs), which exacerbates the computational overheads. In this paper, a computationally efficient method to find dead markings in Petri nets is presented. We first introduce an algorithm to find dead markings by solving an integer linear programming problem. Then, the set of markings in the dead-zone is calculated, including the set of dead markings and the set of bad markings. Then we can find all the FBMs. By using a vector covering approach, the minimal covered set of FBMs is computed. The proposed approach can obtain the dead markings and FBMs by searching only a part of a reachability graph. Finally, examples are provided to demonstrate the proposed method.