An Efficient Method of Deadlock Detection and Recovery for Flexible Manufacturing Systems by Resource Flow Graphs

Deadlocks are a highly undesirable situation in flexible manufacturing systems (FMSs). This article presents a direct and novel method to detect such markings by constructing the resource flow graph of a Petri net that models an FMS and to recover such markings by adding a set of recovery transitions. First, an algorithm is developed to build a new kind of directed graph called the resource flow graph of a Petri net. Resource flow graphs can well represent the competition for shared resources by different processes. Second, based on the resource flow graph, loop graphs can be found. Furthermore, partial deadlock markings can be easily detected due to their relationship with loop graphs. Then, we propose an algorithm to design a set of recovery transitions for loop graphs that are enabled at partial deadlock markings. The proposed approach can detect partial deadlock markings without generating a complete reachability graph of a Petri net and the resulting net is deadlock-free with all reachable markings by adding the obtained recovery transitions. Finally, some widely used examples are provided to demonstrate the proposed approach.
Note to Practitioners
—The occurrence of deadlocks in an FMS tends to cause unnecessary productivity costs and even catastrophic results. In the framework of Petri nets, reachability graph analysis can usually obtain a maximally permissive supervisor of a plant. However, it is rather inefficient since it suffers from the state explosion problem. In this particular research, we develop an off-line deadlock detection and recovery policy by setting a group of virtual events that are not present in a physical model. The proposed approach is computationally efficient since it does not require to generate a reachability graph. It guarantees that the resulted system is deadlock-free with its all original reachable markings.