Parallel and Sequential Mutual Exclusions for Petri Net Modeling of Manufacturing Systems with Shared Resources

The design of Petri net models is the first step for control, validation, performance analysis, and simulation using Petri nets for automated manufacturing systems. These systems share many resources such as robots, machines, and material movers. Previous modeling methods need to be extended to guarantee the desired properties of the Petri nets for general cases where possible deadlocks result from inappropriate initial markings or net structures for systems with shared resources. Boundedness, liveness, and reversibility are the properties necessary to control practical manufacturing systems and are important in order to conduct system performance analysis. The research reported provides a theoretical basis for Petri net synthesis methods that can be used to model systems with shared resources, and to make the resulting nets bounded, live, and reversible. Two resource-sharing concepts, parallel mutual exclusion (PME) and sequential mutual exclusion (SME), are formulated in the context of Petri net theory. A PME models a resource shared by distinct independent processes, and an SME is a sequential composition of PME’s, modeling a resource shared by sequentially related processes. Then the conditions under which a net containing such structures remains bounded, live, and reversible are derived. Future work will extend PME and SME to more general cases.