Optimal Enforcement of Liveness for FMSs Modelled with S⁴PR Petri Nets

Optimal enforcement of liveness for flexible manufacturing systems (FMSs) modeled with S4PR Petri-Nets (PNs). We optimize controlling of FMSs which are required with multiple resource acquisitions are permitted while concurrent operations in a job process are forbidden. This paper implements a system of sequential systems with shared resources (S4PRs) that have efficiency and significance to describe the interaction processes of FMSs. In particular, control transitions (CTs) are designed and implemented to quickly and effectively make PNs able to adapt to these automatic changes. The influence of CTs is the capability of PN to make a Reachability Graph (RG) fully live in terms of generating effective methods for all resources of FMS to be preserved. Sufficient examples are illustrated to demonstrate that PNs containing modeled FMS needed to be simulated, and are much more efficient.