Liveness of an extended S3PR

Most existing prevention methods tackle the deadlock issue arising in flexible manufacturing systems modeled with Petri nets by adding monitors and arcs. Instead, this paper presents a new one based on a characteristic structure of WS3PR, an extension of System of Simple Sequential Processes with Resources (S3PR) with weighted arcs. The numerical relationships among weights, and between weights and initial markings are investigated based on simple circuits of resource places, which are the simplest structure of circular wait, rather than siphons. A WS3PR satisfying a proposed restriction is inherently deadlock-free and live by configuring its initial markings. A set of polynomial algorithms are developed to implement the proposed method. Several examples are used to illustrate them.