An algorithm to find the minimal initial markings of resource places ensuring liveness of finite-capacity S3PR

Abstract

Deadlock prevention can be achieved by configuring proper initial markings to obtain a live Petri net model. For a class of Petri nets called finite-capacity Systems of Simple Sequential Processes with Resources (S3PR), an algorithm is proposed to find the minimal initial markings of resource places ensuring its liveness. First, conditions on initial markings of resource places are computed under which the strict minimal siphons (SMS) can never be emptied. Then, the minimal initial markings of resource places are computed to ensure liveness of the net. By the proposed algorithm, a live net can be obtained without changing the structure of the original model. The main practical implication of our work is that it can lower the facility cost. A simple example is used to illustrate the application of the algorithm.