A Critical-Siphon Approach to Fastest Deadlock Controller for S3PR

Abstract

The authors developed a theory to show that exactly one monitor is required for the set of siphons in the family of 2-compound siphons and how to assign its initial markings. This avoids redundant monitors and the unnecessary associated computational burden. Neither reachability graph nor minimal siphon needs to be computed to achieve polynomial complexity—essential for large systems. This chapter redevelops the theory more formally and further applies this approach to two well-known S3PR to obtain a controller full or near maximally permissive, where Weighted Control (WC) arcs are nevertheless necessary to keep the controlled model maximally permissive. However, optimal control for siphons involving WC arcs are still under research. As many as possible for simpler structures are desired to reduce WC arcs. In addition, fast computation is important for dynamic reconfiguration situations. The authors develop a single theorem to identify the condition where WC places cannot be replaced by Ordinary Control (OC) arcs, while others can be replaced.