A new optimal control policy for a well-known S3PR (systems of simple sequential processes with resources)

Abstract

There are many studies reported in the literature comparing the effectiveness of new control policies by testing them against a well-known S3PR (systems of simple sequential processes with resources) model. We propose a new approach that recovers the system from empty-siphon states to former live states. It therefore attains the same number of states as the original uncontrolled model by adding monitors (and control arcs) similar to the prevention approach. There is no need to perform a reachability analysis. INA (integrated net analyser) analysis indicates that the resulting controlled model is live and reaches all 26,750 states (in the uncontrolled model), more than the maximally permissive 21,581 states. Only seven monitors are employed, fewer than in most other approaches. This arises from the fact that no new problematic siphons are generated due to the added monitors. We discuss the disadvantages (a variant of the scheme to overcome the disadvantages is also discussed) and physical meaning of the policy. We further propose a lossless approach by colouring some arcs. This not only avoids material loss, but also tackles the livelock problem.