Improvement of Suboptimal Siphon- and FBM-Based Control Model of a Well-Known S3PR

Siphon-based deadlock control of Flexible Manufacturing System (FMS) runs faster by avoiding reachability analysis, but reaches fewer states than an optimal. First-met bad marking (FBM) method requires more monitors, but reaches more states by refining some monitors with smaller (hence less disturbed) controller regions. However, the same refinement leads to more monitors for other siphons, which can be combined without losing states. This paper develops the formal theory to uncover the secret behind the above discrepancy. It improves the siphon-based approach to reach more states while using fewer monitors. Note to Practitioners-Siphon-based deadlock control (SBDC) prevents siphons from becoming unmarked by adding monitors to problematic siphons. Siphon is a structure object or a set of places. Once it becomes empty of tokens, it stays so, and all output transitions of places in the siphon become permanently dead. The controller region (CR) may include unmarked places disturbing more on the uncontrolled model and thus is less permissive than the FBM method whose CR covers only marked places and is the most permissive method to synthesize controllers with no weighted control (WC) arcs. However, monitors for the same siphon may be merged into one without losing states. Thus, the SBDC method employs fewer monitors than the FBM one but reaches fewer states. This paper develops the theory to uncover this secret and improve both methods.