A Refined Siphon-Based Deadlock Prevention Policy for a Class of Petri Nets
Shouguang Wang, Xin Guo, Oussama Karoui, MengChu Zhou, Dan You, Abdullah Abusorrah
Abstract
Resource allocation systems (RASs) exist in various fields of modern society. The deadlock control problem is a crucial issue in control theory of RAS. This work is concentrated on a special class of shared resource and process-oriented Petri nets whose initial marking can have only a token in every resource place. Using mixed-integer programming (MIP) and iterative siphon control, we present a two-stage deadlock prevention policy. In particular, a modified MIP technique is developed for the first stage to compute a specific type of emptiable siphons and a siphon control method introducing monitors with related arcs whose weights all equal to one is established in the second stage. This policy leads to a maximally permissive liveness-enforcing supervisor and such an obtained controlled net is ordinary. Moreover, it avoids the exhaustive enumeration of siphons and the reachability analysis. Examples are provided to explain the policy.