Deadlock Prevention Policy for S4PR Nets Based on Siphon

Computational efficiency and behavioral permissiveness are important criteria for evaluating the performance of deadlock control strategies. How to achieve an effective tradeoff between these criteria is a hot research topic in the field of deadlock prevention. Toward this end, a new iterative deadlock prevention policy based on mixed integer programming is proposed for a class of Petri nets called systems of sequential systems with shared resources (<inline-formula> <tex-math notation="LaTeX">$S^{4}PR$ </tex-math></inline-formula>) nets. In each iteration, a minimal bad siphon is first calculated using the new approach, and a monitor is then designed to forbid all <inline-formula> <tex-math notation="LaTeX">$S^{\prime }$ </tex-math></inline-formula>-<italic>bad</italic> markings that turn the siphon S into a bad siphon. The algorithm terminates when no bad siphon is detected. The resultant system derived from the proposed approach has more permissive behavior compared with that derived from existing policies. Furthermore, optimal controlled systems can be obtained for some <inline-formula> <tex-math notation="LaTeX">$S^{4}PR$ </tex-math></inline-formula> nets. Moreover, the computational efficiency of the algorithm is low because computation of the reachability graph and complete siphon enumeration are avoided.