A polynomial complexity deadlock avoidance method for a class of flexible manufacturing systems

Computational complexity is one of most important criteria in evaluating the performance of deadlock control methods. Based on Petri net models, a polynomial deadlock avoidance method is addressed for a class of flexible manufacturing systems (FMSs) with key resources. It is first proved that there are three kinds of reachable markings in these FMSs: safe ones, deadlock, and secondary deadlock. Second, an algorithm with polynomial complexity to determine the safety of a new marking resulting from a safe one is presented. It adopts a one-step look-ahead method and two-step look-ahead one to prohibit the firings of transitions that result in deadlock and secondary one, respectively. Thus, a polynomial deadlock avoidance policy for a class of FMSs with key resources is established. An illustrative example is provided to demonstrate the efficiency of the proposed method.