Event Circular Waits and Their Analysis via Petri Nets

Deadlock control of automated manufacturing systems has been widely investigated in recent decades. According to classical Coffman theory, resource circular wait (RW) is viewed as a necessary condition for deadlocks to occur. However, the fact is not as simple as so. Counterexamples are presented to show that RWs do not necessarily appear together with deadlocks. Event circular waits (EWs) are proposed as an alternative to represent a fundamental necessary condition of deadlocks. First, we present the formal definitions of EWs in a type of Petri nets, i.e., weighted augmented marked graphs (WAMGs), and show that EWs are more general and essential than RWs in describing the cause of deadlocks. Second, we show a new classification of siphons, i.e., types I, II, III, and IV, and illustrate the relationship between undermarked siphons and EWs in the WAMGs. Third, we show that EWs are more efficient than RWs for deadlock avoidance since deadlocks can be avoided earlier at a specified marking by using EWs rather than RWs. Several examples are given to clarify the theory throughout this paper