Resource-Transition Circuits and Siphons for Deadlock Control of Automated Manufacturing Systems

The resource-transition circuit ( RTC) and siphon are two different structural objects of Petri nets and used to develop deadlock control policies for automated manufacturing systems. They are related to the liveness property of Petri net models and thus used to characterize and avoid deadlocks. Based on them, there are two kinds of methods for developing deadlock controllers. Such methods rely on the computation of all maximal perfect RTCs and strict minimal siphons (SMSs), respectively. This paper concentrates on a class of Petri nets called a system of simple sequential processes with resources, establishes the relation between two kinds of control methods, and identifies maximal perfect RTCs and SMSs. A graph-based technique is used to find all elementary RTC structures. They are then used to derive all RTCs. Next, an iterative method is developed to recursively construct all maximal perfect RTCs from elementary ones. Finally, a one-to-one correspondence between SMSs and maximal perfect RTCs and, hence, an equivalence between two deadlock control methods are established.