On Intrinsically Live Structure of a Class of Generalized Petri Nets Modeling FMS

The deadlock control and liveness-enforcement are mostly implemented based on siphons in most existing work using structural theory. Our previous work has revealed a kind of intrinsically live structures in a class of generalized Petri nets called systems of simple sequential processes with weighted resources allocation (WS3PR). The liveness-enforcement is achieved by analyzing the structure including weight information and reconfiguring the initial marking of resource places without considering the initial token counts in idle process places. This work extends it to a more general class than WS3PR. Instead of siphons, a new concept of structural objects is defined to carry weight information and reflect the circular waits of resources. The numerical relationship between initial markings of resource places and weights of arcs is investigated to yield an intrinsically live structure-based liveness-enforcing method that requires no external monitors. The work provides an insight into structures of generalized Petri nets and a new revenue to achieve the desired deadlock control. Several examples are used to illustrate the proposed method.