A revised MIP method to deal with livelocks in a class of generalized Petri nets

摘要

Both deadlocks and livelocks can result in the serious problems in running process of flexible manufacturing systems (FMSs). Current siphon detection approaches based on mixed integer programming (MIP) cannot detect siphons that cause livelocks in a system of sequential systems with shared resources (S~4R), a typical class of Petri net models of FMSs. This study proposes a revised MIP method to directly solve the smart siphons associated with livelocks or deadlocks in Petri nets. Accordingly, the corresponding control places (CPs) are added for the solved smart siphons to make them max'-controlled. Thus an original S~4R system with deadlocks or livelocks can be turned into the live controlled one. Compared with the existing methods in the literature, the proposed method is more general and powerful. A theoretical analysis and two examples are given to demonstrate its efficiency and practical potentials.