Fault tolerant liveness analysis for a class of Petri nets

Although Petri nets have been widely used in the analysis of manufacturing systems, real systems usually suffer from failure prone resources, which makes it difficult to apply existing Petri net analysis methods to control manufacturing systems based on Petri net theory. Existing Petri net theory is deficient in analyzing the liveness property for systems with unreliable resources. Reachability analysis is feasible only for small systems. This paper bridges the gap between existing Petri net theory and its application to real manufacturing systems. This paper focuses on fault tolerant analysis of existing Petri net theory. The paper considers the persistent production control problem of a class of Petri nets called marked graph (MG)-refined nets, a class for modeling manufacturing systems with flexible production routing and heterogeneous, failure prone resources. The new class of MG-refined nets is differentiated from existing Petri nets in that the number of tokens in the net is not conserved to model the effects of unreliable resources. We characterize fault tolerant conditions for MG-refined nets. For MG-refined nets, we propose the concept of persistent production, a weaker condition than liveness to produce the products of a given type of production process for manufacturing systems.