On the Equilibrium Sets of Topologically Equal Conflict Timed Continuous Petri Nets

Abstract

Abstract This work deals with the study of equilibrium markings (states) in a class of Timed Continuous Petri Nets (TCPNs) under infinite server semantics. First, by adopting a structural approach, a qualitative analysis of the equilibrium sets in Choice-Free (CF) TCPN systems is presented. It is based on the analysis of the slowest conservative subsystems of the system. This allows us to define a structural component named the Maximal Limiting Subnet (MLS). Then, some properties of the equilibrium sets in CF-TCPN systems are stated in terms of its MLS. Next, connectivity of the equilibrium sets, an important property for the global controllability of the system, is studied. It is shown that CF-TCPN systems always exhibit this property. Finally, the previous results are extended to Topologically Equal Conflict TCPN systems. However, it is also shown that connectivity is not necessarily fulfilled in general systems.