Concurrent generalized Petri nets: regenerative conditions

Concurrent generalized Petri nets (CGPNs) are a subclass of Markov regenerative stochastic Petri nets, characterized by timed transitions with general distributed firing times (GEN transitions), that become enabled simultaneously while no other GEN transitions can be activated during their enabling periods. In their original definition, CGPNs were identified through a study of their state space; hence they are recognized only after the construction of their tangible reachability graphs. In this paper, we present sufficient conditions representing a first step in the definition of an alternative method for the characterization of this type of models. The method is based on the structural analysis of the net, it does not require the generation of its tangible reachability graph, and is thus computationally convenient. Moreover, an advantage of this method is that it can also be applied in the case of models characterized by large state spaces, and is hence prone to be analysed via simulation using regenerative techniques. The criteria that we propose represent the basis for a preliminary analysis of the model in order to verify its membership of the class of CGPNs whose numerical solution always requires the construction of the tangible reachability graph and the characterization of the underlying Markov regenerative process.