A characterization of the stochastic process underlying a stochastic Petri net

Stochastic Petri nets (SPN's) with generally distributed firing times can model a large class of systems, but simulation is the only feasible approach for their solution. We explore a hierarchy of SPN classes where modeling power is reduced in exchange for an increasingly efficient solution. Generalized stochastic Petri nets (GSPN's), deterministic and stochastic Petri nets (DSPN's), semi-Markovian stochastic Petri nets (SM-SPN's), timed Petri nets (TPN's), and generalized timed Petri nets (GTPN's) are particular entries in our hierarchy. Additional classes of SPN's for which we show how to compute an analytical solution are obtained by the method of the embedded Markov chain (DSPN's are just one example in this class) and state discretization, which we apply not only to the continuous-time case (PH-type distributions), but also to the discrete case.>