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