Stochastic Petri nets (SPNs) with generally distributed firing times are isomorphic to generalized semi-Markov processes (GSMPs), but simulation is the only feasible approach for their solution. The authors explore a hierarchy of SPN classes where modeling power is reduced in exchange for an increasingly efficient solution. Generalized stochastic Petri nets (GSPNs), deterministic and stochastic Petri nets (DSPNs), semi-Markovian stochastic Petri nets (SM-SPNs), timed Petri nets (TPNs), and generalized timed Petri nets (GTPNs) are particular entries in the hierarchy. Additional classes of SPNs for which it is shown how to compute an analytical solution are obtained by the method of the embedded Markov chain (DSPNs are just one example in this class) and state discretization, which the authors apply not only to the continuous-time case (PH-type distributions), but also to the discrete case.
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