Equivalence and Lumpability of FSPNs

We consider equivalence relations for Fluid Stochastic Petri Nets (FSPNs). Based on equivalence relations for Stochastic Petri Nets (SPNs), which are derived from lumpability for Markov Chains, and from lumpability for certain classes of differential equations, we define an equivalence relation for FSPNs. Lumpability for the differential equations is based on a finite discretization approach and permutations of the fluid part of the FSPN. As for other modeling formalisms, the availability of an appropriate equivalence relation allows one to aggregate sets of equivalent states into single states. This state space reduction can be exploited for a more efficient analysis of FSPNs using a discretization approach. Lumpable equivalence relations can be computed from an appropriately discretized state space of the stochastic process or directly from the FSPN.