Symmetries in stochastic Petric nets - Construction of the symbolic graph

The main purpose of this paper is to give a method for construction of the reduced reachability graph for Stochastic Petri Nets (SPN), the symbolic graph. This construction is achieved by exploiting the structural symetries in the net using the theory of bisimulation of places for detecting isomorphic parts in the net. The symbolic graph, being isomorphic to an agregated Markov chain, may be used to prove qualitative properties as liveness, boundness,... Moreover, this reduced graph make more easy the computation of the performance measures of interest as the mean number of tokens in a place, the mean number of firing transition... We have so developped a tool, SSPN (Stochastic Symetric Petri nets), far generating the symbolic graph and deducing qualitatives and quantitatives properties.