Structured Characterization of the Markov Chain of Phase-Type SPN

This paper presents a characterization of the Markovian state space of a Stochastic Petri Nets with phase-type distribution transitions as a union of Cartesian products of a set of “components” of the net. The method uses an abstract view of the net based on the vectors of enabling degrees of phase-type transitions, as well as on the sets of “interrupted clients”. Following the decomposition used for the state space characterization, a tensor algebra expression for the infinitesimal generator (actually for its rate matrix) is given, that allows the steady state probability to be computed directly from a set of matrices of the size of the components, without the need of storing the whole infinitesimal generator.