Efficient Handling of Phase-Type Distributions in Generalized Stochastic Petri Nets

We study the introduction of transitions with Phase-type distribution firing time in (bounded) generalized stochastic Petri nets. Such transitions produce large increases of both space and time complexity for the computation of the steady state probabilities of the underlying Markov chain. We propose a new approach to limit this phenomenon while keeping full stochastic semantics of previous works. The method is based on a structural decomposition of the net. We establish conditions under which this decomposition leads to a tensor expression of the generator of the chain. The tensor expression is used to solve the chain with an iterative method.ou