Computational algorithms for product form solution stochastic Petri nets

In this paper we show that the steady-state probability distribution of stochastic Petri nets (SPNs) with product form solution can be efficiently computed using an algorithm whose space and time complexities are polynomial in the number of places and in the number of tokens in the initial marking of the SPN. Basic to the derivation of such an algorithm is a product form solution criterion proposed by J. L. Coleman et al. (1992). The algorithm relies on the derivation of a recursive expression of the normalization constant that is a generalization of that derived by J. P. Buzen (1973) for multiple class product form queuing networks with load independent service centers.