Deriving the performance indices in product-form stochastic Petri nets: Open problems and simulation

Stochastic Petri nets are an important formalism used for the performance evaluation of computer and communication systems as well as other fields like bioin-formatics and logistics. Despite its high flexibility and modelling power, one of the problems of quantitative analyses based on stochastic Petri nets is the state space explosion, i.e., the high cardinality reached by the state space of even a structurally small SPN. As a consequence a direct analysis of the Markovian processes underlying the models is not feasible. Product-form Petri nets are a class of stochastic Petri nets whose invariant measure can be expressed as a product of functions, each of which depends only on a marking of a single place. Nevertheless, for the effective computation of the performance indices the computation of the stationary distribution is required. In this paper we propose a classification of product-form stochastic Petri nets based on the availability of algorithms for the computation of their stationary performance indices. Moreover, in case simulation is required, we introduce two stopping criteria that exploit the product-form property of the nets