Modelling retrial-upon-conflict systems with product-form stochastic Petri nets

In this paper we consider a particular class of stochastic Petri nets that admits a product-form stationary distribution under general conditions (independent exponentially distributed firing time). We show that the structure of the these stochastic Petri nets is appropriate for modelling systems in which several components compete for a resource and conflicts may arise during the contention that require to newly perform the operation after a recovery time. Examples of these systems are wireless stations competing for a channel or processes operating on the same database concurrently. We derive the performance indices as functions of the model parameters, i.e., firing rates, probabilities of conflicts, number of competing components.