Product Form Solution for Stochastic Automata Networks with synchronizations

We present a class of Stochastic Automata Networks (SAN) which exhibit a product form solution if some generalized flow equations are satisfied. Unlike previous models on SAN with product form solutions, our model allows synchronizations between automata. This class of SAN is a generalization of Jackson's queueing networks and Gelenbe's networks with positive and negative customers . 1 Introduction Stochastic Automata Networks (SAN for short) have been proposed by B. Plateau [10] as a modeling paradigm to allow easy representation and evaluation of parallel systems. It is clearly understood now that SAN are a particular case of a stochastic extension of Process Algebra. Therefore new results in the context on SAN will often be easily translated into other models based on process algebra. The first method associated to Stochastic Automata Networks was a numerical resolution of steady-state distribution of the Markov chain associated to a SAN [11]. It consists of a improvement of the po..