A Characterization of Product-form Stationary Distributions for Queueing Systems in Random Environment

We consider continuous-time Markov chains representing queueing systems in random environment and we obtain necessary and sufficient conditions for having product-form stationary distributions. The related topics of partial balance and the ESTA property are also studied. As an illustration, we apply the results to study the stationary distributions of Jackson networks in random environment. For models that do not satisfy the product-form conditions, we develop a product-form approximation, which is proved to be very good for models evolving in a slowly changing random environment. We justify this fact and we propose a methodology for estimating the error of this approximation.