On the Non-existence of Product-form Solutions for Queueing Networks with Retrials

During the last two decades, several authors have identified several classes of queueing networks (with batch movements, negative customers, signals etc.) that have product-form stationary distributions. On the contrary, there is a very slow progress in the analytic investigation of queueing networks with retrials and there does not exist a single example of such a network with a product-form stationary distribution. In this note we prove the non-existence of product-form solutions for queueing networks with retrials, using a recent characterization of product-form networks.