Product-form queueing networks with batches

A Markovian queue, with both batch arrivals and batch departures, is first shown to have a geometric queue length probability distribution at equilibrium under certain conditions. From this a product-form solution follows directly for networks of such queues at equilibrium, by application of the reversed compound agent theorem (RCAT). The method is illustrated using small batches of sizes 1 and 2, as well as geometric sizes