A CORRESPONDENCE BETWEEN PRODUCT-FORM BATCH-MOVEMENT QUEUING-NETWORKSAND SINGLE-MOVEMENT NETWORKS

A number of recent papers have exhibited classes of queueing networks, with batches of customers served and routed through the network, whic h have generalised product-form equilibrium distributions. In this pap er we look at these from a new viewpoint. In particular we show that, under standard assumptions, for a network to possess an equilibrium di stribution that factorises into a product form over the nodes of the n etwork for all possible transition rates, it is necessary and sufficie nt that it be equivalent to a suitably-defined single-movement network . We consider also the form of the state space for such networks.