| Abstract: | We study queueing networks with instantaneous transitions of sequential batch departures and sequential batch arrivals. Unlike most of the existing models, this network is shown not to have a product form solution. An "extra arrival condition" is introduced under which the network is shown to possess a product form stationary distribution. Fur- thermore, the product form solution serves as a stochastic upper bound for the original network without the extra arrival process. The results include many queueing network models reported in the literature, e.g. the assembly transfer networks recently introduced by Miyazawa and Taylor, as special cases. We show that the network with the extra arrival process is "structurally reversible" in the sense that its reversed process has the same network structure. Local balances for this network are presented and discussed. |
