A stochastic lower bound for assemble-transfer batch service queueing networks

Miyazawa and Taylor (1997) introduced a class of assemble-transfer batch se rvice queueing networks which do not have tractable stationary distribution . However by assuming a certain additional arrival process at each node whe n it is empty, they obtain a geometric product-form stationary distribution which is a stochastic upper bound for the stationary distribution of the o riginal network. In this paper we develop a stochastic lower bound for the original network by introducing an additional departure process at each nod e which tends to remove all the customers present in it. This model in comb ination with the aforementioned upper bound model gives a better sense for the properties of the original network.