Networks of Non-homogeneous M/G/oo Systems

Abstract

For a network of G/oo service facilities, the transient joint distribution of the facility populations is found to have a simple Poisson product form with simple explicit formula for the means. In the network it is assumed that: a) each facility has an infinite number of servers; b) the service time distributions are general; c) external traffic is non-homogenous in time; d) arrivals have random or deterministic routes through the network possibly returning to the same facility more than once; e) arrivals use the facilities on their route sequentially or in parallel (as in the case of a circuit switched telecommunication network). The results have relevance to communication networks and manufacturing systems.