Decomposition and aggregation in queueing networks

Abstract

This chapter considers the decomposition and aggregation of multiclass queueing networks with state-dependent routing. Combining state-dependent generalisations of quasi-reversibility and biased local balance, sufficient conditions are obtained under which the stationary distribution of the network is of product-form. This product-formfactorises into one part that describes the nodes of the network in isolation, and one part that describes the routing and the global network state. It is shown that a decomposition holds for general nodes if the input-output behaviour of these nodes is suitably compensated by the state-dependent routing function.When only a subset of the nodes is of interest, it is shown that the other nodes may be aggregated into nodes that only capture their global behaviour. The results both unify and extend existing classes of product-form networks, as is illustrated by several cases and an example of an assembly network.