On a theory of interacting queues

Abstract

We present a possible way to extend queuing theory to account for interactions between adjacent queues in a packet-switched network. The interaction between queues arises because of the influence of the routing protocol on each switching decision and the stochastic nature of packet lengths and inter-arrival times. Both the methodology and the analysis tools are adaptations of methods of statistical mechanics and are presented in outline here. The justification for their use lies in experimental evidence given in [1,2,3] that aggregate, core-network IP traffic exhibits quasi-Markovian properties. In this paper, we focus on the interaction between pairs of queues, either in a cascaded arrangement, or connected to the same switching fabric, in the presence of an idealised routing protocol.