Abstract We present a possible way to study large-size packet-switched networks capable of accounting for interactions between adjacent queues. 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. The justification for their use lies in recent experimental evidence indicating that aggregate, core-network IP traffic, exhibits quasi-Markovian properties when the network is heavily loaded.In this paper, we present a general methodology and introduce approximations that greatly simplify the analysis. These approximations, are owing to the quasi-Markovian nature of the traffic and the large size of the network.