Condensation in large closed Jackson networks

Abstract

We consider finite closed Jackson networks with N first come, first serve nodes and M customers. In the limit $M \to \infty, N \to \infty, M/N \to \lambda > 0$, we get conditions when mean queue lengths are uniformly bounded and when there exists a node where the mean queue length tends to $\infty$ under the above limit (condensation phenomena, traffic jams), in terms of the limit distribution of the relative utilizations of the nodes. In the same terms, we also derive asymptotics of the partition function and of correlation functions.