A Technique for Computing Sojourn Times in Large Networks of Interacting Queues

Abstract

Consider a large number of interacting queues with symmetric interactions. In the asymptotic limit, the interactions between any fixed finite subcollection become negligible, and the overall effect of interactions can be replaced by an empirical rate. The evolution of each queue is given by a time inhomogeneous Markov process. This may be considered a technique for writing dynamic Erlang fixed-point equations. We explore this as a tool to approximate sojourn time distributions.