Queues in Series via Interacting Particle Systems

In this paper, we consider a serial network with very large (infinite) number of single server queues. Initially, the network is empty. The input process to the network is Poisson with rate less than one (unsaturated case) or one (saturated case) and the service times at each queue is exponential with mean one. We exploit results for interacting particle systems, in particular, the zero-range and simple-exclusion processes to investigate the approach to equilibrium of this network. We derive the hydrodynamic limit of this queueing network which dramatically describes the transient behavior of this network.