Tandem Brownian queues

Abstract

We analyze a two-node tandem queue with Brownian input. We first derive an explicit expression for the joint distribution function of the workloads of the first and second queue, which also allows us to calculate their exact large-buffer asymptotics. The nature of these asymptotics depends on the model parameters, i.e., there are different regimes. By using sample-path large-deviations (Schilder’s theorem) these regimes can be interpreted: we explicitly characterize the most likely way the buffers fill.