Transient analysis of Brownian queues

We analyze a single-node network with Brownian input. We first derive an explicit expression for the joint distribution function of the workloads at two different times, which also allows us to calculate their covariance and 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 buffer fills.