Tandem Brownian queues

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. This research has been funded by the Dutch BSIK/BRICKS (Basic Research in Informatics for Creating the Knowledge Society) project. M. Mandjes is also affiliated with the Korteweg-de Vries Institute, University of Amsterdam, The Netherlands, and EURANDOM, Eindhoven, The Netherlands.