Bursty traffic and finite capacity queues

Traffic on high-speed networks is expected to be "bursty". This has spurred interest in the queueing properties of bursty traffic models, such as Markov additive processes. These processes have by now been studied extensively by many authors, but almost exclusively in the infinite buffer setting. This paper deals with the case of a finite-buffered queue loaded with bursty traffic. It shows how to calculate the exact solution for the queue length distribution and overflow rate in equilibrium, and also how to find efficient upper and lower bounds for these quantities. In addition, the large buffer asymptotic behaviour of the queue length distribution and overflow rate are studied for a queue loaded with general traffic, using large deviation techniques.