Priority queues with Gaussian input: a path-space approach to loss and delay asymptotics.

Abstract

Priority queueing is the basic technique for providing real-time Quality of Service to packet-based networking. The mathematical analysis of priority queues with general traffic models is, however, prohibitively difficult, in particular when the traffic is long-range dependent. This paper provides some important steps forward in this direction. Our analysis is the first mathematically rigorous treatment of path-space large deviations of priority queues with class-wise heterogeneous Gaussian input having an arbitrary correlation structure. This includes the computation of the most probable paths that lead to overflow in one of the queues. Compared with earlier work on the same topic, the paper provides three novel contributions: a new representation of the workload in the low-priority queues, an exact characterization of the most probable paths, and an extension of the analysis to virtual waiting times, in addition to queue lengths.

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