Most probable path techniques for gaussian queueing systems

Abstract

This paper is a review of an approach to queueing systems where the cumulative input is modelled by a general Gaussian process with stationary increments. The examples include priority and Generalized Processor Sharing systems, and a system where service capacity is allocated according to predicted future demand. The basic technical idea is to identify the most probable path in the threshold exceedance event, or a heuristic approximation of it, and then use probability estimates based on this path. The method is particularly useful for long-range dependent traffic and complicated traffic mixes, which are difficult to handle with traditional queueing theory.