A maximum entropy queue length distribution for the G/G/1 finite capacity queue

Abstract

A new “hybrid” analytic framework, based on the principle of maximum entropy, is used to approximate the queue length distribution of a G/G/1 finite buffer queue. Robust recursive relations are derived and asymptotic connections to the infinite capacity queue are established. Furthermore, “equivalence” principles are applied to analyse two-stage cyclic queues with general service times and favourable comparisons with global balance solutions are made. Numerical examples provide useful information on how critically system behaviour is affected by the distributional form of interarrival and service patterns. It is shown that the maximum entropy solution predicts the bottleneck “anomaly” and also it defines bounds on system performance. Comments on the implication of the work to the analysis and aggregation of computer systems are included.