Maximum entropy and the G/G/1/N queue

Summary A new hybrid analytic framework, based on the principle of maximum entropy, is used to derive a closed form expression for the queue length distribution of a G/G/1 finite capacity queue. It is shown that Birth-Death homogeneous recursions for a single resource queue are special cases of maximum entropy one-step transitions which can be applied either in an operational or stochastic context. Furthermore, an equivalence relationship is used to analyse two-stage cyclic queueing networks with general service times, and favourable comparisons are made with global balance and approximate results. Numerical examples provide useful information on how critically system behaviour is affected by the distributional form of interarrival and service patterns. Comments on the implication of the work to the performance analysis and aggregation of computer systems are included.Some of the material included in this paper has been presented to the Performance '86 and ACM Sigmetrics 1986 Joint Conference on Computer Modelling, Measurement and Evaluation, May 28–30, 1986, University of North Carolina, USA