Approximate Analysis of a G/G/c/PR Queue

Abstract

The principle of maximum entropy (ME) is used to analyse a stable G/G/c/PR queue with general interarrivai and service times, c (> 2) parallel servers and R (> 2) priority classes under preemptive resume (PR) scheduling. The form of the joint state probability is characterised, subject to the existence of constraint information involving normalisation, marginal mean queue lengths and the probabilities of having a least number j of busy servers with jobs of class r. For R = 2, new closed-form approximations for the marginal state probabilities (per class), as explicit functions of the above constraints, are derived. Moreover, these ME solutions are also applied, in conjunction with the method of class aggregation, to the case of an arbitrary number of classes R (> 2). To illustrate the utility of the ME solutions the Generalised Exponential (GE) model is used to approximate general distributions with known first two moments, and exact as well as approximate stochastic analysis is carried out for estimating the associated constraints of interest. Numerical examples illustrate the accuracy of the proposed approximations in relation to simulations involving different interarrivai and service time distributions per class. Concluding remarks and comments on the extension of the work to the analysis of general queueing networks are included.