ME-based approximations for general discrete-time queueing models

Abstract

Product-form approximations, based on the principle of Maximum Entropy (ME), are characterised for general multi-buffered and shared buffer discrete-time queueing models with Arrivals First (AF) and Departures First (DF) buffer management policies. The arrival process at each queue is assumed to be bursty and it is modelled by a Compound Bernoulli Process (CBP) with geometrically distributed bulk sizes. The forms of the joint, aggregate and marginal state probabilities, as well as basic performance measures such as mean queue length and cell-loss probability, are analytically established at equilibrium via appropriate mean value constraints and the generating function approach. Consequently, efficient recursive expressions of low computational cost are established. Focusing on a shared buffer ATM switch architecture under DF policy, validation tests against simulation show that the ME approximation has a very good error level. Further experimentation illustrates the credibility of the ME solutions and carries out performance comparisons between multi-buffered and shared buffer ATM switch architectures.