Performance Analysis of a Poisson-Pareto Queue over the Full Range of System Parameters

There have been many queuing analyses for a single server queue fed by an M/G/ ∞ traf-fic process, in which G is a Pareto Distribution, that focus on certain limiting conditions. In this paper we enhance the so-called Quasi-Stationary (QS) approximation – a queuing analysis introduced previously that provides an algorithm for computation of an accurate approximation for the stationary queue distribution, applicable to the entire range of system parameters. By numerical evaluation of the QS approximation and the asymptotic approx-imations (large buffer, many sources, and heavy traffic) over an extremely wide range of parameter values we are able to graphically display consistency of the QS approximation with all the asymptotic results. We demonstrate that the accuracy of the asymptotic approx-imations is satisfactory only in limited regions of the system parameter space