An asymptotic analysis of complete sharing policy

Abstract

A model is considered which has several classes of customers arriving in independent Poisson processes at a multiserver facility and requiring a specific number of servers for a random period of time (arbitrarily distributed with a finite mean). If these servers cannot be provided, the customers are cleared. The problem is to determine the blocking probabilities. The exact expression is available but is complicated. The authors apply a novel approximation method of ensemble averaging for the asymptotic analysis of blocking in such systems. The method gives simple expressions for the average performance measures without an explicit computation of the normalization constant of the steady-state probability distribution. The computation of blocking probability and of other performance measures is reduced to computing a root of a simple algebraic equation. The obtained expressions are shown to be asymptotically correct.