The Ergodic Queue Length Distribution for Queueing Systems with Finite Capacity

Abstract

LetM(t) be the queue length process for anM/G/1 queue with finite queue capacityL.A simple expression is given for the ergodic queue length distributionPL(m) =p{M(∞) =m}, in terms of certain Green's function elements for a Markov processMkimbedded inM(t). The ergodic distribution for the imbedded process and that for the original process are shown to differ in the presence of finite queue capacity. The ergodic queue length distribution forG/M/1 with finite queue capacity is also exhibited.