The Number Served in a Head Of The Line Priority Queue with General Service

Abstract

In this paper, using the supplementary variable method, the head-of-the-line priority queueing system with general service time distributions have been studied to obtain an expression for the Laplace transform of the generating function of the joint probability distribution of the number of priority and non-priority units in the queue at time t, and the number of units served (including non-priority units) in time t. In particular cases, explicit solution for the model with exponential service time distributions have been obtained; expression for the joint distribution of the queue length and the number served in time t, for an M/G/1 queue has also been derived.