Waiting Time in Bulk Service Queues

Abstract

Thequeuing process considered is that in which customers arrive at random and form a single queue in order of arrival. They are served in batches, the size of the batch being either a fixed number or the size of the queue, whichever is the smaller. Assuming that the queue is in equilibrium, the Laplace transform of the waiting time distribution is derived from the probability generating function of the queue length distribution. Expressions are obtained for the mean and variance of the waiting time, and a brief discussion is included of the computation of these quantities when the time intervals between successive epochs of service are independently distributed in a χ2distribution with an even number of degrees of freedom. A short table of numerical results is given.