Letter to the Editor—A Queuing System with Bulk Service

A simple queuing system is envisaged that is similar to a car ferry departing at regular intervals, or to a plant of fixed capacity processing work that can arrive only at regular intervals. The integral equation is found that relates the queue properties to the pattern of arrival of work. By analysis of this integral equation it is found that when the mean rate of arrival of work x̄_p approaches the plant capacity (unity), the product of the mean queue length x̄_q and 1 − x̄_p approaches one half the variance of the arrival distribution.