The Computation of Optimal Control Limits for a Queue with Batch Services

We study the optimal control of a queueing system with Poisson input and a server capable of serving an infinite number of customers per batch. It is known that the optimal type of control policy is a control limit policy: service should begin if and only if the number of waiting customers is at least as large as some control limit. Our objective is to find the control limit that minimizes the long run average cost of waiting and service charges. We determine the cost as a function of the control limit, present properties of the cost function and optimal control limit, present easily computable upper and lower bounds for the optimal control limit and an algorithm for finding the optimal control limit.