Optimal Average-Cost Policy for a Queue with Start-Up and Shut-Down Costs

This paper examines pure stationary policies for starting and stopping service in a single-server queue with respect to the state space consisting of queue length and whether or not the service facility is operating. Almost any such policy is shown to be equivalent to one that depends on two parameters. For a wide class of cost functions, the “almost any” is shown to be without loss of optimality in the sense of average cost per unit time over an infinite horizon. The results are largely distribution-free and are obtained with random-walk arguments. They apply also to certain repair problems and to production smoothing problems in which demand is a renewal process and goods are made sequentially.