Monotonic and insensitive optimal policies for control of queues with undiscounted costs

The authors consider the problem of controlling the service and/or arrival rates in queues, with the objective of minimizing the total expected cost to reach state zero. They present a unified, simple method for proving that an optimal policy is monotonic in the number of customers in the system. Applications to average-cost minimization over an infinite horizon are given. Both exponential and nonexponential models are considered; the essential characteristic is a left-skip-free transition structure and a nondecreasing (not necessarily convex) holding-cost function. Some of the present results are insensitive to service-time distributions.