Dynamic admission and service rate control of a queue

This paper investigates a queueing system in which the controller can perform admission and service rate control. In particular, we examine a single-server queueing system with Poisson arrivals and exponentially distributed services with adjustable rates. At each decision epoch the controller may adjust the service rate. Also, the controller can reject incoming customers as they arrive. The objective is to minimize long-run average costs which include: a holding cost, which is a non-decreasing function of the number of jobs in the system; a service rate cost c(x), representing the cost per unit time for servicing jobs at rate x; and a rejection cost κ for rejecting a single job. From basic principles, we derive a simple, efficient algorithm for computing the optimal policy. Our algorithm also provides an easily computable bound on the optimality gap at every step. Finally, we demonstrate that, in the class of stationary policies, deterministic stationary policies are optimal for this problem.