K Competing Queues With Geometric Service Requirements and Linear Costs: The uc-rule is Always Optimal

J.S. Baras , D.-J. Ma, and A. Makowski

Systems and Control Letters, Vol. 6, No. 3,  pp. 173-180, August 1985.

Abstract

In this note, a discrete-time system of K competing queues with geometric service requirements and arbitrary arrival patterms is studied. When the cost per slot is linear in the queue sizes, it is shown that the uc-rule minimizes the expected discounted cost over the infinite horizon.