Structure of Optimal Policies in Complex Queuing Systems

This paper examines a class of M/G/S queuing reward systems with heterogeneous servers and heterogeneous customers. With the help of two simple results, we show that the policy that maximizes average reward per unit time over an infinite horizon possesses a certain structured form, which for several examples is quite intuitive and for others is not so intuitive. We also show that when the policy improvement method is used to find the optimal policy, only policies with the structured form need be considered, an obvious computational simplification. Computational results are discussed briefly.