The Optimality of Full Service Policies

The structure of optimal service rate adjustment policies is considered here for single server, multiple server, and arborescence network models. It is shown that a full service policy, namely, always using the highest effective service rate, is optimal under general conditions. The criteria are the long-run averages of the cost per customer served and the cost per unit time. Underlying costs are assumed to include waiting time penalties and rates depending on the number of customers in the system and on the pace at which service is proceeding. The only essential restriction on probability distributions or costs is that the highest service rate minimizes the expected cost of serving a customer.