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Capacity Design and Service Quality Control in a Queuing System

We consider a finite-capacity single-server queuing system in which the problems of capacity design and service quality control are integrated. The amount of time spent on servicing a customer is used as a measure of the quality of service provided. The expected reward from servicing is assumed to be a nondecreasing function of the service duration, while a linear holding cost is assumed for customers waiting in the system. We maximize the long-run average return per unit time by optimally controlling the quality of service to be provided as a function of the workload facing the server for different waiting-room capacities. We show that the optimal control policy for a given capacity is monotone and also examine the effect of varying the system capacity on the optimal control policy. Furthermore, we analyze the design problem of selecting an optimal capacity by assuming that an optimal service control policy will be followed for each system capacity.