Computing Optimal Control Limits for GI/M/S Queuing Systems with Controlled Arrivals

We consider a GI/M/s queuing system that is controlled by either accepting or rejecting arriving customers. Under weak conditions on the cost structure, Stidham (Stidham, S., Jr., 1978. Socially and individually optimal control of arrivals to a GI/M/1 queue. Management Sci.24 1598–1610.) showed that a control limit policy is optimal. In this paper we show how the special structure of this queuing system can be exploited to develop efficient procedures to determine an optimal control limit. An explicit algorithm for computing the optimal control as well as an example and some computational results are included.