Average optimal policies in a controlled queueing system with dual admission control

We consider a controlled M/M/I queueing system where customers may be subje ct to two potential rejections. The first occurs upon arrival and is depend ent on the number of customers in the queue and the service rate of the cus tomer currently in service. The second, which may or may not occur, occurs immediately prior to the customer receiving service. That is, after each se rvice completion the customer in the front of the queue is assessed and the service rate of that customer is revealed. If the second decision-maker re commends rejection, the customer is denied service with a fixed probability . We show the existence of long-run average optimal monotone switching-curv e policies. Further, we show that the average reward is increasing in the p robability that the second decisionmaker's recommendation of rejection is h onored, applications include call centers with delayed classifications and manufacturing systems when the server is responsible for multiple tasks.