On the optimality of a maintenance queueing system

We consider a finite single-server maintenance queue with multiple types of customers. The difference between customers' types is defined by the offered rewards. We show that the optimal admission control policy for maximizing the long-run average reward per unit time has a trunk reservation structure. Meanwhile, if the equipment is off, there exists a threshold of the queue length, above which the optimal repair speed is increasing in the queue length and below which the optimal repair speed is 0.