Optimal admission policies for a finite queue with bursty arrivals

We consider a service system with a single server, a finite waiting room and two classes of customers with deterministic service time. Primary jobs arrive at random and are admitted whenever there is room in the system. At the beginning of each period, secondary jobs can be admitted from an infinite pool. A revenue is earned upon admission of each job, with the primary jobs bringing a higher contribution than the secondary jobs, the objective being to maximize the total discounted revenue over an infinite horizon. We model the system as a discrete time Markov decision process and show that a monotone admission policy is optimal when the number of primary arrivals has a fixed distribution. Moreover, when the primary arrival distribution varies with time according to a finite state Markov chain, we show that the optimal policy is conditionally monotone and that the numerical computation of an optimal policy, in this case, is substantially more difficult than in the case of stationary arrivals.This research was supported in part by the National Science Foundation, under grant ECS-8803061, while the author was at the University of Arizona.