Bias optimality in a queue with admission control

We consider a finite capacity queueing system in which each arriving customer offers a reward. A gatekeeper decides based on the reward offered and the space remaining whether each arriving customer should be accepted or rejected. The gatekeeper only receives the offered reward if the customer is accepted. A traditional objective function is to maximize the gain, that is the long-run average reward. It is quite possible, however, to have several different gain optimal policies that behave quite differently, Bias and Blackwell optimality are more refined objective functions that can distinguish among multiple stationary, deterministic gain optimal policies. This paper focuses on describing the structure of stationary, deterministic optimal policies and extending this optimality to distinguish between multiple gain optimal policies. We show that these policies are of trunk reservation form and must occur consecutively. We then prove that we can distinguish among these gain optimal policies using the bias or transient reward and extend to Blackwell optimality.