Bias optimality in a queue with admission control

We consider a finite capacity queueing system in which each arriving custom er offers a reward. A gatekeeper decides based on the reward offered and th e space remaining whether each arriving customer should be accepted or reje cted. The gatekeeper only receives the offered reward if the customer is ac cepted. A traditional objective function is to maximize the gain, that in t he long-run average reward Tt is quite possible, however, to have several d ifferent gain optimal policies that behave quite differently, Bias and Blac kwell optimality are more refined objective functions that can distinguish among multiple stationary, deterministic gain optimal policies This paper f ocuses nn describing the structure of stationary, deterministic, optimal po licies and extending this optimality to distinguish between multiple gain o ptimal policies. We show that these policies are of trunk reservation form and must occur consecutively. We then prove that we can distinguish among t hese gain optimal policies using the bias or transient reward and extend to Blackwell optimality.