# BIAS OPTIMALITY IN A QUEUE WITH ADMISSION CONTROL

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Mark E. Lewis

Industrial and Operations Engineering

University of Michigan

1205 Beal Avenue

Ann Arbor, MI 48109-2117

Hayriye Ayhan and Robert D. Foley

School of Industrial and Systems Engineering

Georgia Institute of Technology

Atlanta, GA 30332-0205

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. However, it is quite possible
to have several different gain optimal policies that behav 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.