Bias Optimal Admission Policies for a Nonstationary Multi-Class Queueing System

Mark E. Lewis
Industrial and Operations Engineering Department
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 where arriving customers offer various rewards which are paid only upon acceptance into the system. The gatekeeper, whose objective is to ``maximize'' rewards decides if the reward offered is sufficient to accept or reject the arriving customer. Suppose the arrival rates, service rates, and system capacity are changing over time in a known manner.  We show that all bias optimal policies are of trunk reservation form. Furthermore,  we give sufficient conditions for the bias optimal policy to be monotonic in time. Bias optimality can be considered to be a refinement of maximizing the long-run average reward. A counter-example shows that the increasing/decreasing cases are not symmetric.