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Bias optimal admission control policies for a multiclass nonstationary queueing system

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Mark E. Lewis ,
Hayriye Ayhan  and
Robert D. Foley
Mark E. Lewis*
Affiliation:
University of Michigan
Hayriye Ayhan*
Affiliation:
Georgia Institute of Technology
Robert D. Foley*
Affiliation:
Georgia Institute of Technology
*
∗ Postal address: Department of Industrial and Operations Engineering, University of Michigan, 1205 Beal Avenue, Ann Arbor, MI 48109-2117, USA. Email address: melewis@engin.umich.edu
∗∗ Postal address: School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA.
∗∗ Postal address: School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA.
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Abstract

We consider a finite-capacity queueing system where arriving customers offer rewards which are paid 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 (a refinement of long-run average reward optimal) policies are of threshold form. Furthermore, we give sufficient conditions for the bias optimal policy to be monotonic in time. We show, via a counterexample, that if these conditions are violated, the optimal policy may not be monotonic in time or of threshold form.

Keywords

Dynamic programmingapplicationssensitive optimalityqueuesnonstationaryoptimal controlmonotone policies

MSC classification

Primary: 90C40: Markov and semi-Markov decision processes
Secondary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 1 , March 2002 , pp. 20 - 37
Copyright
Copyright © Applied Probability Trust 2002 

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