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Bias optimal admission control policies for a multiclass nonstationary queueing system

  • Mark E. Lewis (a1), Hayriye Ayhan (a2) and Robert D. Foley (a2)

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.

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Corresponding author

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.

References

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Bias optimal admission control policies for a multiclass nonstationary queueing system

  • Mark E. Lewis (a1), Hayriye Ayhan (a2) and Robert D. Foley (a2)

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