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Optimal admission control for a single-server loss queue

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Kyle Y. Lin  and
Sheldon M. Ross
Kyle Y. Lin*
Affiliation:
Virginia Tech
Sheldon M. Ross*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA 24061, USA. Email address: kylin@vt.edu
∗∗ Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA.
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Abstract

This paper presents a single-server loss queueing system where customers arrive according to a Poisson process. Upon arrival, the customer presents itself to a gatekeeper who has to decide whether to admit the customer into the system without knowing the busy–idle status of the server. There is a cost if the gatekeeper blocks a customer, and a larger cost if an admitted customer finds the server busy and therefore has to leave the system. The goal of the gatekeeper is to minimize the total expected discounted cost on an infinite time horizon. In the case of an exponential service distribution, we show that a threshold-type policy—block for a time period following each admission and then admit the next customer—is optimal. For general service distributions, we show that a threshold-type policy need not be optimal; we then present a sufficient condition for the existence of an optimal threshold-type policy.

Keywords

Queueoptimal controlcoupling methods

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90C40: Markov and semi-Markov decision processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 2 , June 2004 , pp. 535 - 546
Copyright
Copyright © Applied Probability Trust 2004 

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