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Average optimal policies in a controlled queueing system with dual admission control

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Mark E. Lewis
Mark E. Lewis*
Affiliation:
University of Michigan
*
∗ Postal address: Department of Industrial and Operations Engineering, University of Michigan, 1205 Beal Avenue, Ann Arbor, MI 48109-2117, USA. Email address: [email protected]
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Abstract

We consider a controlled M/M/1 queueing system where customers may be subject to two potential rejections. The first occurs upon arrival and is dependent on the number of customers in the queue and the service rate of the customer currently in service. The second, which may or may not occur, occurs immediately prior to the customer receiving service. That is, after each service completion the customer in the front of the queue is assessed and the service rate of that customer is revealed. If the second decision-maker recommends rejection, the customer is denied service with a fixed probability. We show the existence of long-run average optimal monotone switching-curve policies. Further, we show that the average reward is increasing in the probability that the second decision-maker's recommendation of rejection is honored. Applications include call centers with delayed classifications and manufacturing systems when the server is responsible for multiple tasks.

Keywords

Markov and semi-Markov processesqueueing theory

MSC classification

Primary: 90C40: Markov and semi-Markov decision processes
Secondary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 2 , June 2001 , pp. 369 - 385
Copyright
Copyright © Applied Probability Trust 2001 

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