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The performance of index-based policies for bandit problems with stochastic machine availability

Published online by Cambridge University Press:  01 July 2016

R. T. Dunn*
Affiliation:
University of Newcastle upon Tyne
K. D. Glazebrook*
Affiliation:
University of Newcastle upon Tyne
*
Postal address: Department of Statistics, University of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU, UK.
∗∗ Email address: [email protected]

Abstract

We consider generalisations of two classical stochastic scheduling models, namely the discounted branching bandit and the discounted multi-armed bandit, to the case where the collection of machines available for processing is itself a stochastic process. Under rather mild conditions on the machine availability process we obtain performance guarantees for a range of controls based on Gittins indices. Various forms of asymptotic optimality are established for index-based limit policies as the discount rate approaches 0.

Type
General Applied Probability
Copyright
Copyright © Applied Probability Trust 2001 

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