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

Part of: Computer system organization Operations research and management science

Published online by Cambridge University Press:  01 July 2016

R. T. Dunn  and
K. D. Glazebrook
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: kevin.glazebrook@newcastle.ac.uk
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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.

Keywords

average-overtaking optimalaverage-reward optimalbranching banditdiscounted rewardsGittins indexmachine breakdownsmulti-armed bandit problemparallel machinessuboptimality bound

MSC classification

Primary: 90B36: Scheduling theory, stochastic
Secondary: 68M20: Performance evaluation; queueing; scheduling 90B22: Queues and service
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 33 , Issue 2 , June 2001 , pp. 365 - 390
Copyright
Copyright © Applied Probability Trust 2001 

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