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Open bandit processes and optimal scheduling of queueing networks

Published online by Cambridge University Press:  01 July 2016

Tze Leung Lai  and
Zhiliang Ying
Tze Leung Lai*
Affiliation:
Stanford University
Zhiliang Ying*
Affiliation:
Columbia University
*
∗Postal address: Department of Statistics, Stanford University, Stanford, CA 94305, USA.
∗∗ Postal address: Department of Statistics, Box 10 Mathematics, Columbia University, New York, NY 10027, USA.
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Abstract

Asymptotic approximations are developed herein for the optimal policies in discounted multi-armed bandit problems in which new projects are continually appearing, commonly known as ‘open bandit problems’ or ‘arm-acquiring bandits’. It is shown that under certain stability assumptions the open bandit problem is asymptotically equivalent to a closed bandit problem in which there is no arrival of new projects, as the discount factor approaches 1. Applications of these results to optimal scheduling of queueing networks are given. In particular, Klimov&s priority indices for scheduling queueing networks are shown to be limits of the Gittins indices for the associated closed bandit problem, and extensions of Klimov&s results to preemptive policies and to unstable queueing systems are given.

Keywords

OPEN AND CLOSED BANDIT PROBLEMSDYNAMIC PROGRAMMINGOPTIMAL STOPPINGPREEMPTIVE AND NON-PREEMPTIVE POLICIESPRIORITY INDICES
Type
Research Article
Information
Advances in Applied Probability , Volume 20 , Issue 2 , June 1988 , pp. 447 - 472
Copyright
Copyright © Applied Probability Trust 1988 

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Footnotes

Research supported by the National Science Foundation and the Army Research Office.

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