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A Restless Bandit Model for Resource Allocation, Competition, and Reservation

Author

Listed:
  • Jing Fu

    (School of Mathematics and Statistics, University of Melbourne, Melbourne, Victoria 3010, Australia)

  • Bill Moran

    (Department of Electrical and Electronic Engineering, University of Melbourne, Melbourne, Victoria 3010, Australia)

  • Peter G. Taylor

    (School of Mathematics and Statistics, University of Melbourne, Melbourne, Victoria 3010, Australia)

Abstract

We study a resource allocation problem with varying requests and with resources of limited capacity shared by multiple requests. It is modeled as a set of heterogeneous restless multiarmed bandit problems (RMABPs) connected by constraints imposed by resource capacity. Following Whittle’s relaxation idea and Weber and Weiss’ asymptotic optimality proof, we propose a simple policy and prove it to be asymptotically optimal in a regime where both arrival rates and capacities increase. We provide a simple sufficient condition for asymptotic optimality of the policy and, in complete generality, propose a method that generates a set of candidate policies for which asymptotic optimality can be checked. The effectiveness of these results is demonstrated by numerical experiments. To the best of our knowledge, this is the first work providing asymptotic optimality results for such a resource allocation problem and such a combination of multiple RMABPs.

Suggested Citation

  • Jing Fu & Bill Moran & Peter G. Taylor, 2022. "A Restless Bandit Model for Resource Allocation, Competition, and Reservation," Operations Research, INFORMS, vol. 70(1), pages 416-431, January.
    • Handle: RePEc:inm:oropre:v:70:y:2022:i:1:p:416-431
    DOI: 10.1287/opre.2020.2066
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