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

• 成果类型: Article
• 署名作者: Fu, Jing; Moran, Bill; Taylor, Peter G.
• 署名单位: University of Melbourne; University of Melbourne
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2020.2066
• 发表日期: 2022
• 页码: 416-431
• 关键词: restless bandits; Resource sharing; Markov Decision Process

摘要

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.