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We study a resource allocation problem with varying requests, and withresources of limited capacity shared by multiple requests. It is modeled as aset of heterogeneous Restless Multi-Armed Bandit Problems (RMABPs) connected byconstraints imposed by resource capacity. Following Whittle's relaxation ideaand Weber and Weiss' asymptotic optimality proof, we propose a simple policyand prove it to be asymptotically optimal in a regime where both arrival ratesand capacities increase. We provide a simple sufficient condition forasymptotic optimality of the policy, and in complete generality propose amethod that generates a set of candidate policies for which asymptoticoptimality can be checked. The effectiveness of these results is demonstratedby numerical experiments. To the best of our knowledge, this is the first workproviding asymptotic optimality results for such a resource allocation problemand such a combination of multiple RMABPs.

A Restless Bandit Model for Resource Allocation, Competition and Reservation