  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 Multi-Armed 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.
