A Restless Bandit Model for Resource Allocation, Competition and Reservation

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 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.

Energy-Efficient Job-Assignment Policy With Asymptotically Guaranteed Performance Deviation

“…Following the ideas of [22], [35], [36], we then obtain a corollary of [36, Proposition 5] as follows.…”

“…x m with x − 0 = 0, and f 0,h i,a (x) ∈ R J and f h i,a (x) ∈ R hS0 with 0 < a < 1 are appropriate functions as described in [36] such that Q h is Lipschitz continuous in x.…”