A Restless Bandit Model for Resource Allocation, Competition and Reservation

TL;DR

This paper introduces a novel resource allocation model using Restless Multi-Armed Bandit Problems, providing asymptotic optimality results and a method to evaluate candidate policies, supported by numerical experiments.

Contribution

It presents the first asymptotic optimality results for a resource allocation problem involving multiple interconnected RMABPs and proposes a general method to verify policy optimality.

Findings

Proposed a simple, asymptotically optimal policy for the model.

Provided a sufficient condition for policy asymptotic optimality.

Demonstrated effectiveness through numerical experiments.

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.