General notions of indexability for queueing control and asset management

TL;DR

This paper generalizes the concept of indexability for dynamic resource allocation problems, including divisible resources, and demonstrates its application to queueing and asset management models with promising heuristic performance.

Contribution

It introduces new notions of indexability for flexible resource allocation problems and applies them to queueing and asset management models with theoretical and numerical validation.

Findings

Indexability is established for models with increasing, concave service rates.

Asset indexability is shown under diminishing returns laws.

Greedy index heuristics perform well in numerical studies.

Abstract

We develop appropriately generalized notions of indexability for problems of dynamic resource allocation where the resource concerned may be assigned more flexibility than is allowed, for example, in classical multi-armed bandits. Most especially we have in mind the allocation of a divisible resource (manpower, money, equipment) to a collection of objects (projects) requiring it in cases where its over-concentration would usually be far from optimal. The resulting project indices are functions of both a resource level and a state. They have a simple interpretation as a fair charge for increasing the resource available to the project from the specified resource level when in the specified state. We illustrate ideas by reference to two model classes which are of independent interest. In the first, a pool of servers is assigned dynamically to a collection of service teams, each of which mans a service station. We demonstrate indexability under a natural assumption that the service rate delivered is increasing and concave in the team size. The second model class is a generalization of the spinning plates model for the optimal deployment of a divisible investment resource to a collection of reward generating assets. Asset indexability is established under appropriately drawn laws of diminishing returns for resource deployment. For both model classes numerical studies provide evidence that the proposed greedy index heuristic performs strongly.