Towards minimum loss job routing to parallel heterogeneous multiserver queues via index policies

TL;DR

This paper develops a low-complexity, index-based routing policy for heterogeneous multiserver queues that nearly minimizes loss rates, outperforming existing policies in computational efficiency and empirical performance.

Contribution

It introduces a novel second-order Whittle's restless bandit index policy for dynamic routing in heterogeneous queues, with theoretical and empirical validation.

Findings

RB index policy is nearly optimal across tested instances.

Proposed policy outperforms previous index policies.

Policy reduces to shortest queue routing in symmetric cases.

Abstract

This paper considers a Markovian model for the optimal dynamic routing of homogeneous traffic to parallel heterogeneous queues, each having its own finite input buffer and server pool, where buffer and server-pool sizes, as well as service rates, may differ across queues. The main goal is to identify a heuristic index-based routing policy with low complexity that consistently attains a nearly minimum average loss rate (or, equivalently, maximum throughput rate). A second goal is to compare alternative policies, with respect to computational demands and empirical performance. A novel routing policy that can be efficiently computed is developed based on a second-order extension to Whittle's restless bandit (RB) index, since the latter is constant for this model. New results are also given for the more computationally demanding index policy obtained via policy improvement (PI), including that it reduces to shortest queue routing under symmetric buffer and server-pool sizes. A numerical study shows that the proposed RB index policy is nearly optimal across the instances considered, and substantially outperforms several previously proposed index policies.