Control Policies Approaching HGI Performance in Heavy Traffic for Resource Sharing Networks

TL;DR

This paper develops simple threshold-based control policies for resource sharing networks that achieve near-optimal performance in heavy traffic, matching the Hierarchical Greedy Ideal benchmark.

Contribution

It introduces a new class of threshold-based policies for broad resource sharing networks that converge to the HGI performance in heavy traffic.

Findings

Policies achieve convergence to HGI performance in heavy traffic

Applicable to broad families of resource sharing networks

Conditions satisfied by all studied examples

Abstract

We consider resource sharing networks of the form introduced in the work of Massouli\'{e} and Roberts(2000) as models for Internet flows. The goal is to study the open problem, formulated in Harrison et al. (2014), of constructing simple form rate allocation policies for broad families of resource sharing networks with associated costs converging to the Hierarchical Greedy Ideal performance in the heavy traffic limit. We consider two types of cost criteria, an infinite horizon discounted cost, and a long time average cost per unit time. We introduce a sequence of rate allocation control policies that are determined in terms of certain thresholds for the scaled queue length processes and prove that, under conditions, both type of costs associated with these policies converge in the heavy traffic limit to the corresponding HGI performance. The conditions needed for these results are satisfied by all the examples considered in Harrison et al. (2014).