Insensitivity of Proportional Fairness in Critically Loaded Bandwidth Sharing Networks

TL;DR

This paper demonstrates that proportional fairness in bandwidth sharing networks exhibits insensitivity in heavy traffic conditions for a broad class of job size distributions, revealing invariant distributions independent of second moments.

Contribution

It proves the insensitivity conjecture for a dense class of distributions, extending understanding of proportional fairness in critical load scenarios.

Findings

Invariant distribution admits a product form under critical loading.

Heavy traffic limit invariant distribution is insensitive to second moments.

Analysis introduces a uniform convergence result for a fluid model.

Abstract

Proportional fairness is a popular service allocation mechanism to describe and analyze the performance of data networks at flow level. Recently, several authors have shown that the invariant distribution of such networks admits a product form distribution under critical loading. Assuming exponential job size distributions, they leave the case of general job size distributions as an open question. In this paper we show the conjecture holds for a dense class of distributions. This yields a key example of a stochastic network in which the heavy traffic limit has an invariant distribution that does not depend on second moments. Our analysis relies on a uniform convergence result for a fluid model which may be of independent interest.