Work

Insensitivity of proportional fairness in critically loaded bandwidth sharing networks

Year: 2026

Type: article

Abstract: Proportional fairness is a popular service allocation mechanism to describe and analyze the performance of data networks at flow level. Several authors have shown that the invariant distribution of networks operating according to proportional fairness admits a product form distribution under critical loading. They focus however on exponential job size distributions, leaving the case of general job size distributions as an open question. Motivated by this, we consider a network operating under proportional fairness where the job size distributions are of phase-type. We establish a heavy-traffic process limit theorem and show that the invariant distribution of the limit process is determined by the first moments of the job sizes only. Our analysis relies on a uniform convergence result for a fluid model.

Source: Queueing Systems

DOI: 10.1007/s11134-026-09978-1

Authors: Maria Vlasiou, Jiheng Zhang, Bert Zwart

Institutions: Eindhoven University of Technology, University of Twente, Hong Kong University of Science and Technology, Centrum Wiskunde & Informatica

Language: English

Topic: Advanced Queuing Theory Analysis

Subfield: Management Information Systems

Field: Business, Management and Accounting

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Technische Universiteit Eindhoven, Nederlandse Organisatie voor Wetenschappelijk Onderzoek