Insensitivity of proportional fairness in critically loaded bandwidth sharing networks

Maria Vlasiou, Jiheng Zhang, Bert Zwart

Research output: Working paperPreprintAcademic

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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 that product form in heavy traffic still holds for general distributions, thus settling the conjecture. More importantly, we establish insensitivity of proportional fairness in heavy traffic.
Original languageEnglish
Number of pages31
Publication statusPublished - 2014
Externally publishedYes


  • Brownian approximations
  • Lyapunov functions
  • Network utility maximization


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