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June 2007 Structural properties of proportional fairness: Stability and insensitivity
Laurent Massoulié
Ann. Appl. Probab. 17(3): 809-839 (June 2007). DOI: 10.1214/105051606000000907


In this article we provide a novel characterization of the proportionally fair bandwidth allocation of network capacities, in terms of the Fenchel–Legendre transform of the network capacity region. We use this characterization to prove stability (i.e., ergodicity) of network dynamics under proportionally fair sharing, by exhibiting a suitable Lyapunov function. Our stability result extends previously known results to a more general model including Markovian users routing. In particular, it implies that the stability condition previously known under exponential service time distributions remains valid under so-called phase-type service time distributions.

We then exhibit a modification of proportional fairness, which coincides with it in some asymptotic sense, is reversible (and thus insensitive), and has explicit stationary distribution. Finally we show that the stationary distributions under modified proportional fairness and balanced fairness, a sharing criterion proposed because of its insensitivity properties, admit the same large deviations characteristics.

These results show that proportional fairness is an attractive bandwidth allocation criterion, combining the desirable properties of ease of implementation with performance and insensitivity.


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Laurent Massoulié. "Structural properties of proportional fairness: Stability and insensitivity." Ann. Appl. Probab. 17 (3) 809 - 839, June 2007.


Published: June 2007
First available in Project Euclid: 22 May 2007

zbMATH: 1125.60104
MathSciNet: MR2326233
Digital Object Identifier: 10.1214/105051606000000907

Primary: 60K25, 68M20, 90B15

Rights: Copyright © 2007 Institute of Mathematical Statistics


Vol.17 • No. 3 • June 2007
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