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December 2009 Proportional fairness and its relationship with multi-class queueing networks
N. S. Walton
Ann. Appl. Probab. 19(6): 2301-2333 (December 2009). DOI: 10.1214/09-AAP612


We consider multi-class single-server queueing networks that have a product form stationary distribution. A new limit result proves a sequence of such networks converges weakly to a stochastic flow level model. The stochastic flow level model found is insensitive. A large deviation principle for the stationary distribution of these multi-class queueing networks is also found. Its rate function has a dual form that coincides with proportional fairness. We then give the first rigorous proof that the stationary throughput of a multi-class single-server queueing network converges to a proportionally fair allocation.

This work combines classical queueing networks with more recent work on stochastic flow level models and proportional fairness. One could view these seemingly different models as the same system described at different levels of granularity: a microscopic, queueing level description; a macroscopic, flow level description and a teleological, optimization description.


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N. S. Walton. "Proportional fairness and its relationship with multi-class queueing networks." Ann. Appl. Probab. 19 (6) 2301 - 2333, December 2009.


Published: December 2009
First available in Project Euclid: 25 November 2009

zbMATH: 1198.60039
MathSciNet: MR2588246
Digital Object Identifier: 10.1214/09-AAP612

Primary: 60K25, 60K30
Secondary: 68K20, 90K15

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.19 • No. 6 • December 2009
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