Proportional fairness and its relationship with multi-class queueing networks

Details Proportional fairness and its relationship with multi-class queueing networks Proportional fairness and its relationship with multi-class queueing networks

2008-09-16

arxiv.org/abs/0809.2697v3

Annals of Applied Probability 2009, Vol. 19, No. 6, 2301-2333

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AAP612 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

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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