The Annals of Applied Probability

Proportional fairness and its relationship with multi-class queueing networks

N. S. Walton

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 19, Number 6 (2009), 2301-2333.

Dates
First available in Project Euclid: 25 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1259158773

Digital Object Identifier
doi:10.1214/09-AAP612

Mathematical Reviews number (MathSciNet)
MR2588246

Zentralblatt MATH identifier
1198.60039

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22] 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx]
Secondary: 90K15 68K20

Keywords
Multi-class queueing network proportional fairness bandwidth sharing stochastic flow level model insensitivity product form stationary distribution proportionally fair state space collapse

Citation

Walton, N. S. Proportional fairness and its relationship with multi-class queueing networks. Ann. Appl. Probab. 19 (2009), no. 6, 2301--2333. doi:10.1214/09-AAP612. https://projecteuclid.org/euclid.aoap/1259158773


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