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February 2014 Qualitative properties of $\alpha$-fair policies in bandwidth-sharing networks
D. Shah, J. N. Tsitsiklis, Y. Zhong
Ann. Appl. Probab. 24(1): 76-113 (February 2014). DOI: 10.1214/12-AAP915

Abstract

We consider a flow-level model of a network operating under an $\alpha$-fair bandwidth sharing policy (with $\alpha>0$) proposed by Roberts and Massoulié [Telecomunication Systems 15 (2000) 185–201]. This is a probabilistic model that captures the long-term aspects of bandwidth sharing between users or flows in a communication network.

We study the transient properties as well as the steady-state distribution of the model. In particular, for $\alpha\geq1$, we obtain bounds on the maximum number of flows in the network over a given time horizon, by means of a maximal inequality derived from the standard Lyapunov drift condition. As a corollary, we establish the full state space collapse property for all $\alpha\geq1$.

For the steady-state distribution, we obtain explicit exponential tail bounds on the number of flows, for any $\alpha>0$, by relying on a norm-like Lyapunov function. As a corollary, we establish the validity of the diffusion approximation developed by Kang et al. [Ann. Appl. Probab. 19 (2009) 1719–1780], in steady state, for the case where $\alpha=1$ and under a local traffic condition.

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D. Shah. J. N. Tsitsiklis. Y. Zhong. "Qualitative properties of $\alpha$-fair policies in bandwidth-sharing networks." Ann. Appl. Probab. 24 (1) 76 - 113, February 2014. https://doi.org/10.1214/12-AAP915

Information

Published: February 2014
First available in Project Euclid: 9 January 2014

zbMATH: 1304.60102
MathSciNet: MR3161642
Digital Object Identifier: 10.1214/12-AAP915

Subjects:
Primary: 60K20 , 68M12
Secondary: 68M20

Keywords: $\alpha$-fair , Bandwidth-sharing policy , heavy traffic , state space collapse

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.24 • No. 1 • February 2014
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