Qualitative properties of α-fair policies in bandwidth-sharing networks
Name
Shah-2014-Qualitative properties of.pdf
Size
285.7 KB
Format
Adobe PDF
Checksum (MD5)
4a7d62defd7dfe29bbbf54f20a14d64d
Author(s)
Zhong, Y.
Shah, Devavrat
Tsitsiklis, John N
Date Issued
February 2014
Journal
The Annals of Applied Probability
Publisher
Institute of Mathematical Statistics
Citation
Shah, D., J. N. Tsitsiklis, and Y. Zhong. “Qualitative Properties of α-Fair Policies in Bandwidth-Sharing Networks.” The Annals of Applied Probability 24, no. 1 (February 2014): 76–113. © Institute of Mathematical Statistics, 2014
Version
Final published version
Abstract
We consider a flow-level model of a network operating under an α-fair bandwidth sharing policy (with α > 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 α ≥ 1, 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 α ≥ 1.
For the steady-state distribution, we obtain explicit exponential tail bounds on the number of flows, for any α > 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 α = 1 and under a local traffic condition.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Massachusetts Institute of Technology. Operations Research Center
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1214/12-AAP915
