Qualitative properties of α-fair policies in bandwidth-sharing networks
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...
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| Format: | Article |
| Language: | en_US |
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Institute of Mathematical Statistics
2014
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| Online Access: | http://hdl.handle.net/1721.1/85689 https://orcid.org/0000-0003-0737-3259 https://orcid.org/0000-0003-2658-8239 |
| _version_ | 1811092312691834880 |
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| author | Zhong, Y. Shah, Devavrat Tsitsiklis, John N |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Zhong, Y. Shah, Devavrat Tsitsiklis, John N |
| author_sort | Zhong, Y. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T15:16:25Z |
| format | Article |
| id | mit-1721.1/85689 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:16:25Z |
| publishDate | 2014 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | mit-1721.1/856892023-03-01T02:10:57Z Qualitative properties of α-fair policies in bandwidth-sharing networks Zhong, Y. Shah, Devavrat Tsitsiklis, John N 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 Shah, Devavrat Tsitsiklis, John N. 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. National Science Foundation (U.S.) (Project CCF-0728554) 2014-03-17T20:16:04Z 2014-03-17T20:16:04Z 2014-02 2012-10 Article http://purl.org/eprint/type/JournalArticle 1050-5164 http://hdl.handle.net/1721.1/85689 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 https://orcid.org/0000-0003-0737-3259 https://orcid.org/0000-0003-2658-8239 en_US http://dx.doi.org/10.1214/12-AAP915 The Annals of Applied Probability 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. application/pdf Institute of Mathematical Statistics Institute of Mathematical Statistics |
| spellingShingle | Zhong, Y. Shah, Devavrat Tsitsiklis, John N Qualitative properties of α-fair policies in bandwidth-sharing networks |
| title | Qualitative properties of α-fair policies in bandwidth-sharing networks |
| title_full | Qualitative properties of α-fair policies in bandwidth-sharing networks |
| title_fullStr | Qualitative properties of α-fair policies in bandwidth-sharing networks |
| title_full_unstemmed | Qualitative properties of α-fair policies in bandwidth-sharing networks |
| title_short | Qualitative properties of α-fair policies in bandwidth-sharing networks |
| title_sort | qualitative properties of α fair policies in bandwidth sharing networks |
| url | http://hdl.handle.net/1721.1/85689 https://orcid.org/0000-0003-0737-3259 https://orcid.org/0000-0003-2658-8239 |
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