Qualitative properties of α-fair policies in bandwidth-sharing networks
Author(s)Zhong, Y.; Shah, Devavrat; Tsitsiklis, John N.
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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.
DepartmentMassachusetts 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
The Annals of Applied Probability
Institute of Mathematical Statistics
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
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