Mathematics – Probability
Scientific paper
2011-04-12
Mathematics
Probability
Scientific paper
We consider a flow-level model of a network operating under an \alpha -fair bandwidth sharing policy (with \alpha > 0) proposed by Roberts and Massouli\'{e} (2000). 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 >= 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 \alpha >= 1. 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, different from the standard Lyapunov function used in the literature. As a corollary, we establish the validity of the diffusion approximation developed by Kang et al (2009), in steady state, for the case where \alpha = 1.
Shah Devavrat
Tsitsiklis John N.
Zhong Yafang
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