Qualitative Properties of $\alpha$-Fair Policy in Bandwidth Sharing Networks

Abstract:

We consider the flow-level model of a network operating under the $\alpha$-fair bandwidth sharing policy ($\alpha$ > 0) proposed by Roberts and Massoulie (2000). This probabilistic model has been proposed to capture the long-term behavior in terms of sharing of the network bandwidth among users or flows by the congestion control mechanism in the current Internet. The necessary and sufficient conditions for the existence of steady-state distribution of flows under this model were established by Bonald and Massoulie (2001), de Veciana et al (2001).

In this paper, we study the transient properties of the model as well as further analyze the steady-state distribution. In particular, we analyze the excursion of maximum number of flows that remain in the network over a given time horizon for $\alpha \geq 1$ by means of a novel maximal inequality derived from the standard Lyapunov drift condition. As a consequence, we establish the strong state space collapse property for all $\alpha \geq 1$.

For the steady-state distribution, we obtain explicit exponential tail bound for the number of flows for all $\alpha > 0$ by means of a careful analysis of the normed version of the standard Lyapunov function studied in the literature. As an implication, we establish the validity of the diffusion approximation in the steady-state for $\alpha = 1$ developed by Kang et al (2009).

Biography:

Yuan Zhong is a third-year Ph.D student in the Operations Research Center, co-advised by Professor John Tsitsiklis and Professor Devavrat Shah. He works on the area of stochastic networks.