Qualitative properties of $\alpha$-fair policies in bandwidth-sharing networks

Abstract

We consider a flow-level model of a network operating under an $\alpha$-fair bandwidth sharing policy (with $\alpha >0$) 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 $\alpha \ge 1$, 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 $\alpha \ge 1$. 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. 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 $\alpha =1$ and under a local traffic condition.

Published in at http://dx.doi.org/10.1214/12-AAP915 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Validity of heavy traffic steady-state approximations in generalized Jackson Networks
• Fluid model for a network operating under a fair bandwidth-sharing policy
• State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy
• Qualitative Properties of alpha-Weighted Scheduling Policies

Cited by in corpus (3)

• Optimal queue-size scaling in switched networks
• Heavy-Traffic Insensitive Bounds for Weighted Proportionally Fair Bandwidth Sharing Policies
• Centralized Congestion Control and Scheduling in a Datacenter