QUALITATIVE PROPERTIES OF α-FAIR POLICIES IN BANDWIDTH-SHARING NETWORKS

• 成果类型: Article
• 署名作者: Shah, D.; Tsitsiklis, J. N.; Zhong, Y.
• 署名单位: Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP915
• 发表日期: 2014
• 页码: 76-113
• 关键词: state-space collapse; large deviations; performance; STABILITY; time

摘要

We consider a flow-level model of a network operating under an a-fair bandwidth sharing policy (with alpha > 0) proposed by Roberts and Massoulie [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 >= 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. 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.