Fluid Limits for Bandwidth-Sharing Networks with Rate Constraints

• 成果类型: Article
• 署名作者: Remerova, Maria; Reed, Josh; Zwart, Bert
• 署名单位: New York University; Vrije Universiteit Amsterdam; University System of Georgia; Georgia Institute of Technology
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2013.0641
• 发表日期: 2014
• 页码: 746-774
• 关键词: proportional fairness; performance analysis; STABILITY; distributions; optimality; overload; services; queues; POLICY; MODEL

摘要

Bandwidth-sharing networks as introduced by Roberts and Massoule [Roberts JW, Massoule L (1998) Bandwidth sharing and admission control for elastic traffic. Proc. ITC Specialist Seminar, Yokohama, Japan], Massoulie and Roberts [Massoulie L, Roberts JW (1999) Bandwidth sharing: Objectives and algorithms. Proc. IEEE Infocom. (Books in Statistics, New York), 1395-1403] model the dynamic interaction among an evolving population of elastic flows competing for several links. With policies based on optimization procedures, such models are of interest both from a queueing theory and operations research perspective. In the present paper, we focus on bandwidth-sharing networks with capacities and arrival rates of a large order of magnitude compared to transfer rates of individual flows. This regime is standard in practice. In particular, we extend previous work by Reed and Zwart [Reed J, Zwart B (2010) Limit theorems for bandwidth-sharing networks with rate constraints. Revised, preprint http://people.stern.nyu.edu/jreed/Papers/BARevised.pdf] on fluid approximations for such networks: we allow interarrival times, flow sizes, and patient times (i.e., abandonment times measured from the arrival epochs) to be generally distributed, rather than exponentially distributed. We also develop polynomial-time computable fixed-point approximations for stationary distributions of bandwidth-sharing networks, and suggest new techniques for deriving these types of results.