Fluid Limits for Bandwidth-Sharing Networks with Rate Constraints

Bandwidth-sharing networks as introduced by Roberts and Massoulie [Roberts JW, Massoulie 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.e...

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