TY - JOUR

T1 - Fluid limits for Bandwidth-Sharing Networks with Impatience.

AU - Remerova, M.

AU - Reed, J.

AU - Zwart, A.P.

PY - 2014

Y1 - 2014

N2 - Bandwidth-sharing networks as introduced by Roberts and Massoulié [Roberts JW, Massoulié L (1998) Bandwidth sharing and admission control for elastic traffic. Proc. ITC Specialist Seminar, Yokohama, Japan], Massoulié and Roberts [Massoulié 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. © 2014 INFORMS.

AB - Bandwidth-sharing networks as introduced by Roberts and Massoulié [Roberts JW, Massoulié L (1998) Bandwidth sharing and admission control for elastic traffic. Proc. ITC Specialist Seminar, Yokohama, Japan], Massoulié and Roberts [Massoulié 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. © 2014 INFORMS.

U2 - 10.1287/moor.2013.0641

DO - 10.1287/moor.2013.0641

M3 - Article

SN - 0364-765X

VL - 39

SP - 746

EP - 774

JO - Mathematics of Operations Research

JF - Mathematics of Operations Research

ER -