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August 2004 Fluid model for a network operating under a fair bandwidth-sharing policy
F. P. Kelly, R. J. Williams
Ann. Appl. Probab. 14(3): 1055-1083 (August 2004). DOI: 10.1214/105051604000000224


We consider a model of Internet congestion control that represents the randomly varying number of flows present in a network where bandwidth is shared fairly between document transfers. We study critical fluid models obtained as formal limits under law of large numbers scalings when the average load on at least one resource is equal to its capacity. We establish convergence to equilibria for fluid models and identify the invariant manifold. The form of the invariant manifold gives insight into the phenomenon of entrainment whereby congestion at some resources may prevent other resources from working at their full capacity.


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F. P. Kelly. R. J. Williams. "Fluid model for a network operating under a fair bandwidth-sharing policy." Ann. Appl. Probab. 14 (3) 1055 - 1083, August 2004.


Published: August 2004
First available in Project Euclid: 13 July 2004

zbMATH: 1066.60093
MathSciNet: MR2071416
Digital Object Identifier: 10.1214/105051604000000224

Primary: 60K30 , 90B15

Keywords: bandwidth sharing , Brownian model , flow level Internet model , fluid model , invariant manifold , Lagrange multipliers , Lyapunov function , reflected Brownian motion , simultaneous resource possession , workload , α-fair

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.14 • No. 3 • August 2004
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