The Annals of Applied Probability

Fluid model for a network operating under a fair bandwidth-sharing policy

F. P. Kelly and R. J. Williams

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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.

Article information

Ann. Appl. Probab., Volume 14, Number 3 (2004), 1055-1083.

First available in Project Euclid: 13 July 2004

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Zentralblatt MATH identifier

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx] 90B15: Network models, stochastic

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


Kelly, F. P.; Williams, R. J. Fluid model for a network operating under a fair bandwidth-sharing policy. Ann. Appl. Probab. 14 (2004), no. 3, 1055--1083. doi:10.1214/105051604000000224.

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