The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 14, Number 3 (2004), 1055-1083.
Fluid model for a network operating under a fair bandwidth-sharing policy
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.
Ann. Appl. Probab., Volume 14, Number 3 (2004), 1055-1083.
First available in Project Euclid: 13 July 2004
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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. https://projecteuclid.org/euclid.aoap/1089736278