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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Abstract

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

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

Dates
First available in Project Euclid: 13 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1089736278

Digital Object Identifier
doi:10.1214/105051604000000224

Mathematical Reviews number (MathSciNet)
MR2071416

Zentralblatt MATH identifier
1066.60093

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

Keywords
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

Citation

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


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References

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The Annals of Applied Probability

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