FLUID MODEL FOR A NETWORK OPERATING UNDER A FAIR BANDWIDTH-SHARING
F. P. Kelly and R. J. Williams
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.
Annals of Applied Probability, 14 (2004), 1055-1083.
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Last updated August 4, 2006.