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