  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.
