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.
"Fluid model for a network operating under a fair bandwidth-sharing policy." Ann. Appl. Probab. 14 (3) 1055 - 1083, August 2004. https://doi.org/10.1214/105051604000000224