# Fluid model for a network operating under a fair bandwidth-sharing
policy

**
F. P. Kelly
**

**
R. J. Williams
**

Annals of Applied Probability
14 (2004) 1055-1083.

## 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.

Published pdf;
also available here and as postscript.

State space collapse and diffusion approximation for
a network operating under a fair bandwidth sharing policy.

*
W. Kang, F. P. Kelly, N. H. Lee and R. J. Williams.*

Annals of Applied Probability 19 (2009) 1719-1780.

Citations,
from Google Scholar.