Flow level models of Internet congestion control

Frank Kelly and Ruth Williams
Information Theory and Applications Workshop

Variability in the number of simultaneous flows present can have a substantial impact on the perceived performance of packet networks such as the Internet. While the packet level behaviour of a given set of flows is by now well understood, less is known about the stochastic behaviour of the number of flows in progress on different routes through the network. In this talk we describe recent work on Brownian models of networks in heavy traffic.


Fluid model for a network operating under a fair bandwidth-sharing policy.
F.P. Kelly and R. J. Williams
Annals of Applied Probability 14 (2004) 1055-1083.

Fluid and Brownian approximations for an Internet congestion control model.
W. Kang, F. P. Kelly, N. H. Lee and R. J. Williams
Proceedings of the 43rd IEEE Conference on Decision and Control (2004).