## 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.

References:

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).