Brownian models of congested networks

Frank Kelly
Advanced Network Sciences talk, UC San Diego

Brownian models provide tractable high-level descriptions of networks in a variety of application areas. This talk will review work in two areas: the modelling of multi-path routing in the Internet, and the design of ramp metering policies for highway networks.

In both areas Brownian models are able to exploit the simplifications that arise in heavy traffic, and to make clear the main performance consequences of resource allocation policies.



State space collapse and diffusion approximation for a network operating under a proportional fair sharing policy
W. Kang, F. P. Kelly, N. H. Lee and R. J. Williams
Annals of Applied Probability, to appear.

Heavy traffic on a controlled motorway
F. P. Kelly and R.J. Williams

What we've learned about highway congestion
P. Varaiya
Access 27, Fall 2005, 2-9.