Brownian network models of congestion at flow level

Frank Kelly

Massoulie and Roberts have introduced and studied a flow level model of Internet congestion control, that represents the randomly varying number of flows present in a network where bandwidth is dynamically shared between elastic document transfers.

In this talk the formalism of balanced fluid models and Brownian networks will be used to explore the behaviour of the flow level model in heavy traffic. Particular interest attaches to the phenomenon of entrainment, whereby congestion at some resources may prevent other resources from working at their full capacity.

Joint work with Ruth Williams.

slides , paper

Some references:

The flow level Internet model was introduced in
Bandwidth sharing and admission control for elastic traffic
J. Roberts and L. Massoulie

Weighted alpha-fair allocations were introduced in
Fair end-to-end window-based congestion control
J. Mo and J. Walrand.

Positive recurrence of the Markov process is established by
Stability and performance analysis of networks supporting elastic services
Gustavo De Veciana, Tae-Jin Lee and Takis Konstantopoulos
Impact of fairness on Internet performance
Thomas Bonald and Laurent Massoulie.
The example of what goes wrong without fairness comes from the latter paper.