Brownian network models of congestion at flow level

PPT Slide

Background and motivation

End-to-end congestion control

Fixed point models

Processor sharing models

Issues

Model definition

Network structure (J, R, A)

Rate allocation

Optimization formulation of rate allocation

Examples of -fair allocations

Example

Flow level model

Example: a linear network

Workload for a resource

Workload for two resources

Outline of rest of talk

Stability

What goes wrong without fairness?

Heavy traffic

Balanced fluid model

Fluid model

A potential function

Workloads

Evolution of functions F

State space collapse

The case ? = 1

A star network

Mean field approximation?

Summary

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Home Page: http://www.statslab.cam.ac.uk/~frank