[e2e] link between Kelly's control and TCP's AIMD

Damon Wischik djw1005 at cam.ac.uk
Wed Feb 16 17:31:08 PST 2005

Roy Xu wrote:
> I'm looking for a pointer to literatures that link the
> TCP's (discrete) AIMD to Kelly's (continuous) control formulation.

Kelly's continuous-time formulation uses a differential equation model 
(also called a fluid model) for TCP. You should look at the literature 
which describes this fluid model, starting with

"A Fluid-based Analysis of a Network of AQM Routers Supporting TCP Flows 
with an Application to RED", V. Misra, W. Gong, D. Towsley, SIGCOMM 2000.

There are many links provided at

I have collected some further links at

Look especially at these papers:

"Using partial differential equations to model TCP mice and elephants in 
large IP networks." Marco Ajmone Marsan, Michele Gatetto, Paolo Giaccone, 
Emilio Leonardi, Enrico Schiattarella, Alessandro Tarello.

"A mean-field model for multiple TCP connections through a buffer 
implementing RED", Francois Baccelli, David R. McDonald, Julien Reynier. 
Performance Evaluation, 2002;


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