Mathematical modelling of the Internet

Frank Kelly.

Mathematics Unlimited - 2001 and Beyond,
editors B. Engquist and W. Schmid. Springer-Verlag, Berlin, 2001. 685-702.

Modern communication networks are able to respond to randomly fluctuating demands and failures by adapting rates, by rerouting traffic and by reallocating resources. They are able to do this so well that, in many respects, large-scale networks appear as coherent, self-regulating systems. The design and control of such networks present challenges of a mathematical, engineering and economic nature. This paper outlines how mathematical models are being used to address one current set of issues concerning the stability and fairness of rate control algorithms for the Internet.

Available as postscript or pdf.

This is an extended version of a paper from the Proceedings of the Fourth International Congress on Industrial and Applied Mathematics, 105-116, by kind permission the editors, J.M. Ball and J.C.R. Hunt, and of Oxford University Press.
Pointers to related papers, etc; also Google Scholar.
Ramesh Johari's article Mathematical modeling and control of Internet congestion
SIAM News, volume 33, March 2000.
Ian Grant's article "Congestion control" in Asymptotia.

Frank Kelly's papers