In recent years the Internet has attracted the attention of many theoreticians, eager to understand the remarkable success of this diverse and complex artefact. A central element of the design philosophy that shaped the Internet is the end-to-end argument, and a key illustration of the argument is provided by TCP's congestion avoidance algorithm, due to Jacobson. Why does this algorithm work so well? How might, or should, it evolve in the future? This talk reviews some of the mathematical models that have been developed to help address these questions.
Mathematical modelling of the Internet
Mathematics Unlimited - 2001 and Beyond,
editors B. Engquist and W. Schmid. Springer-Verlag, Berlin (2001), 685-702.
Fairness and stability of end-to-end congestion control