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Modélisation mathématique et simulation de TCP par des méthodes de champ moyen.

Julien Reynier 1
1 TREC - Theory of networks and communications
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt
Abstract : The dramatic spread of the Internet all around us marked the world forever. Is has now become possible to send and receive an almost infinite amount of data to and from anywhere in the world. Not only does this change the way we communicate, it also has a considerable impact on our perception of the world we live in. The Internet revolution is partly due to data transport, often via TCP. The optimization of the information highway is one of the most exciting challenges for the Internet architects. The two introduction chapters of this PhD thesis straightforwardly explain TCP and the related works in the mean field approach. We focus on TCP New-Reno and some particular problems TCP-networks face. Our angle on the issue will mainly be bottleneck congestion. The first part deals with the mathematics of the mean field we develop. First we show a very simple example of what a mean field is, then we develop some theoretical enhancements to finish with the proof of Baccelli-Hong's model for TCP. The second part endeavors to explain our mathematical mean field model to study large TCP controlled population sharing a common resource, namely the bandwidth of some internet access router. We make some simplifying assumptions such as fluid behavior or Little's formula for the window-bandwidth relationship. The evolution of the histogram of the connection window sizes is approximated by a deterministic partial differential equation. From a technical point of view, we can furnish QOS estimations. From a mathematical point of view, compared to the traditional tightness-limit-unicity mean field method, the auxiliary system-coupling methodology that we use offers certain advantages. It is more intuitive and allows us to solve the delay problem which otherwise would be difficult to handle. We then adapt the model to the HTTP case with on-off sources. The third part of the thesis focus on showing practical results we obtain by simulating mean field equations. We first validate the mean field model against discrete event simulators and the N-particle system from which is extracted for large N, then show how such a model is different from (ie. better than) other simpler models. We conclude by simulating the equations which arise from the models which exhibit some interesting congestion behavior.
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Submitted on : Wednesday, July 28, 2010 - 4:29:07 PM
Last modification on : Wednesday, October 14, 2020 - 3:57:54 AM
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  • HAL Id : pastel-00002032, version 1



Julien Reynier. Modélisation mathématique et simulation de TCP par des méthodes de champ moyen.. Modélisation et simulation. Ecole Polytechnique X, 2006. Français. ⟨pastel-00002032⟩



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