Section: New Results

Total variation estimates for the TCP process

Participant : Florent Malrieu.

This is a collaboration with Jean-Baptiste Bardet (université de Rouen), Alejandra Christen (University of Chile), Arnaud Guillin (université de Clermont–Ferrand), and Pierre–André Zitt (université de Paris–Est Marne–la–Vallée).

The TCP window size process appears in the modeling of the famous Transmission Control Protocol used for data transmission over the Internet. This continuous time Markov process takes its values in $[0,\infty )$, is ergodic and irreversible. The sample paths are piecewise linear deterministic and the whole randomness of the dynamics comes from the jump mechanism. The aim of  [27] is to provide quantitative estimates for the exponential convergence to equilibrium, in terms of the total variation and Wasserstein distances, using coupling methods. The technique could be applied to a large class of Markov processes as well.