Total variation estimates for the TCP process

Jean-Baptiste Bardet (Université de Rouen)
Alejandra Christen (Pontificia Universidad Católica de Valparaíso)
Arnaud Guillin (Université Blaise Pascal)
Florent Malrieu (Université de Rennes 1)
Pierre-André Zitt (Université de Bourgogne)

Abstract


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, ∞), 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 the present paper is to provide quantitative estimates for the exponential convergence to equilibrium, in terms of the total variation and Wasserstein distances.

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Pages: 1-21

Publication Date: January 17, 2013

DOI: 10.1214/EJP.v18-1720

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