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Journal Articles Electronic Journal of Probability Year : 2013

Total variation estimates for the TCP process


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 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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Dates and versions

hal-00655462 , version 1 (29-12-2011)
hal-00655462 , version 2 (21-09-2012)



Jean-Baptiste Bardet, Alejandra Christen, Arnaud Guillin, Florent Malrieu, Pierre-André Zitt. Total variation estimates for the TCP process. Electronic Journal of Probability, 2013, 18 (10), pp.1-21. ⟨10.1214/EJP.v18-1720⟩. ⟨hal-00655462v2⟩
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