# On the long time behavior of the TCP window size process

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4 DIONYSOS - Dependability Interoperability and perfOrmance aNalYsiS Of networkS
Inria Rennes – Bretagne Atlantique , IRISA-D2 - RÉSEAUX, TÉLÉCOMMUNICATION ET SERVICES
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 $[0,\infty)$, is ergodic and irreversible. It belongs to the Additive Increase Multiplicative Decrease class of processes. The sample paths are piecewise linear deterministic and the whole randomness of the dynamics comes from the jump mechanism. Several aspects of this process have already been investigated in the literature. In the present paper, we mainly get quantitative estimates for the convergence to equilibrium, in terms of the $W_1$ Wasserstein coupling distance, for the process and also for its embedded chain.
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Journal articles
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https://hal.archives-ouvertes.fr/hal-00338640
Contributor : Djalil Chafaï <>
Submitted on : Tuesday, December 15, 2009 - 10:14:19 PM
Last modification on : Wednesday, September 4, 2019 - 1:52:03 PM
Long-term archiving on: Saturday, November 26, 2016 - 4:01:31 PM

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Djalil Chafai, Florent Malrieu, Katy Paroux. On the long time behavior of the TCP window size process. Stochastic Processes and their Applications, Elsevier, 2010, 120 (8), pp.1518-1534. ⟨10.1016/j.spa.2010.03.019⟩. ⟨hal-00338640v3⟩

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