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On the long time behavior of the TCP window size process

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  • Chafaï, Djalil
  • Malrieu, Florent
  • Paroux, Katy

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,[infinity]), and 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 W1 Wasserstein coupling distance, for the process and also for its embedded chain.

Suggested Citation

  • Chafaï, Djalil & Malrieu, Florent & Paroux, Katy, 2010. "On the long time behavior of the TCP window size process," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1518-1534, August.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:8:p:1518-1534
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    References listed on IDEAS

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    1. Maulik, Krishanu & Zwart, Bert, 2006. "Tail asymptotics for exponential functionals of Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 156-177, February.
    2. Krishanu Maulik & Bert Zwart, 2009. "An extension of the square root law of TCP," Annals of Operations Research, Springer, vol. 170(1), pages 217-232, September.
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    Cited by:

    1. Brandejsky, Adrien & de Saporta, Benoîte & Dufour, François, 2013. "Optimal stopping for partially observed piecewise-deterministic Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3201-3238.
    2. Denis Villemonais, 2020. "Lower Bound for the Coarse Ricci Curvature of Continuous-Time Pure-Jump Processes," Journal of Theoretical Probability, Springer, vol. 33(2), pages 954-991, June.
    3. Montagnon, Pierre, 2020. "Stability of piecewise deterministic Markovian metapopulation processes on networks," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1515-1544.
    4. Fontbona, Joaquin & Guérin, Hélène & Malrieu, Florent, 2016. "Long time behavior of telegraph processes under convex potentials," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 3077-3101.

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