Total variation estimates for the TCP process

Jean Baptiste Bardet, Alejandra Christen, Arnaud Guillin, Florent Malrieu, Pierre André Zitt

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


The TCP window size process appears in the modelling 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.

Original languageEnglish
JournalElectronic Journal of Probability
StatePublished - 2013


  • Additive Increase Multiplicative Decrease Processes
  • Coupling
  • Exponential Ergodicity
  • Network Protocols
  • Piecewise Deterministic Markov Processes
  • Queueing Theory


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