Electronic Journal of Probability

Total variation estimates for the TCP process

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

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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.

Article information

Electron. J. Probab., Volume 18 (2013), paper no. 10, 21 pp.

Accepted: 17 January 2013
First available in Project Euclid: 4 June 2016

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 68M12: Network protocols
Secondary: 60K30 60K25 90B18: Communication networks [See also 68M10, 94A05]

Network Protocols Queueing Theory Additive Increase Multiplicative Decrease Processes (AIMD) Piecewise Deterministic Markov Processes (PDMP) Exponential Ergodicity Coupling

This work is licensed under a Creative Commons Attribution 3.0 License.


Bardet, Jean-Baptiste; Christen, Alejandra; Guillin, Arnaud; Malrieu, Florent; Zitt, Pierre-André. Total variation estimates for the TCP process. Electron. J. Probab. 18 (2013), paper no. 10, 21 pp. doi:10.1214/EJP.v18-1720. https://projecteuclid.org/euclid.ejp/1465064235

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