Open Access
2013 Total variation estimates for the TCP process
Jean-Baptiste Bardet, Alejandra Christen, Arnaud Guillin, Florent Malrieu, Pierre-André Zitt
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Electron. J. Probab. 18: 1-21 (2013). DOI: 10.1214/EJP.v18-1720


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.


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Jean-Baptiste Bardet. Alejandra Christen. Arnaud Guillin. Florent Malrieu. Pierre-André Zitt. "Total variation estimates for the TCP process." Electron. J. Probab. 18 1 - 21, 2013.


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

zbMATH: 1283.68067
MathSciNet: MR3035738
Digital Object Identifier: 10.1214/EJP.v18-1720

Primary: 68M12
Secondary: 60K25 , 60K30 , 90B18

Keywords: Additive Increase Multiplicative Decrease Processes (AIMD) , coupling , exponential ergodicity , Network Protocols , Piecewise Deterministic Markov Processes (PDMP) , Queueing theory

Vol.18 • 2013
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