Total variation estimates for the TCP process

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

doi:10.1214/EJP.v18-1720

Total variation estimates for the TCP process

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

INSTITUTE OF STATISTICS

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

Abstract

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 language	English
Journal	Electronic Journal of Probability
Volume	18
DOIs	https://doi.org/10.1214/EJP.v18-1720
State	Published - 2013

Keywords

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

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10.1214/EJP.v18-1720

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AU - Zitt, Pierre André

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KW - Additive Increase Multiplicative Decrease Processes

KW - Coupling

KW - Exponential Ergodicity

KW - Network Protocols

KW - Piecewise Deterministic Markov Processes

KW - Queueing Theory

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JO - Electronic Journal of Probability

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Total variation estimates for the TCP process

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Keywords

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