Total variation estimates for the TCP process

TL;DR

This paper provides quantitative estimates for the exponential convergence to equilibrium of the TCP window size process, a Markov process modeling Internet data transmission, using total variation and Wasserstein distances.

Contribution

It offers new quantitative bounds on the convergence rates of the TCP process to its equilibrium state, enhancing understanding of its long-term behavior.

Findings

Exponential convergence rates are established for the TCP process.

Quantitative bounds are provided in total variation and Wasserstein distances.

Results improve understanding of the process's ergodic properties.

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, \infty), 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.