On the long time behavior of the TCP window size process

TL;DR

This paper analyzes the long-term behavior of the TCP window size process, a Markov process modeling Internet data transmission, providing quantitative convergence estimates to equilibrium using Wasserstein distances.

Contribution

It offers new quantitative estimates for the convergence to equilibrium of the TCP window size process and its embedded chain.

Findings

Quantitative convergence rates in Wasserstein distance.

Analysis of the embedded chain's convergence behavior.

Insights into the ergodic properties of the process.

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. It belongs to the Additive Increase Multiplicative Decrease class of processes. The sample paths are piecewise linear deterministic and the whole randomness of the dynamics comes from the jump mechanism. Several aspects of this process have already been investigated in the literature. In the present paper, we mainly get quantitative estimates for the convergence to equilibrium, in terms of the $W_1$ Wasserstein coupling distance, for the process and also for its embedded chain.