On the long time behavior of the TCP window size process

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.

💡 Research Summary

The paper provides a rigorous quantitative analysis of the long‑time behavior of the TCP window‑size process, a continuous‑time Markov model that captures the additive‑increase multiplicative‑decrease (AIMD) mechanism underlying the Transmission Control Protocol. The state space is the non‑negative half‑line (