  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.
