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 over the Internet. This continuous time Markov process takes its values in [0,∞), 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 been already investigated in the literature. In the present paper, we mainly get quantitative estimates for the exponential convergence to equilibrium, in terms of the W1 Wasserstein coupling distance, for the process and also for its embedded chain.