On the long time behavior of the TCP window size process

Details On the long time behavior of the TCP window size process On the long time behavior of the TCP window size process

2008-11-13

arxiv.org/abs/0811.2180v3

Stochastic Processes and their Applications 120, 8 (2010) 1518-1534

Mathematics

Probability

Corrections

Scientific paper

10.1016/j.spa.2010.03.019

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.

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