Article ID Journal Published Year Pages File Type
1155807 Stochastic Processes and their Applications 2010 17 Pages PDF
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,∞)[0,∞), and 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 W1W1 Wasserstein coupling distance, for the process and also for its embedded chain.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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