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, ∞), is ergodic and irreversible. The sample paths are piecewise linear deterministic and the whole randomness of the dynamics comes from the jump mechanism. The aim of the present paper is to provide quantitative estimates for the exponential convergence to equilibrium, in terms of the total variation and Wasserstein distances.
Highlights
The TCP window size process appears in the modeling of the famous Transmission Control Protocol used for data transmission over the Internet
As shown in [DGR02, GRZ04, OKM96], a correct scaling of this process leads to a continuous time Markov process, called the TCP window size process
The sample paths of X are deterministic between jumps, the jumps are multiplicative, and the whole randomness of the dynamics relies on the jump mechanism
Summary
The aim of this section is to provide accurate bounds for the moments of Xt. In particular, we establish below that any moment of Xt is bounded uniformly over the initial value X0. One has by direct computation αp(t) = pαp−1(t) − 1 − 2−p αp+1(t)
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