Total variation estimates for the TCP process. (English) Zbl 1283.68067

The primary goal of the authors is to deal with a mathematical treatment of a protocol. 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. 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.


68M12 Network protocols
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
60K25 Queueing theory (aspects of probability theory)
90B18 Communication networks in operations research
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