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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

Sib. Èlektron. Mat. Izv., 2021 Volume 18, Issue 2, Pages 1493–1505 (Mi semr1456)

Probability theory and mathematical statistics

Harris ergodicity of a Split Transmission Control Protocol

S. G. Fossab, M. G. Chebuninac

a Novosibirsk State University, 2, Pirogova str., Novosibirsk, 630090, Russia
b Heriot-Watt University, Edinburgh, EH14 4AS, UK
c Karlsruhe Institute of Technology, Institute of Stochastics, Karlsruhe, 76131, Germany.

Abstract: Additive-increase multiplicative-decrease transmission control protocols are well known and have been studied in numerous papers. It is significantly more difficult to study systems of interacting protocols. We consider a queueing system where both the input intensity and the service intensity follow TCP protocols and the dynamics of the latter depends on both intensities. This type of stochastic system was proposed by Baccelli, Carofiglio and Foss in 2009, who have proved the positive recurrence of the underlying Markov chain and studied a number of statistical properties of the model. In this paper, we introduce a more general stochastic model and prove a stronger statement: the Harris ergodicity of the corresponding Markov chain.

Keywords: split TCP, Markov chains, Harris ergodicity.

UDC: 621.394.74

MSC: 60K25

Received October 13, 2021, published December 2, 2021

DOI: 10.33048/semi.2021.18.112



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© Steklov Math. Inst. of RAS, 2025