Harris Ergodicity of a Split Transmission Control Protocol

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.