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Type: Journal article
Title: Fluid approach to two-sided reflected Markov-modulated Brownian motion
Author: Latouche, G.
Nguyen, G.
Citation: Queueing Systems: Theory and Applications, 2015; 80(1-2):105-125
Publisher: Springer
Issue Date: 2015
ISSN: 0257-0130
Statement of
Guy Latouche, Giang Nguyen
Abstract: We extend to Markov-modulated Brownian motion (MMBM) the renewal approach which has been successfully applied to the analysis of Markov-modulated fluid models. It has been shown recently that MMBM may be expressed as the limit of a parameterized family of Markov-modulated fluid models. We prove that the weak convergence also holds for systems with two reflecting boundaries, one at zero and one at b > 0, and that the stationary distributions of the approximating fluid models converge to the stationary distribution of the two-sided reflected MMBM. In so doing, we obtain a new representation for the stationary distribution. It is factorised into a vector determined by the phase behaviour when the fluid is either at the level 0 or the level b, and a matrix expression characteristic of the process when the fluid is in the open interval (0, b).
Keywords: Markov-modulated linear fluid models; reflected two-sided Markov-modulated Brownian motion; weak convergence; stationary distribution
Rights: © Springer Science+Business Media New York 2015
DOI: 10.1007/s11134-014-9432-8
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Mathematical Sciences publications

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