SINGULARLY PERTURBED MARKOV MODULATED FLUID QUEUES

被引：1

作者：

Dendievel, Sarah ^{[1
,2
]}

Latouche, Guy ^{[3
]}

Liu, Yuanyuan ^{[4
]}

Tang, Yingchun ^{[4
]}

机构：

[1] Haute Ecole ICHEC, Dept ICHEC Brussels Management Sch, QUARESMI Lab, ECAM ISFSC, Blvd Brand Whitlock 4, B-1150 Brussels, Belgium

[2] Univ Ghent, SMACS Res Grp, Dept Telecommun & Informat Proc, Sint Pieternieuwstraat 41, B-9000 Ghent, Belgium

[3] Univ Libre Bruxelles, Fac Sci, CP212 Blvd Triomphe 2, B-1050 Brussels, Belgium

[4] Cent South Univ, Sch Math & Stat, New Campus, Changsha 410083, Hunan, Peoples R China

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2022年 / 43卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Markov modulated fluid models; perturbation analysis; stationary distribution; WIENER-HOPF FACTORIZATION; CHAINS;

D O I：

10.1137/21M1395387

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a Markov modulated fluid queue for which the environment is nearly completely decomposable. Under the basic assumption that both the nearly completely decomposable Markov modulated fluid model and the unperturbed fluid models are positive recurrent, we show that the stationary density of the level can be expanded as convergent power series of the aggregated stationary densities. We go further in the analysis by assuming that one or more of the unperturbed fluid queues is not necessarily positive recurrent. We provide numerical illustration.

引用

页码：377 / 404

页数：28

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