On Matrix-Geometric Solution of Nested QBD Chains

Sung Ho Choi; Bara Kim; Khosrow Sohraby; Bong Dae Choi

doi:10.1023/A:1021884213344

On Matrix-Geometric Solution of Nested QBD Chains

Sung Ho Choi, Bara Kim, Khosrow Sohraby, Bong Dae Choi

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

In this paper, a generalization of the level dependent Quasi-Birth-and-Death (QBD) chains is presented. We analyze nested level dependent QBD chains and provide the complete characterization of their fundamental matrices in terms of minimal non-negative solutions of a number of matrix quadratic equations. Our results provide mixed matrix-geometric solution for the stationary distribution of nested QBD chains. Applications in overload control in communication networks are also discussed.

Original language	English
Pages (from-to)	5-28
Number of pages	24
Journal	Queueing Systems
Volume	43
Issue number	1-2
DOIs	https://doi.org/10.1023/A:1021884213344
Publication status	Published - 2003
Externally published	Yes

Keywords

Fundamental matrix
Level dependent QBD chains
Matrix-geometric solution
Nested QBD chains
Overload control

ASJC Scopus subject areas

Statistics and Probability
Computer Science Applications
Management Science and Operations Research
Computational Theory and Mathematics

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abstract = "In this paper, a generalization of the level dependent Quasi-Birth-and-Death (QBD) chains is presented. We analyze nested level dependent QBD chains and provide the complete characterization of their fundamental matrices in terms of minimal non-negative solutions of a number of matrix quadratic equations. Our results provide mixed matrix-geometric solution for the stationary distribution of nested QBD chains. Applications in overload control in communication networks are also discussed.",

keywords = "Fundamental matrix, Level dependent QBD chains, Matrix-geometric solution, Nested QBD chains, Overload control",

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AU - Choi, Sung Ho

AU - Kim, Bara

AU - Sohraby, Khosrow

AU - Choi, Bong Dae

PY - 2003

Y1 - 2003

N2 - In this paper, a generalization of the level dependent Quasi-Birth-and-Death (QBD) chains is presented. We analyze nested level dependent QBD chains and provide the complete characterization of their fundamental matrices in terms of minimal non-negative solutions of a number of matrix quadratic equations. Our results provide mixed matrix-geometric solution for the stationary distribution of nested QBD chains. Applications in overload control in communication networks are also discussed.

AB - In this paper, a generalization of the level dependent Quasi-Birth-and-Death (QBD) chains is presented. We analyze nested level dependent QBD chains and provide the complete characterization of their fundamental matrices in terms of minimal non-negative solutions of a number of matrix quadratic equations. Our results provide mixed matrix-geometric solution for the stationary distribution of nested QBD chains. Applications in overload control in communication networks are also discussed.

KW - Fundamental matrix

KW - Level dependent QBD chains

KW - Matrix-geometric solution

KW - Nested QBD chains

KW - Overload control

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JO - Queueing Systems

JF - Queueing Systems

IS - 1-2

ER -

On Matrix-Geometric Solution of Nested QBD Chains

Abstract

Keywords

ASJC Scopus subject areas

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