On Matrix-Geometric Solution of Nested QBD Chains

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

Research output: Contribution to journalArticle

6 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 languageEnglish
Pages (from-to)5-28
Number of pages24
JournalQueueing Systems
Volume43
Issue number1-2
DOIs
Publication statusPublished - 2003 Jan 1
Externally publishedYes

Fingerprint

Telecommunication networks
Matrix-geometric solution
Overload
Stationary distribution
Communication networks

Keywords

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

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Management Science and Operations Research

Cite this

On Matrix-Geometric Solution of Nested QBD Chains. / Choi, Sung Ho; Kim, Bara; Sohraby, Khosrow; Choi, Bong Dae.

In: Queueing Systems, Vol. 43, No. 1-2, 01.01.2003, p. 5-28.

Research output: Contribution to journalArticle

Choi, Sung Ho ; Kim, Bara ; Sohraby, Khosrow ; Choi, Bong Dae. / On Matrix-Geometric Solution of Nested QBD Chains. In: Queueing Systems. 2003 ; Vol. 43, No. 1-2. pp. 5-28.
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