On Matrix-Geometric Solution of Nested QBD Chains

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

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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
Issue number1-2
Publication statusPublished - 2003
Externally publishedYes


  • 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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