Asymptotic behavior of the stationary distribution in a finite QBD process with zero mean drift

Bara Kim, Jeongsim Kim, Jisu Lee

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We consider a finite QBD process with m levels. Assuming that the mean drift is 0, we obtain an asymptotic behavior πm(m) ∼ (1 / m) c as m → ∞ in the stationary distribution (π0(m), ..., πm(m)), by finding an explicit expression for vector c. This solves the problem that was conjectured by Miyazawa et al. [Asymptotic behaviors of the loss probability for a finite buffer queue with QBD structure, Stochastic Models 23 (2007) 79 - 95].

Original languageEnglish
Pages (from-to)127-132
Number of pages6
JournalOperations Research Letters
Volume36
Issue number1
DOIs
Publication statusPublished - 2008 Jan 1

Keywords

  • Finite queue
  • QBD process
  • Stationary distribution

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics
  • Modelling and Simulation

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