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

Bara Kim; Jeongsim Kim; Jisu Lee

doi:10.1016/j.orl.2007.03.004

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

Bara Kim, Jeongsim Kim, Jisu Lee

Department of Mathematics

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

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 π_m^(m) ∼ (1 / m) c as m → ∞ in the stationary distribution (π₀^(m), ..., π_m^(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 language	English
Pages (from-to)	127-132
Number of pages	6
Journal	Operations Research Letters
Volume	36
Issue number	1
DOIs	https://doi.org/10.1016/j.orl.2007.03.004
Publication status	Published - 2008 Jan

Keywords

Finite queue
QBD process
Stationary distribution

ASJC Scopus subject areas

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/j.orl.2007.03.004

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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].",

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N2 - 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].

AB - 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].

KW - Finite queue

KW - QBD process

KW - Stationary distribution

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