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

Bibliographical note

Funding Information:
This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment).

Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

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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AU - Kim, Bara

AU - Kim, Jeongsim

AU - Lee, Jisu

N1 - Funding Information: This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment). Copyright: Copyright 2008 Elsevier B.V., All rights reserved.

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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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JF - Operations Research Letters

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

Abstract

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Keywords

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