### 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 (π_{0}^{(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 |
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Pages (from-to) | 127-132 |

Number of pages | 6 |

Journal | Operations Research Letters |

Volume | 36 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2008 Jan 1 |

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### 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

### Cite this

*Operations Research Letters*,

*36*(1), 127-132. https://doi.org/10.1016/j.orl.2007.03.004

**Asymptotic behavior of the stationary distribution in a finite QBD process with zero mean drift.** / Kim, Bara; Kim, Jeongsim; Lee, Jisu.

Research output: Contribution to journal › Article

*Operations Research Letters*, vol. 36, no. 1, pp. 127-132. https://doi.org/10.1016/j.orl.2007.03.004

}

TY - JOUR

T1 - Asymptotic behavior of the stationary distribution in a finite QBD process with zero mean drift

AU - Kim, Bara

AU - Kim, Jeongsim

AU - Lee, Jisu

PY - 2008/1/1

Y1 - 2008/1/1

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

UR - http://www.scopus.com/inward/record.url?scp=37149018571&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=37149018571&partnerID=8YFLogxK

U2 - 10.1016/j.orl.2007.03.004

DO - 10.1016/j.orl.2007.03.004

M3 - Article

AN - SCOPUS:37149018571

VL - 36

SP - 127

EP - 132

JO - Operations Research Letters

JF - Operations Research Letters

SN - 0167-6377

IS - 1

ER -