### 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 |

### 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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## Cite this

Kim, B., Kim, J., & Lee, J. (2008). Asymptotic behavior of the stationary distribution in a finite QBD process with zero mean drift.

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