Asymptotic behavior of the stationary distribution in a finite QBD process with zero mean drift
- Authors
- Kim, Bara; Kim, Jeongsim; Lee, Jisu
- Issue Date
- 1월-2008
- Publisher
- ELSEVIER SCIENCE BV
- Keywords
- QBD process; stationary distribution; finite queue
- Citation
- OPERATIONS RESEARCH LETTERS, v.36, no.1, pp.127 - 132
- Indexed
- SCIE
SCOPUS
- Journal Title
- OPERATIONS RESEARCH LETTERS
- Volume
- 36
- Number
- 1
- Start Page
- 127
- End Page
- 132
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/124466
- DOI
- 10.1016/j.orl.2007.03.004
- ISSN
- 0167-6377
- Abstract
- We consider a finite QBD process with m levels. Assuming that the mean drift is 0, we obtain an asymptotic behavior pi((m))(m) similar to (1/m)c as m -> infinity in the stationary distribution (pi((m))(0), ... , pi((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) 79-951. (c) 2007 Elsevier B.V. All rights reserved.
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