✦ LIBER ✦
Asymptotic behavior of the stationary distribution in a finite QBD process with zero mean drift
✍ Scribed by Bara Kim; Jeongsim Kim; Jisu Lee
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 161 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0167-6377
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✦ Synopsis
We consider a finite QBD process with m levels. Assuming that the mean drift is 0, we obtain an asymptotic behavior (m) m ∼ (1/m)c as m → ∞ in the stationary distribution ( (m) 0 , . . . , (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].