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].
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