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 |
|---|---|
| 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 |
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
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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