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 |
Fingerprint
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
Cite this
Asymptotic behavior of the stationary distribution in a finite QBD process with zero mean drift. / Kim, Bara; Kim, Jeongsim; Lee, Jisu.
In: Operations Research Letters, Vol. 36, No. 1, 01.01.2008, p. 127-132.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Asymptotic behavior of the stationary distribution in a finite QBD process with zero mean drift
AU - Kim, Bara
AU - Kim, Jeongsim
AU - Lee, Jisu
PY - 2008/1/1
Y1 - 2008/1/1
N2 - 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].
AB - 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].
KW - Finite queue
KW - QBD process
KW - Stationary distribution
UR - http://www.scopus.com/inward/record.url?scp=37149018571&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=37149018571&partnerID=8YFLogxK
U2 - 10.1016/j.orl.2007.03.004
DO - 10.1016/j.orl.2007.03.004
M3 - Article
AN - SCOPUS:37149018571
VL - 36
SP - 127
EP - 132
JO - Operations Research Letters
JF - Operations Research Letters
SN - 0167-6377
IS - 1
ER -