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
N1 - Funding Information:
This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment).
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2008/1
Y1 - 2008/1
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
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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 -