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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].