Asymptotic behavior of the stationary distribution in a finite quasi-birth-and-death (QBD) process with zero mean drift

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Article ID:	iaor2009725
Country:	Netherlands
Volume:	36
Issue:	1
Start Page Number:	127
End Page Number:	132
Publication Date:	Jan 2008
Journal:	Operations Research Letters
Authors:	Kim Bara, Kim Jeongsim, Lee Jisu
Keywords:	queues: theory

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.

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