Asymptotic behavior of the stationary distribution in a finite QBD process with zero mean drift

Authors:
Bara Kim;Jeongsim Kim;Jisu Lee
Affiliations:
Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul 136-701, Republic of Korea;Department of Mathematics Education, Chungbuk National University, 12, Gaeshin-dong, Heungduk-ku, Cheongju, Chungbuk 361-763, Republic of Korea;Department of Information and Mathematics, Korea University, 208, Seochang-ri, Jochiwon, Chungnam 339-700, Republic of Korea
Venue:
Operations Research Letters
Year:
2008

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Asymptotic behavior of the loss rate for Markov-modulated fluid queue with a finite buffer

Queueing Systems: Theory and Applications

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Abstract

We consider a finite QBD process with m levels. Assuming that the mean drift is 0, we obtain an asymptotic behavior @p"m^(^m^)~(1/m)c as m-~ in the stationary distribution (@p"0^(^m^),...,@p"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, StochasticModels 23 (2007) 79-95].