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

Authors:
Yutaka Sakuma;Masakiyo Miyazawa
Affiliations:
Department of Information Sciences, Tokyo University of Science, Tokyo, Japan;Department of Information Sciences, Tokyo University of Science, Tokyo, Japan
Venue:
Queueing Systems: Theory and Applications
Year:
2010

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Abstract

We consider a Markov-modulated fluid queue with a finite buffer. It is assumed that the fluid flow is modulated by a background Markov chain which may have different transitions when the buffer content is empty or full. In Sakuma and Miyazawa (Asymptotic Behavior of Loss Rate for Feedback Finite Fluid Queue with Downward Jumps. Advances in Queueing Theory and Network Applications, pp. 195---211, Springer, Cambridge, 2009), we have studied asymptotic loss rate for this type of fluid queue when the mean drift of the fluid flow is negative. However, the null drift case is not studied. Our major interest is in asymptotic loss rate of the fluid queue with a finite buffer including the null drift case. We consider the density of the stationary buffer content distribution and derive it in matrix exponential forms from an occupation measure. This result is not only useful to get the asymptotic loss rate especially for the null drift case, but also it is interesting in its own light.