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Geometric decay in level-expanding QBD models

Author

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  • Liming Liu
  • Masakiyo Miyazawa
  • Yiqiang Zhao

Abstract

Level-expanding quasi-birth-and-death (QBD) processes have been shown to be an efficient modeling tool for studying multi-dimensional systems, especially two-dimensional ones. Computationally, it changes the more challenging problem of dealing with algorithms for two-dimensional systems to a less challenging one for block-structured transition matrices of QBD type with varying finite block sizes. In this paper, we focus on tail asymptotics in the stationary distribution of a level-expanding QBD process. Specifically, we provide sufficient conditions for geometric tail asymptotics for the level-expanding QBD process, and then apply the result to an interesting two-dimensional system, an inventory queue model. Copyright Springer Science+Business Media, LLC 2008

Suggested Citation

  • Liming Liu & Masakiyo Miyazawa & Yiqiang Zhao, 2008. "Geometric decay in level-expanding QBD models," Annals of Operations Research, Springer, vol. 160(1), pages 83-98, April.
    • Handle: RePEc:spr:annopr:v:160:y:2008:i:1:p:83-98:10.1007/s10479-007-0298-6
    DOI: 10.1007/s10479-007-0298-6
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    Cited by:

    1. Yiqiang Q. Zhao, 2022. "The kernel method tail asymptotics analytic approach for stationary probabilities of two-dimensional queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 100(1), pages 95-131, February.

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