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Geometric decay in level-expanding QBD models

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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.

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Authors and Affiliations

  1. Department of Logistics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Liming Liu

  2. Department of Information Sciences, Tokyo University of Science, Noda City, Chiba, 278-8510, Japan

    Masakiyo Miyazawa

  3. School of Mathematics and Statistics, Carleton University, Ottawa, ON, Canada, K1S 5B6

    Yiqiang Q. Zhao

Authors
  1. Liming Liu
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  2. Masakiyo Miyazawa
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  3. Yiqiang Q. Zhao
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Corresponding author

Correspondence to Yiqiang Q. Zhao.

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Liu, L., Miyazawa, M. & Zhao, Y.Q. Geometric decay in level-expanding QBD models. Ann Oper Res 160, 83–98 (2008). https://doi.org/10.1007/s10479-007-0298-6

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  • DOI: https://doi.org/10.1007/s10479-007-0298-6

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