Geometric decay in level-expanding QBD models |
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Authors: | Liming Liu Masakiyo Miyazawa Yiqiang Q Zhao |
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Institution: | (1) Department of Logistics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;(2) Department of Information Sciences, Tokyo University of Science, Noda City, Chiba 278-8510, Japan;(3) School of Mathematics and Statistics, Carleton University, Ottawa, ON, Canada, K1S 5B6 |
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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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Keywords: | Level-expanding QBD Tail asymptotics Two-dimensional system Inventory-queue Join shortest queue |
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