Geometric decay in level-expanding QBD models

Liming Liu, Masakiyo Miyazawa and Yiqiang Zhao ()

Annals of Operations Research, 2008, vol. 160, issue 1, 83-98

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

Keywords: Level-expanding QBD; Tail asymptotics; Two-dimensional system; Inventory-queue; Join shortest queue (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10479-007-0298-6

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