Article ID: | iaor20091348 |
Country: | Netherlands |
Volume: | 160 |
Issue: | 1 |
Start Page Number: | 83 |
End Page Number: | 98 |
Publication Date: | Apr 2008 |
Journal: | Annals of Operations Research |
Authors: | Miyazawa Masakiyo, Liu Liming, Zhao Yiqiang Q. |
Keywords: | Matrix-analytic methods |
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.