Quasi-birth-and-death processes with level-geometric distribution
Date
2003
Authors
Dayar T.
Quessette, F.
Editor(s)
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
SIAM Journal on Matrix Analysis and Applications
Print ISSN
0895-4798
1095-7162
1095-7162
Electronic ISSN
Publisher
SIAM
Volume
24
Issue
1
Pages
281 - 291
Language
English
Type
Journal Title
Journal ISSN
Volume Title
Series
Abstract
A special class of homogeneous continuous-time quasi-birth-and-death (QBD) Markov chains (MCS) which possess level-geometric (LG) stationary distribution is considered. Assuming that the stationary vector is partitioned by levels into subvectors, in an LG distribution all stationary subvectors beyond a finite level number are multiples of each other. Specifically, each pair of stationary subvectors that belong to consecutive levels is related by the same scalar, hence the term level-geometric. Necessary and sufficient conditions are specified for the existence of such a distribution, and the results are elaborated in three examples.