SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, VOL.24, NO.1, PP.281-291, 
2002.

TITLE: Quasi-Birth-and-Death Processes with Level-Geometric Distribution

AUTHORS: Tugrul Dayar and Franck Quessette

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 on three examples.

KEY WORDS: Markov chains, quasi-birth-and-death processes, geometric
distributions

AMS SUBJECT CLASSIFICATIONS: 60J27, 65F50, 65H10, 65F05, 65F10, 65F15