TECHNICAL REPORT BU-CE-0105, BILKENT UNIVERSITY, 
DEPARTMENT OF COMPUTER ENGINEERING

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

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 are 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 are 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.