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.