Dayar T.Quessette, F.2016-02-082016-02-0820030895-47981095-7162http://hdl.handle.net/11693/24542A 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.EnglishGeometric DistributionsMarkov ChainsQuasi-Birth-and-Death ProcessesArticle10.1137/S089547980138914X