Quasi-birth-and-death processes, level-geometric distributions. An aggregation/disaggregation approach

A special class of homogeneous continuous time quasi-birth and death (QBD) Markov chains (MCs) which possess level-geometric (LG) stationary distribution are considered. A functional analytic approach is applied which provides not only a clear analytic interpretation of the concepts introduced elsewhere but also represents a suitable basis for computations. An iterative aggregation/disaggregation method is proposed as tool for numerical computations.