Title: The Role of the Group Inverse in the Ergodicity of Level-Dependent Quasi-Birth-and-Death Processes (LDQBDs)
Speaker: James D. Cordeiro (University of Dayton)
Abstract: Quasi-birth-and-death (QBD) processes are a class of structured Markov chains that extend the classical Birth-Death model by permitting state transitions that may occur between births and deaths. Its level-dependent generalization, the LDQBD, has generated a considerable amount of interest due to the fact that a large number of queueing models belong to this class of processes, and yet an analytic steady-state criterion has not been developed up to the present time. In this presentation, we describe the application of Foster-Lyapunov drift to the determination of necessary and sufficient analytic stability criteria for a subclass of discrete-time LDQBD processes whose transition matrices converge over block rows. Particular emphasis is placed on the role of Markov generalized inverse theory in satisfying the requirements of this drift condition. This is the first known application of the Markov group inverse to an infinite-state process via application to levels of the transition probability matrix.
