Operator-Geometric Stationary Distributions for Markov Chains, with Application to Queueing Models

摘要

This paper considers a class of Markov chains on a bivariate state space whose transition probabilities have a particular block-partitioned structure. The irreducibility condition is discussed as is Neuts' mean drift condition. It is shown that an average mean drift may be necessary, under certain conditions, for positive recurrence. Long-term average mean drift is also examined. Some queueing models are provided and results are demonstrated on various embedded Markov chains.