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This paper deals with the computation of invariant measures and stationary expectations for discrete-time Markov chains governed by a block-structured one-step transition probability matrix. The method generalizes in some respect Neuts’ matrix-geometric approach to vector-state Markov chains. The method reveals a strong relationship between Markov chains and matrix continued fractions which can provide valuable information for mastering the growing complexity of real-world applications of large-scale grid systems and multidimensional level-dependent Markov models. The results obtained are extended to continuous-time Markov chains.

Computation of Invariant Measures and Stationary Expectations for Markov Chains with Block-Band Transition Matrix