Block-structured Markov renewal process is a generalization of Markov renewal process, and it has many key applications in pratice due to various block structures (e.g., QBD process, Markov chains of M/G/1 type). The block-structured Markov renewal process was given a detailed analysis in Li and Zhao [2004], and Chapter 7 in Li's 2010 book: Constructive Computation in Stochastic Models with Applications: RG-Factorizations.

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Block-structured Markov renewal process is a generalization of Markov renewal process. The block-structured Markov renewal process was given a detailed analysis in Li and Zhao [2004] and Chapter 7 in Li's 2010 book: Constructive Computation in Stochastic Models with Applications: RG-Factorizations.
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Block-structured Markov renewal processes