Duality Results for Block-Structured Transition Matrices
In this paper, we consider a certain class of Markov renewal processes
where the matrix of the transition kernel governing the Markov renewal
process possesses some block-structured property, including repeating
rows. Duality conditions and properties are obtained on two probabilistic
measures which often play a key role in the analysis and computations
of such a block-structured process. The method used here unifies two
different concepts of duality.
Applications of duality are also provided,
including a characteristic theorem concerning recurrence and transience
of a transition matrix with repeating rows and a batch arrival queueing
model.
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