Duality results for block-structured transition matrices
1999 ◽
Vol 36
(4)
◽
pp. 1045-1057
◽
Keyword(s):
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.
1999 ◽
Vol 36
(04)
◽
pp. 1045-1057
◽
Keyword(s):
1992 ◽
Vol 29
(01)
◽
pp. 116-128
◽
1969 ◽
Vol 1
(02)
◽
pp. 188-210
◽
1969 ◽
Vol 40
(6)
◽
pp. 1901-1907
◽