Determination of explicit solution for a general class of Markov processes
In this paper, we study both the GI/M/1 type and the M/G/1 type
Markov chains with the special structure
A_0 = omega times beta.
We obtain explicit formulas for matrices R and G, which generalized
earlier results on Markov chains of QBD type.
In the case of GI/M/1 type, we show how to find the maximal eigenvalue
of R, and then that the computation of R is equivalent to that of
x_2. In the case of M/G/1 type, we show that G=1 times beta.
Based on the earlier results, we show that a stable recursion for finding
the stationary probability vectors x_i can be carried out easily.
Two models in application are discussed, as examples of such processes.
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