In this paper, we provide UL-type and LU-type RG-factorizations for an irreducible continuous-time level-dependent quasi-birth-and-death (QBD) process with either finitely-many levels or infinitely-many levels, and then apply the RG-factorizations to solve a class of linear QBD-equations, which is always crucial for analyzing a stochastic model described as a QBD process. Based on the results obtained for the linear QBD-equations, we analyze up-, downand return-integral functionals. We explicitly express the Laplace transforms of the conditional distributions of the three types of stochastic integral functionals and their conditional moments.

In this paper, we provide UL-type and LU-type RG-factorizations for an irreducible continuous-time level-dependent quasi-birth-and-death (QBD) process with either finitely-many levels or infinitely-many levels and then apply the RG-factorizations to solve a class of linear QBD-equations which is always crucial for analyzing a stochastic model described as a QBD process Based on the results obtained for the linear QBD-equations we analyze up-, down-and return-integral functinals We explicityly express the Laplace transforms of the conditional distributions of the three types of stochastic integral functionals and their conditional moments.

In this paper, the censoring technique is used to deal with block-structured Markov renewal processes. Two probabilistic measures the R-and G-measures are defined and a censoring invariant property for the R- and G-measures is obtained The RG-factorization for the ransition probability matrix is dcrivcd based on the Wiener-Hopf type the transition probability matrix consists of two sequences of matrices one is refered to as the probability matrix consists of two sequences of matrices one is referred to as the boundary sequence and the other the repeating sequence Thw, RG-facteiation of the double transformations for the reqeating matrix sequence and four matrix inequalities of the double transformations for the boundary matrix sequence are given.

In this paper, we provide UL-type and LU-type RG-factorizations for an irreducible continuous-time level-dependent quasi-birth-and-death (QBD) process with either finitely-many levels or infinitely-many levels, and then apply the RG-factorizations to solve a class of linear QBD-equations, which is always crucial for analyzing a stochastic model described as a QBD process. Based on the results obtained for the linear QBD-equations, we analyze up-, downand return-integral functionals. We explicitly express the Laplace transforms of the conditional distributions of the three types of stochastic integral functionals and their conditional moments.

In this paper, a unified approach for studying block-structured fluid models is proposed by means of the RG-factorization. When the stochastic environment (or background) is assumed to be a quasi-birth-and-death (QBD) process with either infinitely many levels or finitely many levels, the Laplace transform for the stationary probability distribution of the buffer content is expressed in terms of the R-measure. At the same time, the Laplace-Stieltjes transforms for both the conditional distribution and the conditional mean of a first passage time in such a fluid queue are derived by the same approach.