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 present an algorithmic approach for sensitivity analysis of stationary and transient performance measures of a perturbed continuous-time level-dependent quasi-birth-and-death (QBD) process with infinitely-many levels. By developing a new LU-type RG-factorization using the censoring technique, we obtain the maximal negative inverse of the infinitesimal generator of the QBD process. The derivatives of the stationary performance measures of the QBD process can then be expressed and computed in terms of the maximal negative inverse, overcoming the computational difficulty arising from the use of group inverses of infinite size in the current literature (see Cao and Chen [11]). We also use a stochastic integral functional to study the transient performance measure of the QBD process and show how to use the algorithmic approach for its sensitivity analysis. As an example, a perturbed MAP/PH/1 queue is also analyzed.

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.

We consider the MIMic queue with server multiple vacations, where each of the c servers leaves for a vacation of an exponentially distributed duration when it finds no waiting units in line. If the server returns to an empty waiting line, it immediately takes another vacation. This paper is concerned with the upper triangular structure of Lhe rate matrix R and the determinaLion of the stationary distnbuliolls of queue length and waiting time. The emphasis is on obtaining the conditional stochastic decompositions of the stationary queue length and waiting time conditioned by the event [B=c], where [B=c) denotes the event that all of the c servers are busy.

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.