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.

Retrial queues have been widely used to model many problems arising in telephone switching systems, telecommunication networks, computer networks and computer systems, etc. It is of basic importance to study reliability of retrial queues with server breakdowns and repairs because of limited ability of repairs and heavy influence of the breakdowns on the performance measure of the system. However, so far the repairable retrial queues are analyzed only by queueing theory. In this paper we give a detailed analysis for reliability of retrial queues. By using the supplementary variables method, we obtain the explicit expressions of some main reliability indexes such as the availability, failure frequency and reliability function of the server. In addition, some special queues, for instance, the repairable M/G/1 queue and repairable retrial queue can be derived from our results. These results may be generalized to the repairable multi-server retrial models.

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.

This paper refers to some closed two-stage queueing systems with state-dependent vacation policy. By means of the markovian renewal process and Ihe stochastic decomposition formulas of the quantities in equilibrium for M/G/I vacation models. we derive both stationary distributions of tbe queue length and the cyclic time for the closed stale-dependent vacation model We try to solve the problems of closed sustems by using the known results of the related opened Models, and for the purpose give an example in

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.

In this paper, we consider a BMAP/G/1 retrial queue with a server subject to breakdowns and repairs, where the life time of the server is exponential and the repair time is general. We use the supplementary variable method, which combines with the matrix-analytic method and the censoring technique, to study the system. We apply the RG-factorization of a level-dependent continuous-time Markov chain of M/G/1 type to provide the stationary performance measures of the system, for example, the stationary availability, failure frequency and queue length. Furthermore, we use the RG-factorization of a level-dependent Markov renewal process of M/G/1 type to express the Laplace transform of the distribution of a first passage time such as the reliability function and the busy period.

this paper, we first introduce a symmetric phase type (PH) distribution, and then propose a symmetric exponential-polynomial type (EP) distribution based on the symmetric PH distribution. The class of symmetric EP distributions is illustrated to be so large that an arbitrary symmetric probability density function in L2 (-∞, +∞), which is the space of square integrable functions on the real line, can be approximated in (-∞, +∞) by a sequence of symmetric EP probability density functions. We prove this result by means of a constructive approach based on two orthogonal decompositions: Laguerre spectrum decomposition and Hermite spectrum decomposition. We also provide a moment-based approach for simply determining a symmetric EP probability density function to approximatively express a symmetric random variable under which some moments of the symmetric random variable are given. We further propose multidimensional symmetric PH and EP distributions and provide their useful structures and properties. Finally, we apply the symmetric PH and EP distributions to study the probability Hough transform.

该文从概率的角度提出了两类新的滤波器：对称位相型滤波器和对称梯阶滤波器；证明了对任意给定的非负对称滤波器可用这两类滤波器的序列在（-∞，+∞）内一致逼近；这种序列有着统一的结构形式：对于L（x），文中给出了选择L（x）一些最优准则的解析表达式从而表明L（x）既具有一般性，又易进行解析处理和数值计算，对于已有文献中相关于对称指数滤波器的两类不同形式，例如Li等[6]和Ma等[9]，该文从理论上进一步刻画了它们的内在一致性。

该文研究了基于有限个数据点的随机Hough变换的概率模型。在这个模型中，主要讨论了在随机Hough变换的基本算法中起相当关键作用的两个量：累加器数组的控制阈值以及从图像中提取全部基元所需随机抽样的总次数这两个量对随机Hough变换的算法设计及其终止规则是相当有用的。该文的主要结果包括两部分：其一是对累加器数组引入了多项分布，系统地研究了累加器数组的概率结构及其相互关系。同时也计算了提取全部基元所需的随机抽样总次数的分布、均值和方差。另者是基于不断的随机抽样而使得累加器数组的随机变化作者引入了多维纯生过程，证明了提取全部基元所需随机抽样的总次数服从离散的PH分布，从而它的各阶矩都可用简洁的矩阵形式统一地表出。针对于图像的固有因素，作者也讨论了基元的平稳提取概率。该文的结果为随机Hough变换的进一步研究和应用提供了较为严格的理论依据。

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.