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 theis paper, we study a BMAP/M/1 generalized processor-sharing queue, We propose a RG-factorization approach which can be applied to a wider class ofMarkovian block-structured processor-sharing queues We obtain the expressions for bothe the distribution of the stationary queue length and the Laplace transform of the sojourn time distribution From these two expressions we develop an algorithm to compute the mean and variance of the sojourn time approximately.

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.

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。

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.