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Reliability analysis of M/G/1 queues with general retrial times and server breakdowns

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Progress in Natural Science:Materials International 2006年第5期16卷 464-473页

作者： WANG Jinting (department of mathematics,{2. beijing 100044, China) department of mathematics Beijing Jiaotong University Beijing 100044 China

This paper concerns the reliability issues as well as queueing analysis of M/G/1 retrial queues with general retrial times and server subject to breakdowns and repairs. We assume that the server is unreliable and customers who find the server busy or down are queued in the retrial orbit in accordance with a first-come-first-served discipline. Only the customer at the head of the orbit queue is allowed for access to the server. The necessary and sufficient condition for the system to be stable is given. Using a supplementary variable method, we obtain the Laplace-Stieltjes transform of the reliability function of the server and a steady state solution for both queueing and reliability measures of interest. Some main reliability indexes, such as the availability, failure frequency, and the reliability function of the server, are obtained.

关键词： retrial queues general retrial times reliability server breakdowns and repairs.

Near generalized balanced tournament designs with block sizes 4 and 5

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Science China mathematics 2009年第9期52卷 1927-1938页

作者： SHAN XiuLing1, 2.1 department of mathematics,{2. beijing 100044, China 2.College of mathematics and Information Science, Hebei Normal university, Shijiazhuang 050016, China department of mathematics Beijing Jiaotong University Beijing 100044 China College of mathematics and Information Science Hebei Normal University Shijiazhuang 050016 China

A near generalized balanced tournament design, or an NGBTD(k,m) in short, is a (km+1,k,k-1)-BIBD defined on a (km+1)-set V . Its blocks can be arranged into an m×(km+1) array in such a way that (1) the blocks in every column of the array form a partial parallel class partitioning V\{x} for some point x, and (2..every element of V is contained in precise k cells of each row. In this paper, we completely solve the existence of NGBTD(4,m) and almost completely solve the existence of NGBTD(5,m) with four exceptions.

关键词： near generalized balanced tournament designs frame generalized doubly resolvable packing constructions existence 05B05

Estimates for eigenvalues of Laplacian operator with any order

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Science China mathematics 2007年第8期50卷 1078-1086页

作者： Fa-en WU~(1+) Lin-fen CAO~2.1 department of mathematics,{2.jiaotong university,{2.100044,China 2.department of mathematics,Henan Normal university,Xinxiang 453007,China department of mathematics Beijing Jiaotong University Beijing 100044 China department of mathematics Henan Normal University Xinxiang 453007 China

Let D be a bounded domain in an n-dimensional Euclidean space ? n . Assume that $$0 < \lambda _1 \leqslant \lambda _2..leqslant \cdots \leqslant \lambda _k \leqslant \cdots $$ are the eigenvalues of the Dirichlet Lapl... 详细信息

Let D be a bounded domain in an n-dimensional Euclidean space ? n . Assume that $$0 2..leqslant \cdots \leqslant \lambda _k \leqslant \cdots $$ are the eigenvalues of the Dirichlet Laplacian operator with any order l: $$\left\{ \begin{gathered} ( - \vartriangle )^l u = \lambda u, in D \hfill \\ u = \frac{{\partial u}}{{\partial \vec n}} = \cdots = \frac{{\partial ^{l - 1} u}}{{\partial \vec n^{l - 1} }} = 0, on \partial D \hfill \\ \end{gathered} \right.$$ . Then we obtain an upper bound of the (k+1)-th eigenvalue λ k+1 in terms of the first k eigenvalues. $$\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )} \leqslant \frac{2..{n}[4l(n + 2..- 2..^{\tfrac{2..{2.. \left\{ {\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{2..{2.. \lambda _i^{\tfrac{{l - 1}}{l}} \sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{2..{2.. \lambda _i^{\tfrac{2..{l}} } } } \right\}^{\tfrac{2..{2.. $$ . This ineguality is independent of the domain D. Furthermore, for any l ? 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2..onsidered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang.

关键词： Dirichlet problem eigenvalue estimate Laplacian operator 35P15 58G2.

Techniques for searching first integrals by Lie group and application to gyroscope system

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Science China mathematics 2005年第8期48卷 1135-1143页

作者： HU Yanxia & GUAn Keying department of mathematics, School of Science,{2. beijing 100044, China 1. department of mathematics School of Science Beijing Jiaotong University 100044 Beijing China

In the paper, the methods of finding first integrals of an autonomous system using one-parameter Lie groups are discussed. A class of nontrivial one-parameter Lie groups admitted by the classical gyroscope system is found, and based on the properties of first integral determined by the one-parameter Lie group, the fourth first integral of the gyroscope system in Euler case, Lagrange case and Kovalevskaya case can be obtained in a uniform idea. An error on the fourth first integral in general Kovalevskaya case (A=B=2..zG=0), which appeared in literature is found and corrected.

关键词： one-parameter Lie group first integral gyroscope system

ON THE SINGLE SERVER RETRIAL QUEUE WITH PRIORITY SUBSCRIBERS AND SERVER BREAKDOWNS

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Journal of Systems Science & Complexity 2008年第2期21卷 304-315页

作者： Jinting WANG department of mathematics Beijing Jiaotong University Beijing 100044 China

The author concerned the reliability evaluation as well as queueing analysis of M1, M2..1, G2.. retrial queues with two different types of primary customers arriving according to independent Poisson flows. In the case of blocking, the first type of customers can be queued whereas the second type of customers must leave the service area but return after some random period of time to try their luck again. The author assumes that the server is unreliable and it has a service-type dependent, exponentially distributed life time as well as a service-type dependent, generally distributed repair time. The necessary and sufficient condition for the system to be stable is investigated. Using a supplementary variable method, the author obtains a steady-state solution for queueing measures, and the transient as well as the steady-state solutions for reliability measures of interest.

关键词： Priority queues reliability retrial queues server breakdowns.

ON THE LINEAR CONVERGENCE OF PC-METHOD FOR ACLASS OF LINEAR VARIATIONAL INEQUALITIES

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Journal of Computational mathematics 1999年第2期17卷 199-208页

作者： Nai-hua Xiu(department of mathematics, Nothern {2.university, beijing 100044, China Instituteof Applied mathematics, Chinese Academy Of Sciences, beijing 100080, China) 北方交通大学数学系北京

This paper studies the linear convergence properties of a class of the projection and contraction methods for the affine variational inequalities, and proposes a necessary and sufficient condition under which PC-Metho... 详细信息

关键词： affine variational inequality projection and contraction method linear convergence

TRANSPORTATION NETWORKS:OLD AND NEW

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Applied mathematics(A Journal of Chinese Universities) 1996年第3期11卷 251-272页

作者： LIU YANPEI(department of mathematics,Northern {2.university, beijing 100044) department of mathematics Northern Jiaotong University Beijing

This paper shows a number of Problems in pure and applied mathematicsthat are solved by constructing transportation ***,it also shows thatall the solutions are characterized by forbidden configurations which are not ***,all the characterizations are much related to the graphic method which wasfound by Chinese for solving a kind of the transportation problem in the fifties.

关键词： Mathematical programming,transportation problem,network graphic method forbidden configuration.

Some properties on multivariate filter banks with a matrix factorization

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Progress in Natural Science:Materials International 2005年第2期15卷 20-30页

作者： LIAN Qiaofang1, XIAO Hongying2. and CHEN Qiuhui3(1. department of mathematics,{2. beijing 100044, China 2. Institute of mathematics, Academy of mathematics and System Sciences, Chinese Academy of Sciences, beijing 100080, China 3. department of Scientific Computing and Computer Applications, Zhongshan university, Guangzhou 5102.5, China) department of mathematics Beijing Jiaotong University Beijing 100044 China. Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China. department of Scientific Computing and Computer Applications Zhongshan University Guangzhou 510275 China

A class of multivariate filter banks with a matrix factorization has been developed by Chen et al. The main purpose of this paper is to discuss some further properties of this kind of filter bank, such as the completeness, accuracy of the corresponding scaling functions and the relationships with Daubechies' wavelets and the multi-wavelets provided by Chui and Lian. Moreover, some examples are given to show that this kind of filter bank has a higher accuracy for the scaling functions.

关键词： filter banks completeness accuracy matrix factorization

Existence of the solutions and the attractors for the large-scale atmospheric equations

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Science China Earth Sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1 & GUO Boling2... department of {2., {2..ormal university, {2..00875, China 2..Institute of Applied Physics and Computational {2., {2..00080, China 1. department of mathematics Beijing Normal University Beijing 100875 China 2..Institute of Applied Physics and Computational mathematics Beijing 100080 China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.