矩阵非中心Г－分布

本文定义了矩阵形式的非中心－分布。它将常见的一元Ｇａｍｍａ分布，非中心Ｘ２－分布，和多元分析中的中心则Ｗｉｓｈａｒｔ分布，非中心Ｆ－分布等纳入一个整体，进而推导了它的特征函数与特征根的分布密度函数，为一些检验奠定了基础．     

矩阵非中心Г—分布

本文定义了矩阵形式的非中心Г－分布，它将常见的一元Ｇａｍｍａ分布，非中心ｘ＾２－分布，和多元分析中的中心Ｗｉｓｈａｒｔ分布，非中心Ｆ－分布等纳入一个整体，进而推导了它的特征函数与特征根的分布密度函数，为一些检验奠定了基础。     

一个渐近的分布概率式

本文给出了一个渐近分布概率式的推广形式，并运用概率论知识给出它的一个证明     

一个渐近的分布概率式

本给出了一个渐近分布概率式的推广形式，并运用概率论知识给出它的一个证明。     

寿命分布NBUE性质的一个新刻画及应用

本文介绍绝对连续型NBUE寿命分布的一个新的刻画：一个寿命分布具有NBUE性当且仅当它随机地大于具有相应的平衡分布的随机变量。讨论了此刻画在可靠性与寿命检验中的应用，并建立了严格NBUE性的一个非参数检验方法。     

混合整参数贝塔分布及其应用

本文给出了一个新的指数型分布,它是整参数贝塔分布Be(k+1,n-k)对于整数n的截0至k的截尾泊松分布的混合分布.论文给出了这一分布的统计意义和数字特征,并通过一个例子说明了它的一个应用.     

如何发现世界上最安静的敌潜艇

我们建立了一个数学模型；用以探测一个大型移动目标，譬如说一艘潜艇．并且计算出潜艇的大小和它移动的速度、方向．探测过程仅依赖于一个普通噪声环境受到的扰动我们作了一系列合理的假设，分析了潜艇的运动以及它对背景噪声场的影响．运动潜艇吸收、反射噪声声波，由此产生的多普勒效应，是原噪声场的一个扰动．这种扰动可被探测器（如压电麦克风）捕获．在对潜艇的形状与材料作了假设的基础上，我们推导出在一个单频单幅噪声场中潜艇回波的频谱分布．这个频谱分布类似伞形，简称伞形分布．频谱带宽可用于计算潜艇航速．伞形分布曲线下的面积可用于计算潜艇等效截面积，根据频谱的中心频率与噪声频率的差异，可计算出它的移动方向我们引入了对数频率坐标．基于卷积理论，计算出了在宽带噪声场中潜艇的回波．这样，通过反卷积，就可以简化为上述己解决的若这艘潜艇置于一单频单幅噪声场中应有的情况．根据反卷积后的回波分布，即可根据本文中提到的方法，得到需要的结果．我们还把这个模型推广到实际中，给出了一个伺服系统和一个可行的方案．文中最后就模型优缺点和问题本身的局限性作了讨论．考虑到实际的应用，提出了一些新的构想，并预想了这类问题今后可能的发展方向．     

用分布核空间刻画象征空间OpSm1

在五十年代，人们就建立了象征与分布核的形式上的联系；但这之后象征学派和Calderon-Zygmund学派一直处于分立的状态.即使对于OpSm1,1，也只是对于它的一个子空间给出了刻画，这里用分布核空间刻画象征空间OpSm11     

关于模N的原根与它的逆的差的奇数幂及其推广

本文研究了模ｎ的原根ａ与它的逆ａ差的奇数幂分布性质，并给出了(?)的一个渐近公式．     

天梯模型和风险率有上界的寿命分类类

本文介绍的天梯模型是一种广泛的寿命分布模型。利用此模型在总结现有分布类基础上引伸出一个风险率有上界的寿命分布类。新分布类是有理ＬＳ变换分布类和位相型分布类的真推广，且更具优良的封闭性质。此外，新分布类可看作一类非齐次Ｍａｒｋｏｖ链的首通时间分布，因此它与随机模型理论有着密切的联系。     

Loss probability in a finite discrete-time queue in terms of the steady state distribution of an infinite queue

We consider a discrete-time single-server queue with arrivals governed by a stationary Markov chain, where no arrivals are assumed to occur only when the Markov chain is in a particular state. This assumption implies that off-periods in the arrival process are i.i.d. and geometrically distributed. For this queue, we establish the exact relationship between queue length distributions in a finite-buffer queue and the corresponding infinite-buffer queue. With the result, the exact loss probability is obtained in terms of the queue length distribution in the corresponding infinite-buffer queue. Note that this result enables us to compute the loss probability very efficiently, since the queue length distribution in the infinite-buffer queue can be efficiently computed when off-periods are geometrically distributed. This revised version was published online in June 2006 with corrections to the Cover Date.     

L^2-策略休假下可修的M_1+M_2/G^x(M/G)/1匹配排队系统分析

双输人匹配排队系统是通常排队系统的一种推广．本文对该系统考察了Ｌ２－策略休假和服务台可修的两个重要因素．其中假定系统有两个不同的Ｐｏｉｓｓｏｎ输入，两类顾客按１：１作成一批进行服务，服务台的寿命服从指数分布，服务时间，修理时间和休假时间都服从一般连续型分布，利用向量马氏过程方法，得到了该排队系统的一些重要的稳态排队论指标和可靠性指标．     

Rare event asymptotics for a random walk in the quarter plane

This paper presents a novel technique for deriving asymptotic expressions for the occurrence of rare events for a random walk in the quarter plane. In particular, we study a tandem queue with Poisson arrivals, exponential service times and coupled processors. The service rate for one queue is only a fraction of the global service rate when the other queue is non-empty; when one queue is empty, the other queue has full service rate. The bivariate generating function of the queue lengths gives rise to a functional equation. In order to derive asymptotic expressions for large queue lengths, we combine the kernel method for functional equations with boundary value problems and singularity analysis.     

Extreme and high-level sojourns of the single server queue in heavy traffic

This study characterizes the behavior of large queue lengths in heavy traffic. We show that the distribution of the maximum queue length in a random time interval for a queueing systems in heavy traffic converges to a novel extreme value distribution. We also study the processes that record the times that the queue length exceeds a high level and the cumulative time the queue is above the level. We show that these processes converge in distribution to compound Poisson processes. This revised version was published online in June 2006 with corrections to the Cover Date.     

A polling model with an autonomous server

This paper considers polling systems with an autonomous server that remains at a queue for an exponential amount of time before moving to a next queue incurring a generally distributed switch-over time. The server remains at a queue until the exponential visit time expires, also when the queue becomes empty. If the queue is not empty when the visit time expires, service is preempted upon server departure, and repeated when the server returns to the queue. The paper first presents a necessary and sufficient condition for stability, and subsequently analyzes the joint queue-length distribution via an embedded Markov chain approach. As the autonomous exponential visit times may seem to result in a system that closely resembles a system of independent queues, we explicitly investigate the approximation of our system via a system of independent vacation queues. This approximation is accurate for short visit times only.      

Queue Length Distribution in a FIFO Single-Server Queue with Multiple Arrival Streams Having Different Service Time Distributions

This paper considers the queue length distribution in a class of FIFO single-server queues with (possibly correlated) multiple arrival streams, where the service time distribution of customers may be different for different streams. It is widely recognized that the queue length distribution in a FIFO queue with multiple non-Poissonian arrival streams having different service time distributions is very hard to analyze, since we have to keep track of the complete order of customers in the queue to describe the queue length dynamics. In this paper, we provide an alternative way to solve the problem for a class of such queues, where arrival streams are governed by a finite-state Markov chain. We characterize the joint probability generating function of the stationary queue length distribution, by considering the joint distribution of the number of customers arriving from each stream during the stationary attained waiting time. Further we provide recursion formulas to compute the stationary joint queue length distribution and the stationary distribution representing from which stream each customer in the queue arrived.     

On a generic class of two-node queueing systems

This paper analyzes a generic class of two-node queueing systems. A first queue is fed by an on–off Markov fluid source; the input of a second queue is a function of the state of the Markov fluid source as well, but now also of the first queue being empty or not. This model covers the classical two-node tandem queue and the two-class priority queue as special cases. Relying predominantly on probabilistic argumentation, the steady-state buffer content of both queues is determined (in terms of its Laplace transform). Interpreting the buffer content of the second queue in terms of busy periods of the first queue, the (exact) tail asymptotics of the distribution of the second queue are found. Two regimes can be distinguished: a first in which the state of the first queue (that is, being empty or not) hardly plays a role, and a second in which it explicitly does. This dichotomy can be understood by using large-deviations heuristics. This work has been carried out partly in the Dutch BSIK/BRICKS project.     

On optimal polling policies

In a single-server polling system, the server visits the queues according to a routing policy and while at a queue, serves some or all of the customers there according to a service policy. A polling (or scheduling) policy is a sequence of decisions on whether to serve a customer, idle the server, or switch the server to another queue. The goal of this paper is to find polling policies that stochastically minimize the unfinished work and the number of customers in the system at all times. This optimization problem is decomposed into three subproblems: determine the optimal action (i.e., serve, switch, idle) when the server is at a nonempty queue; determine the optimal action (i.e., switch, idle) when the server empties a queue; determine the optimal routing (i.e., choice of the queue) when the server decides to switch. Under fairly general assumptions, we show for the first subproblem that optimal policies are greedy and exhaustive, i.e., the server should neither idle nor switch when it is at a nonempty queue. For the second subproblem, we prove that in symmetric polling systems patient policies are optimal, i.e., the server should stay idling at the last visited queue whenever the system is empty. When the system is slotted, we further prove that non-idling and impatient policies are optimal. For the third subproblem, we establish that in symmetric polling systems optimal policies belong to the class of Stochastically Largest Queue (SLQ) policies. An SLQ policy is one that never routes the server to a queue known to have a queue length that is stochastically smaller than that of another queue. This result implies, in particular, that the policy that routes the server to the queue with the largest queue length is optimal when all queue lengths are known and that the cyclic routing policy is optimal in the case that the only information available is the previous decisions.This work was supported in part by NSF under Contract ASC-8802764.     

Optimal Prediction of Times and Queue Lengths in the M/G/1 Queue

This paper presents optimal mean-square predictors for several variables in a FIFO M/G/1 queue. In particular, conditional expectation predictors are derived for the number in the queue, time in the queue, and the waiting time, with a previous number in the queue as the basis for the prediction. The relationships between the predictors are derived, and the basic properties are illustrated with examples.