多级适应性休假排队系统的PH封闭性

对多级适应性休假的M/G/1排队系统,若休假时间服从位相型(PH)分布,我们证明了随机分解中的附加队长和附加延迟分别是离散和连续的PH随机变量,并给出其不可约PH表示,作为特例,国内外广泛研究的多重休假和单重休假系统,随机分解中的附加随机变量对PH分布都是封闭的。     

重尾数据的混合Erlang分布拟合方法

PH分布具有良好的解析性质,重尾数据的PH近似是随机模型分析中的重要课题.混合Erlang分布是一种常见的PH分布,本文利用EM方法给出了重尾数据的混合Erlang分布拟合算法,通过Matlab软件对两类常见重尾数据进行实验,结果令人满意.最后,文章对混合Erlang分布拟合算法的进一步改进做了总结.     

多维Erlang混合的次序统计量及其在多生命理论中的应用（英文）

本文研究来自多维Erlang混合分布的具有相关性的随机变量的次序统计量并将相关结论应用到多生命理论中.利用熟知的数学归纳法推导出次序统计量分布密度函数的解析表达式并证明其分布为一维Erlang混合分布,寿险精算理论中常见的重要统计量可以算出精确解.这一结论将随机变量相互独立情形下的结果推广到变量存在相关性的情形.     

同步N—策略多重休假M／M／c排队

研究了具有同步N-策略多重休假的M／M／c排队系统．在休假时间服从相型（PH）分布的假设下，给出了系统的稳态指标．证明在已知服务台全忙并且系统中顾客数大于或等于N的条件下，条件随机变量可分解成独立随机变量之和，其中一个是无休假经典M／M／c系统中的对应条件变量，另一个是休假引起的附加随机变量     

闸门式PH休假的PH／PH／1／N排队系统研究

本文利用准生灭过程理论,系统地研究了闸门式多重PH休假的PH/PH/1/N排队系统的随机结构和性态,给出了队长、等待时间和忙期等结果,讨论了系统的随机扰动界估计。     

离散型随机变量的次序统计量的分布

本文论述了离散型随机变量的次序统计量的分布律及其有关理论。     

关于次序统计量数学期望的两个恒等式的简证及其应用

给出了最大最小次序统计量分布函数和密度函数的恒等式,从而在随机变量独立同分布情形下,给出了关于次序统计量数学期望的两个恒等式的简捷证法.最后将几个恒等式应用于威布尔分布的最大次序统计量的分布及其数字特征的计算.     

关于离散型随机变量次序统计量分布矩阵对称性猜想的探索

本文研究了离散型随机变量次序统计量的分布矩阵的对称性 ,获得了二个定理 .定理 1　服从等概率二点分布或等概率三点分布的离散型随机变量的次序统计量的分布矩阵是对称矩阵 .定理 2　取值有限且等概率的离散型随机变量的次序统计量的分布矩阵具有中心对称性 .     

离散时间排队MAP/PH/3

本文研究具有马尔可夫到达过程的离散时间排队MAP/PH/3,系统中有三个服务台,每个服务台对顾客的服务时间均服从位相型分布。运用矩阵几何解的理论,我们给出了系统平稳的充要条件和系统的稳态队长分布。同时我们也给出了到达顾客所见队长分布和平均等待时间。     

GI／PH／1休假排队系统队长的随机分解

对空竭服务、多重休假规则的GI/PH/1排队系统的稳态行为给出了详尽分析。在休假时间服从负指数分布情况下,讨论了到达点嵌入Markov链的结构、平衡条件和稳态队长。证明稳态队长可分解成两个独立随机变量之和。     

On families of distributions characterized by certain properties of ordered random variables

In this work, we obtain new characterizations of certain probability distributions by relations with different ordered random variables. Such variables include order statistics, sequential maxima, and records. We consider relations that include not only upper, but also lower record values. The presented ordered objects are based on sequences of independent random variables with a common continuous distribution function. We also investigate equalities in the distribution of sequential maxima exposed by various random shifts. These shifts (one-sided or two-sided) have exponential distributions. Certain theorems and their corollaries present corresponding characterizations of distributions by relations of such a type. In addition, we consider exponentially shifted order statistics such that simple relations among them also characterize certain probability distributions. All of the presented results yield a set of characterizations of various distributions. For particular cases, we present the relations that characterize families of classical exponential and logistic distributions.     

服务台可修的GI/PH/1排队系统

本文讨论服务台可修的GI/PH/1排队,其中服务台寿命和修复时间也是PH变量。首先证明系统在稳态下可转化为一个等价的经典GI/PH/1模型,然后给出系统的各种稳态指标。此外,对修复后重新服务和累积服务两种不同模型,我们给出了统一的处理。     

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本文研究毁伤目标离散时间的概率分布和PH表示.在射击时间间隔服从离散PH分布的条件下,本文导出了不考虑发现目标因素和考虑该因素二种情况下,毁伤目标时间的离散PH表示与分布.同时,文章用实例说明了求毁伤目标离散时间的PH表示、概率分布和毁伤目标平均离散时间的方法.     

THE MATCHED QUEUEING SYSTEM GI。PH/PH/1

ＴＨＥＭＡＴＣＨＥＤＱＵＥＵＥＩＮＧＳＹＳＴＥＭＧＩ。ＰＨ／ＰＨ／１ＸＵＧＵＡＮＣＨＵＩ（ＧＵＡＮＧ－ＨＵＩＨＳＶ）（徐光煇）；ＨＥＱＩＭＩＮＧ（何启明）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙ...     

离散PH分布的一个封闭性质及其应用

本证明了离散PH分布的一个封闭性质并讨论了它在离散时间排队研究中的应用。     

Approximations to the distributions of ordered distance random variables

Summary In the present note we give short proofs of asymptotic theorems for the distributions of extreme and intermediate ordered distance random variables. Moreover, a quick goodness-of-fit test is proposed which is based on a single intermediate ordered distance random variable.     

The matched queueing system GIoPh/Ph/1

We study the matched queueing system GIoPH/PH/1, where the type-I input is a renewal process, the type-II input is a PH renewal process, and the service times are i.i.d. random variables with PH-distributions. First, a condition is given for the stationarity of the system. Then the distributions of the number of type-I customers at the arrival epoches of type-I customers and the number of type-I customers at an arbitrary epoch are derived. We also discuss the occupation time and the waiting time. Their L.S. transforms are derived. Finally, we discuss some problems in numerical computation.This research is supported by the National Natural Science Foundation of China and partially by the Institute of Mathematics, the Chinese Academy of Sciences.     

Some new results on unimodality of generalized order statistics and their spacings

Because of the importance of ordered random variables and, in general, generalized order statistics (GOSs), in many branches of Statistics, a wide interest has been shown in investigating unimodality and strong unimodality of such random variables. Assuming certain restrictions on the model parameters and distributions, some authors have shown unimodality of GOSs. In this article, we shall provide some new results on unimodality of GOSs based on the population distribution function which contain and strengthen several known findings in this regard. A counterexample is also provided for the cases where the results are not valid in general. Unimodality of arbitrary spacings of GOSs based on exponential distributions is also discussed.     

On the Convergence Rates of Extreme Generalized Order Statistics

A classical result of extreme value theory yields that in case of a linear normalization three possible types of limit distributions are possible. As proved recently a similar classification of the limit distributions holds for extreme generalized order statistics which provide a general concept of ordered random variables. In this paper, we derive results for the convergence rates of the nth and (n-r+1)st generalized order statistic, respectively. It turns out that the rate is highly influenced by the choice of the normalizing sequence. Moreover, we show that a uniform bound of order 1/n holds for underlying generalized Pareto distributions, whereas for the standard normal distribution the convergence might be very slow. Similar results for ordinary order statistics are included.     

PH/M/c可修排队系统

研究了一个修理工和c个服务台的可修排队系统.假设顾客的到达过程为PH更新过程,服务台在忙时与闲时具有不同的故障率.顾客的服务时间、服务台的寿命以及服务台的修理时间均服从指数分布.通过建立系统的拟生灭过程,得到了系统稳态分布存在的充要条件.利用矩阵几何解方法,给出了系统的稳态队长.在此基础上,得到了系统的某些排队论和可靠性指标.