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Concerning the problem that network congestion risk of computer network service system for some data frames having a full priority of transmission, a method about nonpreemptive limited-priority M/M/n/m queuing system model was proposed. Firstly, as the parameter r of limited-priority was introduced into the model, the data frame with full priority was converted to the one with limited priority. Secondly, in order to lower the risk of computer network service system and stabilize the network system further, the fairness among different priorities was studied in the model. Moreover, by making use of Total Probability Theorem, three results of the models, the average waiting time, the average dwelling time and the average queue length were obtained.     

M/M/1排队系统中的维修策略

以平均报酬率为目标函数的维修策略问题引入可修排队系统.在M/M/1/模型下,利用几何过程描述服务台随机退化过程,考虑了基于服务台失效次数N的策略,即当失效次数到达N次时,对服务台进行替换.根据更新报酬定理,获得了基于维修次数N的平均报酬率的表达式.     

N策略工作休假M/M/1排队

考虑策略工作休假M/M/1排队,简记为M/M/1(N-WV)。在休假期间,服务员并未完全停止工作而是以较低的速率为顾客服务。用拟生灭过程和矩阵几何解方法,我们给出了有直观概率意义的稳态队长和稳态条件等待时间的分布。此外,我们也得到了队长和等待时间的条件随机分解结构及附加队长和附加延迟的分布。     

A Note on Queueing System M/M/1

A new formula is given for the queue length distribution functions of queueingsystem M/M/1.Based on this formula and renewal theory,a new and simple proof ofthe ergodicity of queueing system M/M/1 is given.     

运用Mathematica软件包模拟M/M/1队列

运用Mathematica软件包模拟一个M/M/1队列问题,显现该软件包对于数学研究与教学的重要价值.通过对问题的分析制定模拟方案,利用计算机仿真形象地展示排队过程.其方法适用于一般队列问题.     

线性规划中大M法的参数M估值问题

在线性规划的单纯形法中,为求初始的可行基有著名的大M法,即惩罚因子法.在通常的运筹学教材中,只说明当M充分大时,大M法是有效的,并没有给出参数M的确切估计值.现给出一个确定的常数M0,并证明当M>M0时,大M法收敛于原问题的最优解.     

M/M/1算子的复谱

研究偏微分方程形式的M/M/1排队模型的主算子在左半复平面中的谱,证明集合{γ∈C|R_γ≤-(λ+μ)}包含于该模型主算子的连续谱与剩余谱的并集.由此指出偏微分方程形式的M/M/1排队模型和常微分方程形式的M/M/1排队模型的本质区别.     

M/M/1算子的其它特征值

证明对一切θ∈（0,1）,θ（2（λμ）~（1/2）-λ-μ）都是偏微分方程形式的M/M/1排队模型主算子的几何重数为1的特征值.     

M/M/∞ Queues in series with non-homogeneous inputs

This paper studies the transient behaviour of tandem queueing system consisting of an arbitrary number r of queues in series with infinite server service facility at each queue. Poisson arrivals with time dependent parameter and exponential service times have been assumed. Infinite server queues realistically describe those queues in which sufficient service capacity exist to prevent virtually any waiting by the customer present. The model is suitable for both phase type service as well services in series. Very elegant solutions have been obtained and it has been shown that if the queue sizes are initially independent and Poisson then they remain independent and Poisson for all t.     

M/M/C休假排队系统-综述

本文介绍了带有各种休假策略的Ｍ／Ｍ／Ｃ休假排队的研究方法及结果,在所有服务台全的条件下,我们证明了系统的稳态队长和稳态等待时间可分解成两个独立随机变量和和,其中一个随机变量愉是相应的经典Ｍ／Ｍ／Ｃ排队的稳态队长与稳态等待时间。     

M／M／1算子的另一个特征值

证明2√λμ-λ-μ是偏微分方程形式的M／M／1排队模型主算子的几何重数为1的特征值．     

Ass（M／N） and Ann（M／N） on the Noetherian Module M

Let R is a noetherian ring,M is a finitely generated R-module.This paper studies the relationbetween associated prime Ass(M/N)and annihilator Ann(M/N),and has given the necessary andsufficient conditions of Ass(M/N)=Ann(M/N).     

On Möbius form and Möbius isoparametric hypersurfaces

An umbilic-free hypersurface in the unit sphere is called MSbius isoparametric if it satisfies two conditions, namely, it has vanishing MSbius form and has constant MSbius principal curvatures. In this paper, under the condition of having constant MSbius principal curvatures, we show that the hypersurface is of vanishing MSbius form if and only if its MSbius form is parallel with respect to the Levi-Civita connection of its MSbius metric. Moreover, typical examples are constructed to show that the condition of having constant MSbius principal curvatures and that of having vanishing MSbius form are independent of each other.     

非强占优先权下的M/M/1排队

分析带有两个优先权的非强占M/M/1系统的性能,用补充变量法构造向量马尔可夫过程对此排队系统的状态转移方程进行分析,得到两类顾客在非强占优先权的队长联合分布的母函数,进一步讨论,得出了服务台被两类顾客占有和闲置的概率以及两类信元各自的平均队长.     

M/M/c排队驱动的流模型分析

研究了一个多台排队系统队长过程作为外部随机环境的流模型.使用Laplace变换(LT)方法,发现缓冲器容量(库存量)分布的LT具有简洁的幂结构.进一步地,借助于Laplace-Stieltjes变换(LST)和LT之间的内在关系,给出了库存量分布的LST及平均库存量.最后,借助于一些数值例子刻画了系统参数对平均库存量及空库概率的影响.     

M/M/∞随机服务系统的一个递推方法

本文提出一个处理 M/M/∞随机服务系统瞬时行为的交错递推方法.由此不仅可得瞬时状态分布,还给出各种二维随机过程及输出过程的分布、一系列瞬时条件分布、诸过程的瞬时相关系数.最后,当 t 充分大时,对各种瞬时概率给出方便的渐近公式.     

关于M/M/1系统方程的瞬态解

经典的M/M/1随机服务系统的排队方程是{G_0~＇(t)=-λG_0(t)+μG_1(t),G_k~＇(t)=λG_(k-1)(t)-(λ+μ)G_k(t)+μG_(k+1)(t),k=1,2,…,其中G_k(t)表示在时刻t系统内恰有k个顾客的概率.在一般初始条件下方程(1)的解已由Clarke用母函数方法求出:G_k(t)=e~(-(λ+μ)t)[(λ/μ)~(k/2)I_k(2t(λμ~(1/2))+(λ/μ)~((k-1)/2)I_(k+1)(2t(λμ~(1/2))