基于排队论的专项汽修厂维修台配置数量研究

为了解决因维修台配置不合理而导致的专项汽修厂排队等待的问题,运用排队论等理论和方法,采用先到先修理与维修台带有优先权相结合的排队规则,将维修台配置数量问题转化为两类型服务台排队问题,建立了单队列M/M/s1+s2/K/∞/FCFS+PS排队模型.通过对某专项汽修厂相关的数据采集和分析,得到了模型所需的变量和参数,运用边际效益法进行优化,得到了节假日和非节假日客流高峰期的最优维修台配置数量.通过对系统服务强度、系统资源限制和服务时间段等因素的分析,既能保证排队系统可以在不同时间段内对维修台配置数量进行调整,又能缩小最优值的求解范围.     

M/E_k/1排队系统的最优流控制

通过两种经典方案,即非合作最优化方案和合作最优化方案,对M/E_k/1排队系统的最优流控制问题进行研究.在这两种方案下,给出了最优流控制的解,并对解的性质进行分析.     

一个非时齐马氏过程

<正> 本文研究了一个非时齐马氏过程,考虑其瞬时性质与渐近性质.过程的实际背景是成批到来无限束的 M(t)/M(t)/∞排队问题,排队过程的到来的强度,批量的大小与服务的强度均随时间变化.§1.引言由于实践范围的扩大,若干重要马氏过程的非时齐情况在近年来都得到深入研究.本文旨在考虑一个出现于排队论中的非时齐马氏过程 (在排队论中非时齐过程的重要性早已在[2]中指出过).     

带有Bernoulli控制策略的M/M/1多重休假排队模型

研究具有Bernoulli控制策略的M/M/1多重休假排队模型: 当系统为空时, 服务台依一定的概率或进入闲期, 或进入普通休假状态, 或进入工作休假状态. 对该模型, 应用拟生灭(QBD)过程和矩阵几何解的方法, 得到了过程平稳队长的具体形式, 在此基础上, 还得到了平稳队长和平稳逗留时间的随机分解结果以及附加队长分布和附加延迟的LST的具体形式. 结果表明, 经典的M/M/1排队, M/M/1多重休假排队, M/M/1多重工作休假排队都是该模型的特殊情形.     

多服务台排队系统的组装策略

本文讨论了(e,d)-策略多重休假的M/M/c排队,这是—个M/M/c-e和M/M/c排队的“组装”策略,为系统设计提供更大的灵活性．使用拟生灭过程方法,给出了稳态队长分布．进一步地,利用条件Erlang分布的一些有趣的性质,给出了等待时间分布的简洁表达式．最后,得到稳态指标的条件随机分解结果．     

古典风险模型的破产概率与M/G/1忙期的最大工作量的分布

本文考虑了古典风险模型与排队论中M/G/1模型关系, 利用古典风险模型的破产概率导出了M/G/1中一个忙期内最大工作量的分布.     

多级适应性休假的M/G/1排队

在经典M/G/1排队中引入多级适应性休假规则,得到稳态队长、等待时间分布和随机分解,并给出忙期、假期、在线期分布.单重休假和多重休假模型是本文中模型的两个极端情况.     

超市收银台最优数量的设置

本文运用排队论理论对超市多个M/M/1/∞/∞的排队系统进行研究,将M/M/s/∞/∞与多个M/M/1/∞/∞进行对比,然后通过对结果进行对比分析、参赛的灵敏度分析,确定出收银台的最佳数量.     

校园网端口数的设计和收费

针对校园网通信端口数的设计和收费问题,进行了深入的分析和研究,建立了M/M/n/n/∞型损失制的微分方程排队论模型.通过具体数据,研究了用户数与通信端口数的关系,端口的平均使用率以及设计了一种分段计时收取线路调节费的方案,并通过数据拟合得到了用户的抱怨度,利用MATLAB求得了所有的结果.     

拟线性双曲方程组经典解存在区间的下界

本文利用特征线的方法,得到关于拟线性双曲方程组Cauchy问题经典解的一致先验估计.这样的估计给出了系统经典解存在区间的下界.     

M/M/1排队系统四个指标的渐近性质

应用 C0 -半群理论研究 M/M/1排队系统中四个指标 :系统中顾客的平均等待时间 ,顾客的平均逗留时间 ,顾客总数和等待服务的顾客总数的渐近性质 ,得到这四个指标的渐近稳定性结果 .     

M/M/m/m防空系统射击效能的排队概率特性

研究了具有消失制的M/M/m/m防空系统的射击效能,利用排队论及随机运筹学的有关知识,在模型的条件与假设下给出了其平稳状态的队长的分布律πk,平均工作的防空武器数E,敌机的突防概率πm,忙期长度等指标.     

Numerical methods in the theory of viscoelasticity

Formulas are given for calculating the coefficients of differential operators of defining equations on the basis of given approximations of the relaxation kernels in the form of the sum of exponential curves. As the defining equations it is suggested to use quadrature formulas into which are substituted the relaxation kernels found experimentally without preliminary analytic approximation. A three-dimensional difference problem of the linear isotropic theory of viscoelasticity is formulated. The direct and inverse -transformation establishing the correspondence between the viscoelastic and elastic difference problems is introduced. The specific characteristics of the use of the net, Ritz, finite-element, and variation-difference methods in solving problems of viscoelasticity theory are examined. A method facilitating the arrangement of the information on relaxation kernels in a computer memory is indicated.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 417–428, May–June, 1973.     

Contribution to the theory of elastic strain distribution in two-component composites

A method analogous to the known limit theorem methods of the theory of probability is proposed for establishing the law of distribution of the random elastic deformation of the structure of a composite with a nonordered arrangement of two isotropic components. It is shown that under certain conditions the strains are distributed according to a law that approximates the sum of two normal distributions.S. M. Kirov Ural Polytechnic Institute, Sverdlovsk. Translated from Mekhanika Polimerov, No.4, pp. 616–622, July–August, 1973.     

The adjoint braid arrangement as a combinatorial Lie algebra via the Steinmann relations

We study a certain discrete differentiation of piecewise-constant functions on the adjoint of the braid hyperplane arrangement, defined by taking finite-differences across hyperplanes. In terms of Aguiar-Mahajan's Lie theory of hyperplane arrangements, we show that this structure is equivalent to the action of Lie elements on faces. We use layered binary trees to encode flags of adjoint arrangement faces, allowing for the representation of certain Lie elements by antisymmetrized layered binary forests. This is dual to the well-known use of (delayered) binary trees to represent Lie elements of the braid arrangement. The discrete derivative then induces an action of layered binary forests on piecewise-constant functions, which we call the forest derivative. Our main result states that forest derivatives of functions factorize as external products of functions precisely if one restricts to functions which satisfy the Steinmann relations, which are certain four-term linear relations appearing in the foundations of axiomatic quantum field theory. We also show that the forest derivative satisfies the Lie properties of antisymmetry the Jacobi identity. It follows from these Lie properties, and also crucially factorization, that functions which satisfy the Steinmann relations form a left comodule of the Lie cooperad, with the coaction given by the forest derivative. Dually, this endows the adjoint braid arrangement modulo the Steinmann relations with the structure of a Lie algebra internal to the category of vector species. This work is a first step towards describing new connections between Hopf theory in species and quantum field theory.     

关于M/M/n排队模型的动态解及稳定性

文章讨论动态 M/M/n排队模型 ,运用算子半群理论证明了该模型动态正解的存在唯一性 .并进一步表明零点是系统的一个本征值 ,相应的本征函数为系统的一个定态正解 ,系统的动态正解强稳定到定态解     

Optimal gainshare/painshare in alliance projects

Alliances are popularly used in delivering infrastructure. However, discussion is ongoing as to what is the optimal gainshare/painshare arrangement. This paper derives a result for the optimal gainshare/painshare between risk-averse parties, where the level of aversion may range from very large to being risk neutral. The derivation is based on solving an optimization problem using concepts from agency theory. The influence of the parties’ level of risk aversion and outcome uncertainty is examined. Practitioners were engaged in a designed exercise in order to validate the approach and propositions. The paper shows that: (i) the optimal gainshare/painshare arrangement in alliances is linear in the project outcome; (ii) the optimal gain/pain share to the contractor should decrease with increasing contractor level of risk aversion and/or decreasing owner level of risk aversion; and (iii) the outcome uncertainty has no influence on the optimal gainshare/painshare. The paper provides those who write alliance contracts with recommendations on gainshare/painshare. This study casts new light on establishing optimal alliance arrangements in the construction industry.     

Borel状态空间非平稳MDP的平均方差准则

本文考虑具有 Ｂｏｒｅｌ状态空间和行动空间非平稳 ＭＤＰ的平均方差准则．首先,在遍历条件下,利用最优方程,证明了关于平均期望目标最优马氏策略的存在性．然后,通过构造新的模型,利用马氏过程的理论,进一步证明了在关于平均期望目标是最优的一类马氏策略中,存在一个马氏策略使得平均方差达到最小．作为本文的特例还得到了 Ｄｙｎｋｉｎ Ｅ． Ｂ．和 Ｙｕｓｈｋｅｖｉｃｈ Ａ． Ａ．及 Ｋｕｒａｎｏ Ｍ．等中的主要结果．     

M/M/1算子的特征值及其应用(英文)

讨论 Ｍ／Ｍ／１算子的谱特征,证明０是 Ｍ／Ｍ／１算子的几何重数为 １的特征值,并且对应的特征向量是正的,作为应用给出了排队论中四个指标：系统中顾客的平均逗留时间,顾客的平均等待时间,顾客总数及等待的顾客总数的计算方法．