离散的SI和SIS传染病模型的研究

为了描述个体的死亡、染病者的恢复以及疾病的传染,引入了相应的概率.基于总种群中个体数量为常数的假设,根据染病者能否恢复分别建立了具有生命动力学的离散SI和SIS传染病模型.所得到的结果显示:它们具有与相应连续模型相同的动力学性态,并确定了各自的阈值.在它们的阈值之下,传染病最终将灭绝;在它们的阈值之上,传染病将会发展成为地方病,染病者的数量将趋向于一确定的正常数.     

高中数学专题研究的一个案例──关于沪闵路─春申路口红绿灯时间设置合理性的研究

一、专题的背景与分析 　　1. 背景 　　闵行区的沪闵路─春申路口是交通特别拥挤的交叉路口之一.家住莘庄地区的同学有一个共同的感受,在他们到校或回家路上必经的沪闵路─春申路口时常遇到塞车现象.……     

报童模型及ARMA预测在航空配餐问题中的应用

航班承载人数的不确定性,造成航空公司在配餐中利润的流失,现存的配餐模式存在较多的浪费.本文利用基于损失厌恶的报童模型和ARMA时间序列分析模型对深圳航空公司某航班的配餐份数进行了建模分析和预测,并通过对两种模型输出的比较,得出了长期预测与短期预测的模型应用理论.将实际的历史数据代人到模型中验证,其结果优于经验模式下的配餐盈利情况.本文所采用的研究方法和研究结果对航空公司的精益发展有建设性的意义.     

巧解一道"牛吃草"问题

"牛吃草"问题又称为消长问题,是17世纪英国伟大的科学家牛顿提出来的.典型牛吃草问题的条件是假设草的生长速度固定不变,不同头数的牛吃光同一片草地所需的天数各不相同,求若干头牛吃这片草地可以吃多少天.由于吃的天数不同,草又是天天在生长的,所以草的存量随吃的天数不断地变化.……     

大钟与六位密码

福尔摩西接到电话的时候正在翻看一本关于城中富翁艾伦王的传奇故事。艾伦王年少时靠贩卖廉价的小闹钟起家,经过几十年的辛勤努力,把自己的事业拓展成了最有名的钟表公司,是本市最有名的富翁。艾伦王年纪已经很大了,身体也不好。他的儿女众多,但是他们和艾伦王的关系并不融洽。大家都猜测他们对艾伦王的财富虎视眈眈。"喂,福尔摩西吗?"约翰焦急的声音从电话那头传过来。"是我。"福尔摩西回应道。     

Drucker-Prager准则可靠度解析

视岩体强度参数为正态分布随机变量,以可靠度理论为基础,推导了Drucker-Prager准则可靠度判别的解析表达式,并通过Monte-Carlo法和一次可靠度方法验证了其正确性.应用所得到的公式分析了岩体强度参数的变异性对屈服准则判别结果的影响.结果表明,强度参数的变异性对Drucker-Prager准则可靠概率的影响程度不尽相同,在变异系数较大的情况下,它们对可靠概率的影响显著,不可忽略.为岩体屈服的可靠度判别提供了一条新思路.     

导数在高考命题中的"五大"热点

导数作为大学的重要内容,进入中学数学教材后,给传统的内容注入了生机与活力,为中学数学命题的研究提供了新视角,新方法.由于导数是研究函数性质的一个很好的工具,它的用途十分广泛,它在解决函数、不等式、解析几何等问题有独到的功能.因此,近几年的高考正逐年加大对导数问题的考查力度,本文通过对07年全国各地高考题的整理和分析寻找命题规律,希望能对今后的教学提供一点复习思路.……     

也谈立体几何中的轨迹问题——从一道调考试题说起

2010-2011学年度武汉市部分学校新高三起点调研测试的一道试题引起了我的注意.原题如下: 在正四面体P-ABC中,M为△ABC内(含边界)一动点,且点M到三个侧面PAB,PBC,PCA的距离成等差数列,则点M的轨迹是 A.一条线段 B.椭圆的一部分 C.双曲线的一部分 D.抛物线的一部分     

股票收益率和新息的尾部估计

利用极值理论来考虑上证综指收益率的尾部.为了选择合理的超越门限,采用平均剩余函数和De-Haan矩估计相结合的方法.在学生t分布和广义误差分布的新患假设下,用GARCH和EGARCH新息的ARMA模型拟合指数收益率,并且使用极值理论的极大似然方法估计模型残差的尾指,估计结果表明收益率的尾指和模型的残差尾指基本一致.     

神奇的骰子

骰子在许多游戏中出现,特别是赌博游戏,当中蕴含了丰富的数学知识,引起了许多数学爱好者们的关注和研究.一个普通的骰子是正六面体,它的六个面分别为数字1,2,3,4,5,6,还有许多不同的骰子、不同的玩法,充满了神奇,但神奇的骰子背后离不开数学知识的支撑.本文将介绍三     

Modelling dynamic network loading ontransportation networks through a continuous

The efforts spent by researchers in the last few years in traffic modelling have been focused on the modelization of dynamic behaviour of the several components making up a transportation system.In the field of traffic assignment, a large number of models and procedures have been proposed in order to perform Dynamic Network Loading (DNL), that is the reproduction of within-day variable link performances once a corresponding Origin/Destination (O/D) demand and users' choice model has been given. These models can be used both to evaluate traffic flows and, what is more relevant, to simulate the effects of regulation strategies on users' behaviour.

In this paper, after a brief review of the state of the art in this field, a continuous dynamic network loading model is proposed; it removes some of the drawbacks of other packet approach models proposed in literature and explicitly allows the en-route modification of the followed path. An algorithmic development of the model and a set of applications on text networks are also proposed.     

交通灯数学模型

主要讨论在假定车流均匀的前提下如何安排路口的交通灯时间才能使路口的交通达到最大限度的畅通.这里交通最大限度通畅的定义是一个交通周期内积存车辆的最大可能长度达到最小.文章首先以最大限度通畅为目标,道路条件、行人通过马路等条件为约束,建立优化模型解决孤立丁字路口的交通灯安排问题,这个模型也适用于孤立十字路口的分析.随后文章建立了多个路口相连时路口交通灯的安排模型.最后,文章讨论了上述几个模型的稳定性以及改进方向.     

城市交通投资结构调整与交通需求互动优化模型研究

城市交通投资结构研究有助于了解交通供给能力特征,缓解城市交通拥堵状况.北京市在过去的十几年来大量的交通资金投入到道路建设中,但并没有从根本上扭转日益突出的交通供需矛盾状况.从交通投资与交通需求的关系出发,探讨投资方向和投资力度对交通供需结构的影响.给出交通投资结构阶段统计特征、分析了北京市"七五"至"十五"时期交通投资系统与交通需求、交通供给和社会经济系统关系.应用多目标优化方法,并运用M atlab软件计算不同交通结构情境下的交通投资取向、结构、管理上提出建议.     

Application of averaging techniques to traffic flow theory

Real traffic data are very versatile and are hard to explain with the so‐called standard fundamental diagram. A simple microscopic model can show that the heterogeneity of traffic results in a reduced mean flow and that the reduction is proportional to the density variance. Standard averaging techniques allow us to evaluate this reduction without having to describe the complex microscopic interactions. Using a second equation for the variance results in a two‐dimensional hyperbolic system that can be put in conservative form. The Riemann problem is completely solved in the case of a parabolic fundamental diagram, and the solutions are compared with the famous second‐order Aw–Rascle–Zhang model in a simulation of lane reduction. Adding a diffusion term results in entropy production, and the diffusive model is studied as well. Finally, a numerical scheme is used and converges to the analytical solution. Copyright © 2016 John Wiley & Sons, Ltd.     

Joint optimization traffic signal control for an urban arterial road

This paper considers the optimal traffic signal setting for an urban arterial road. By introducing the concepts of synchronization rate and non-synchronization degree, a mathematical model is constructed and an optimization problem is posed. Then, a new iterative algorithm is developed to solve this optimal traffic control signal setting problem. Convergence properties for this iterative algorithm are established. Finally, a numerical example is solved to illustrate the effectiveness of the method.     

基于模糊理论的交通安全评价方法的研究

道路交通安全系统的内部结构极为复杂,影响因素众多,各因素都具有模糊性.在综合研究分析国内外道路交通安全评价方法的基础上,对以往发生的道路交通事故资料进行分析,利用模糊评价理论,选取合理评价指标,建立了基于模糊的道路交通安全评价模型,对道路交通的安全性进行合理评价.     

Heavy and light traffic in fluid models with burst arrivals

We consider the problem of finding a heavy and light traffic limits for the steady-state workload in a fluid model having a continuous burst arrival process. Such a model is useful for describing (among other things) the packetwise transmission of data in telecommunications, where each packet is approximated to be a continuous flow. Whereas in a queueing model, each arrival epoch,t _n , corresponds to a customer with a service timeS _n , the burst model is different: each arrival epoch,t _n , corresponds to a burst of work, that is, a continuous flow of work (fluid, information) to the system at rate 1 during the time interval [t _n ,t _n +S _n ]. In the present paper we show that the burst and queueing models share the same heavy-traffic limit for work, but that their behavior in light traffic is quite different.Research supported by the Japan Society for the Promotion of Science, during the author's fellowship in Tokyo.Research funded by C & C Information Technology Research Laboratories, NEC, and the International Science Foundation.     

Integrated modelling and numerical treatment of freeway flow

The effectiveness of macroscopic dynamic freeway flow models at both uninterrupted and interrupted flow conditions is tested. Model implementation is made by finite difference methods developed here for solving the system's governing equations. These schemes are more effective than existing numerical methods, particularly when generation terms are introduced. The modelling alternatives and numerical solution algorithms are compared by employing a data base generated through microscopic simulation. Despite the effectiveness of the proposed numerical treatments, substantial deviations from the data at interrupted flows are still noticeable. In order to improve performance when flow is interrupted, we develop a modelling methodology that takes into account the ramp-freeway interactions so that all freeway components are treated as a system. We show that the coupling effects of the merging traffic streams are significant. Finally, the incremental benefits of using the more sophisticated high-order continuum models are assessed.     

The Asymptotic Workload Behavior of Two Coupled Queues

We consider a system of two coupled queues Q ₁ and Q ₂. When both queues are backlogged, they are each served at unit rate. However, when one queue empties, the service rate at the other queue increases. Thus, the two queues are coupled through the mechanism for dynamically sharing surplus service capacity. We derive the asymptotic workload behavior at Q ₁ for various scenarios where at least one of the two queues has a heavy-tailed service time distribution. First of all, we consider a situation where the traffic load at Q ₁ is below the nominal unit service rate. We show that if the service time distribution at Q ₁ is heavy-tailed, then the workload behaves exactly as if Q ₁ is served in isolation at a constant rate, which only depends on the service time distribution at Q ₂ through its mean. In addition, we establish that if the service time distribution at Q ₁ is exponential, then the workload distribution is either exponential or semi-exponential, depending on whether the traffic load at Q ₂ exceeds the nominal service rate or not. Next, we focus on a regime where the traffic load at Q ₁ exceeds the nominal service rate, so that Q ₁ relies on the surplus capacity from Q ₂ to maintain stability. In that case, the workload distribution at Q ₁ is determined by the heaviest of the two service time distributions, so that Q ₁ may inherit potentially heavier-tailed characteristics from Q ₂.     

加权马尔可夫模型在道路交通受伤人数预测中的应用

为提高交通事故预测的可靠性,首先应用有序聚类的方法建立交通受伤人数的分级标准;然后针对事故受伤人数为相依随机变量的特点,采取以规范化的各阶自相关系数为权重,用加权的马尔可夫链模型来预测未来交通事故受伤人数的升降变化状况;最后以北京市1970-2010年共41年的事故受伤人数为例对该方法进行了具体应用,取得了较为满意的结果,为交通事故受伤人数的预测分析提供了新的途径.