美国数学建模数学竞赛试题及翻译_美国数学建模历年题目

美国数学建模数学竞赛试题及翻译由刀豆文库小编整理，希望给你工作、学习、生活带来方便，猜你可能喜欢“美国数学建模历年题目”。

2009年美国数学建模题

PROBLEM A: Designing a Traffic Circle

Many cities and communities（社区）have traffic circles—from large ones with many lanes（小巷、车道）in the circle(such as at the Triumphal Arch in Paris and the Victory Monument in Bangkok(曼谷))to small ones with one or two lanes in the circle.Some of these traffic circles position a stop sign or a yield sign on every incoming road that gives priority（优先权）to traffic already in the circle;some position a yield sign in the circle at each incoming road to give priority to incoming traffic;and some position a traffic light on each incoming road(with no right turn allowed on a red light).Other designs may also be poible.The goal of this problem is to use a model to determine how best to control traffic flow in, around, and out of a circle.State clearly the objective(s)(客观的、目标)you use in your model for making the optimal（最理想的）choice as well as the factors that affect this choice.Include a Technical Summary of not more than two double-spaced pages that explains to a Traffic Engineer how to use your model to help choose the appropriate flow-control method for any specific traffic circle.That is, summarize the conditions under which each type of traffic-control method should be used.When traffic lights are recommended, explain a method for determining how many seconds each light should remain green(which may vary according to the time of day and other factors).Illustrate how your model works with specific examples.问题A ： 设计圆形交通路口

许多城市和社区有环形通道——从那些繁华、交通拥挤的地方（例如巴黎的凯旋门和曼谷的胜利纪念碑）到拥有一两条车道的小巷。一些圆形交通路口放置了停止或等待信号灯来决定等待中的车辆通行的优先权；一些在路口安置等待信号来控制每条车道的流通量；还有一些在每个路口安置红绿灯(红灯时不允许的向右转)。其他设计也许也是可能的。这个问题的目标是使用模型来确定怎样最好地控制车辆的进、出、绕行的流通量。清楚陈述模型的目标及做出最优选择的原因和影响因素。包括一个给交通工程师的不超过两页关于如何使用模型来选择具体圆形交通路口的适当的流量控制的方法的一个技术总结。也就是说，总结交通控制方法的每种类型应该使用的条件。当能够使用时红绿灯，确定的路灯亮的时间间隔（根据时刻和其他因素变化)。结合具体例子来说明说明模型的使用。

PROBLEM B: Energy and the Cell Phone

This question involves the “energy” consequences of the cell phone revolution.Cell phone usage is mushrooming, and many people are using cell phones and giving up their landline telephones.What is the

consequence of this in terms of electricity use? Every cell phone comes with a battery and a recharger.这个问题涉及到手机革命的能源问题。手机使用率迅速增加，许多人使用手机并放弃了固定电话。这方面的使用会给供电系统带来什么后果？每个手机都配备了电池和充电器。

Requirement 1

Consider the current US, a country of about 300 million people.Estimate from available data the number H of households, with m members each,that in the past were serviced by landlines.Now, suppose that all the landlines are replaced by cell phones;that is, each of the members of the household has a cell phone.Model the consequences of this change for electricity utilization in the current US, both during the transition and during the steady state.The analysis should take into account the need for charging the batteries of the cell phones, as well as the fact that cell phones do not last as long as landline phones(for example, the cell phones get lost and break).要求1

目前认为美国是一个人口约为3亿人的国家，从现有数据估计家庭用电量为h，每个家庭有M个成员，以前是使用座机电话的。现在，假设所有的座机被手机取代，也就是说每个家庭成员都有手机。分别建立美国在过渡转换电能和稳定电能转换的模式下的用电模型，分析应该考虑到对移动电话充电的需要，同时移动电话不能像固定电话那样持续使用也是一个现实问题（比如说移动电话可能会丢失或者损坏）Requirement 2

Consider a second “Pseudo US”——a country of about 300 million people with about the same economic status as the current US.However, this emerging country has neither landlines nor cell phones.What is the optimal way of providing phone service to this country from an energy perspective? Of course, cell phones have many social consequences and uses that landline phones do not allow.A discuion of the broad and

hidden consequences of having only landlines, only cell phones, or a mixture of the two is welcomed.考虑到第二个“伪美国”——一个约3亿人口、具有跟当前美国相同的经济地位的国家，然而，这个新兴国家既没有固定电话也没有移动电话，从这个国家的能源角度看，用什么最佳方式为这个国家提供电话服务，当然，手机有很多固定电话所不具有的用处和社会影响。这个讨论是关于单独使用固定电话或者单独使用移动电话，或者混合使用两种电话带来的广泛或潜在的影响。

Requirement 3

Cell phones periodically need to be recharged.However, many people always keep their recharger plugged in.Additionally, many people charge their phones every night, whether they need to be recharged or not.Model the energy costs of this wasteful practice for a Pseudo US based upon your answer to Requirement 2.Aume that the Pseudo US supplies electricity from oil.Interpret your results in terms of barrels of oil.手机需要定期充电。但是许多人在不考虑手机是否要充电的情况下，总是将充电器一直插在电器插槽上。在前两个假设成立的基础上，建立能源浪费的数学模型。另外，假定美国以石油作为电力来源，计算、解释浪费的石油量。

Requirement 4

Estimates vary on the amount of energy that is used by various recharger types(TV, DVR, computer peripherals, and so forth)when left plugged in

but not charging the device.Use accurate data to model the energy wasted by the current US in terms of barrels of oil per day.在估计不同电器设备（电视、DVR、电脑外围设备等）所使用的能源数量时，电器特性：没有充电设备。要求用精确的数据建立关于当前美国每天所浪费的能源数量的模型，以原油（桶/天）计量。Requirement 5

Now consider population and economic growth over the next 50 years.How might a typical Pseudo US grow? For each 10 years for the next 50 years, predict the energy needs for providing phone service based upon your analysis in the first three requirements.Again, aume electricity is provided from oil.Interpret your predictions in term of barrels of oil.现在考虑人口及经济增长在未来的50年内的情况。如何使这个假设中的美国发展壮大。对于每一个10年的今后50年内进行能源的需求预测，前提是在你前三次的分析基础上而进行的提供的电话服务。另外还有一个假设是：电力来自石油。解释你预测到的石油桶数目。