标题：2009国际建模竞赛题
竞赛介绍
时间2009年美国（国际）大学生数学建模竞赛于2009年2月5日至2月9日举行。  竞赛宣讲内容美国大学生数学建模竞赛（MCM/ICM），是一项国际级的竞赛项目，更是现今各类数学建模竞赛之鼻祖。MCM/ICM 是 Mathematical Contest in Modeling 和 Interdisciplinary Contest in Modeling 的缩写，即“数学建模竞赛”和“交叉学科建模竞赛”。 　　MCM 始于 1985 年，ICM 始于 2000 年，由竞赛的主持者是美国数学及其应用联合会COMAP，并得到美国运筹及工业和应用数学协会、美国工业与应用数学学会、美国数学协会等多个组织的赞助。美国赛着重强调研究问题、解决方案的原创性、团队合作、交流以及结果的合理性。 　　美国国际大学生数学建模竞赛从1985年开始举办，英文全称“Mathematical Contest in Modeling”，缩写为“MCM”。MCM的每个参赛队由3名队员和1名指导教师组成，比赛为期四天，每次只有两个考题，每队只需任选一题。在四天的参赛时间内参赛者可以使用包括计算机、软件包、教科书、杂志和手册等资源。比赛时要求就选定的赛题每个队在连续四天的时间里写出论文，它包括：  赛题插图问题的适当阐述；合理的假设；模型的分析、建立、求解、验证；结果的分析；模型优缺点讨论等。数学建模竞赛宗旨是鼓励大学师生对范围并不固定的各种实际问题予以阐明、分析并提出解法，通过这样一种方式鼓励师生积极参与并强调实现完整的模型构造的过程。以竞赛的方式培养学生应用数学进行分析、推理、证明和计算的能力；用数学语言表达实际问题及用普通人能理解的语言表达数学结果的能力；应用计算机及相应数学软件的能力；独立查找文献，自学的能力，组织、协调、管理的能力；创造力、想象力、联想力和洞察力。他还可以培养学生不怕吃苦、敢于战胜困难的坚强意志，培养自律、团结的优秀品质，培养正确的数学观。我国参赛情况我国一些著名大学从1989年起开始参加这项赛事，并经常在该项赛事中取得令人瞩目的成绩，大大提升了学校的国际知名度，如上海交通大学、浙江大学等。该竞赛每年一届，一般在二月份的一个周末举行，历时四天。每个参赛学校最多报四支队，其中每个系最多报两支队。由于比赛时间正值中国农历新年，为我国大学师生参赛带来了一定困难。
竞赛详情
竞赛题目PROBLEM A: Designing a Traffic Circle
Many cities and communities have traffic circles-from large ones with many lanes in the circle (such as at the Arc de Triomphe in Paris and the Victory Monument in Bangkok) 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 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 possible. 
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) you use in your model for making the optimal 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.
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. 
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 m 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). 
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 discussion of the broad and hidden consequences of having only landlines, only cell phones, or a mixture of the two is welcomed. 
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. Assume that the Pseudo US supplies electricity from oil. Interpret your results in terms of barrels of oil. 
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. 
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, assume electricity is provided from oil. Interpret your predictions in term of barrels of oil.
PROBLEM A: Designing a Traffic Circle
Many cities and communities have traffic circles—from large ones with many lanes in the circle (such as at the Arc de Triomphe in Paris and the Victory Monument in Bangkok) 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 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 possible. 
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) you use in your model for making the optimal 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.
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. 
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 m 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). 
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
A题 设计一个交通环岛
在许多城市和社区都建立有交通环岛，既有多条行车道的大型环岛（例如巴黎的凯旋门和曼谷的胜利纪念碑路口），又有一至两条行车道的小型环岛。有些环岛在进入口设有“停车”标志或者让行标志，其目的是给已驶入环岛的车辆提供行车优先权；而在一些环岛的进入口的逆向一侧设立的让行标志是为了向即将驶入环岛的车辆提供行车优先权；还有一些环岛会在入口处设立交通灯（红灯会禁止车辆右转）；也可能会有其他的设计方案。
这一设计的目的在于利用一个模型来决定如何最优地控制环岛内部，周围以及外部的交通流。该设计的目的在于可利用模型做出最佳的方案选择以及分析影响选择的众多因素。解决方案中需要包括一个不超过两页纸，双倍行距打印的技术摘要，它可以指导交通工程师利用你们模型对任何特殊的环岛进行适当的流量控制。该模型可以总结出在何种情况之下运用哪一种交通控制法为最优。当考虑使用红绿灯的时候，给出一个绿灯的时长的控制方法（根据每日具体时间以及其他因素进行协调）。找一些特殊案例，展示你的模型的实用性。
B题
如题～有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。这方面的用电能使用会带来什么后果？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 m 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号为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。在当前美国这种用电模型即过渡又是稳定的，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 discussion 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、跟当前美国具有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. Assume 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模型 模型是关于当前美国每天所浪费的能源 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, assume 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。获奖论文选登Team #4094 
Round and Round We Go 
February 9, 2009