09年美赛A题优秀论文翻译
09年真题一 全翻译 上传版
Habits are a funny thing.词汇：永恒褒义词+正评价说“习惯是一件有趣的事情”。
好，咱同学，你记住，考试的时候，如果当你看到这句话的时候，你的第一反应就是把funny这个词圈个圈。
Funny这个词是一个永恒褒义词，什么叫做“永恒褒义词”，就是阅读理解当中，永远没有贬义的含义，并且只要这种词一出现，你就知道，作者对他后面所要讨论的事物呈什么评价？呈正评价。
所以你在首段的首句，随便一个位置上打上一个加号，以后我们的课程中，加号就表示“正评价”。
永恒褒义词举例关于永恒褒义词，在这里给咱同学举个例子，你可以简单地记一下。
只要是以下这类词，都是永恒褒义词：decent，colorful，flexible，enchance, consummate，adventurous具有进取精神一般冒险, flawless, original, precipitate促进；interesting。
然后我在这强调一点：有一词常考，但是它不具有感情色彩，就是significance，这个词没有感情色彩，表示“意义，重要性”，好的东西有好的意义，好的重要性。
坏的东西有坏的意义，坏的重要性。
还有一个词也是很多同学经常混淆的，revolution，这个单词表示“革命”，在中国，“革命”是个褒义词，“反革命”是一个贬义词。
这是因为我们这个国家在建国以前，喜欢革命，热爱革命，所以让这个词富有褒贬色彩；但是在国际上，这个词没有感情色彩，revolution这个词的动词就是revolve，表示“公转”，公转个过程中，新事物取代旧事物，这是大自然和谐的转变，没有什么需要歌颂赞美的东西在里面。
所以名词revolution是一个中性词。
那么你告诉我反革命anti-revolution是什么感情色彩？中性词。
这是国际上的看法，那么咱同学告诉我，考试的时候，你以哪一个说法为准？是以中国说法为准，还是以国际说法为准？以国际说法。
美赛数学建模A题翻译版论文
美赛数学建模A题翻译版论文The document was finally revised on 2021数学建模竞赛(MCM / ICM)汇总表基于细胞的高速公路交通模型自动机和蒙特卡罗方法总结基于元胞自动机和蒙特卡罗方法,我们建立一个模型来讨论“靠右行”规则的影响。
首先,我们打破汽车的运动过程和建立相应的子模型car-generation的流入模型,对于匀速行驶车辆，我们建立一个跟随模型,和超车模型。
然后我们设计规则来模拟车辆的运动模型。
我们进一步讨论我们的模型规则适应靠右的情况和,不受限制的情况, 和交通情况由智能控制系统的情况。
我们也设计一个道路的危险指数评价公式。
我们模拟双车道高速公路上交通(每个方向两个车道,一共四条车道),高速公路双向三车道（总共6车道)。
通过计算机和分析数据。
我们记录的平均速度,超车取代率、道路密度和危险指数和通过与不受规则限制的比较评估靠右行的性能。
我们利用不同的速度限制分析模型的敏感性和看到不同的限速的影响。
左手交通也进行了讨论。
根据我们的分析,我们提出一个新规则结合两个现有的规则(靠右的规则和无限制的规则)的智能系统来实现更好的的性能。
1介绍术语假设2模型设计的元胞自动机流入模型跟随模型超车模型超车概率超车条件危险指数两套规则CA模型靠右行无限制行驶规则3补充分析模型加速和减速概率分布的设计设计来避免碰撞4模型实现与计算机5数据分析和模型验证平均速度快车的平均速度密度超车几率危险指数6在不同速度限制下敏感性评价模型7驾驶在左边8交通智能系统智能系统的新规则模型的适应度智能系统结果9结论10优点和缺点优势弱点引用附录。
1 Introduction今天,大约65%的世界人口生活在右手交通的国家和35%在左手交通的国家交通流量。
[worldstandards。
欧盟,2013] 右手交通的国家,比如美国和中国,法规要求驾驶在靠路的右边行走。
多车道高速公路在这些国家经常使用一个规则,要求司机在最右边开车除非他们超过另一辆车,在这种情况下,他们移动到左边的车道、通过，返回到原来的车道。
美赛A题翻译
2017MCMProblemA:Managing TheZambeziRiver管理赞比西河TheKaribaDamontheZambezi River is oneofthelarger dams inAfrica.Its constructionwas controversial, anda2015report bytheInstitute ofRisk Management ofSouth Africaincludedawarningthatthedamis indire need of maintenance.A numberofoptionsareavailabletotheZambezi River Authority(ZRA) thatmight addressthesituation.Threeoptionsinparticular are ofinteresttoZRA:赞比西河上的卡里巴大坝是非洲的一个大水坝。
它的建设是有争议的，南非风险管理研究所2015年的报告包括警告大坝急需维修。
一些由赞比西河管理局（ZRA）所接受的方案，可能会解决问题。
特别是三个ZRA感兴趣的选择：(Option1) Repairingthe existingKaribaDam,修复现有的卡里巴大坝，(Option2)Rebuildingthe existingKaribaDam,or改造现有的卡里巴大坝，或者(Option3) RemovingtheKaribaDam andreplacingitwithaseriesoftentotwentysmaller dams alongtheZambezi River.移除卡里巴大坝并用沿赞比西河一系列的十到二十个小坝取代它。
There aretwomainrequirementsfor this problem:这个问题有两个主要的要求：Requirement1ZRAmanagementrequires a brief assessmentofthethree optionslisted, withsufficientdetailtoprovide an overviewof potential costsand benefitsassociatedwith eachoption. This requirementshouldnot exceedtwo pagesinlength,and mustbe providedinadditiontoyour mainreport.要求一：ZRA管理要求对列出的三个选项作简要评价，提供足够的细节，提供与每个选项相关的潜在成本和效益概述。
2009.9翻译分析
首发：新东方惠瑾发布9.13中口翻译评析发布时间：2009-09-13 作者：惠瑾来源：上海新东方英译汉What is a novel? I say: an invented story. At the same time a story which, though invented, has the power to ring true. True to what? True to life as the reader knows life to be or, it may be, feels life to be. And I mean the adult, the grown-up reader. Such a reader has outgrown fairy tales, and we do not want the fantastic and the impossible. So I say to you that a novel must stand up to the adult tests of reality.You may say:”If one wa nts truth, why not go to the literally true book? Biography or documentary, these amazing accounts of amazing experiences which people have.” Yes, but I am suggesting to you that there is a distinction between truth andso-called reality. The novel does not simply recount experience. And here comes in what is the actual livening spark of the novel: the novelist’s imagination has a power of its own. It does not merely invent, it perceives. It intensifies, therefore it gives power, extra importance, and greater truth to what may well be ordinary and everyday things.小说是什么？我认为是人们创造出来的故事。
09年英语六级阅读翻译~~很有用滴
Crippling health care bills, long emergency-room waits and the inability to find a primary care physician just scratch the surface of the problems that patients face daily.问题重重的医疗保障费用,急诊室前排起的长队,以及无法找到初级护理医生,这些仅是每天要面对的问题中的一部分。
Primary care should be the ba health care system.初级护理应该是所有医疗保障体系的支柱。
Countries with appropriate primary care resources score highly when it comes to health outcomes and cost.有充足的初级护理资源的国家在健康水平和费用支出上都获得甚佳的评价。
The U.S. takes the opposite approach by emphasizing the specialist rather than the primary care physician.美国却反其道而行之,注重专科医生而非初级护理医生。
A recent study analyzed the providers who treat Medicare beneficiaries (老年医保受惠人).最近一项研究分析了负责治疗老年医保受惠人的医生。
The startling finding was that the average Medicare patient saw a total of seven doctors—two primary care physicians and five specialists—in a given year. Contrary to popular belief, the more physicians taking care of you don’t guarantee better care.这项令人震惊的研究发现,老年医保受惠人平均每天要看七名医生----包括两名初级护理医生和五名专科医生。
2009年考研英语二真题全文翻译答案超详解析(原MBA)
2009 年全国硕士研究生入学统一考试英语（二）试题答案与解析Section I Use of English一、文章题材结构分析本文是一篇说明文，摘自2008 年 6 月26 日The New York Times。
文章主要介绍了世界石油价格的变化的原因以及给世界带来的改变。
第一段主要介绍了近年来石油价格的上涨以及其背后的原因。
第二、三段主要介绍了石油价格的改变对国家相互之间的关系带来的影响。
第四、五段分别具体的介绍了世界石油价格的变化给德国与美国来带的影响。
二、试题分析1.【答案】C【解析】本题主要考查词义辨析和熟词生义，A 项come，B 项gone，D 项arrived 都表示“到，到达”的含义。
C项cross 意为“穿过”，这里是引申含义“突破”。
这句话指“价格已经突破100 美元每桶”，与上文的“16 美元一桶”做比较。
2.【答案】D【解析】本题考查动词与介词词组的搭配。
解题重点在于空后面的一个介词词组from …to…表示一个范围。
A 项covered 意为“覆盖”一般指地理范围；B 项discovered 发现；C 项arranged 安排；C 项D 项的动词都与介词词组搭配不合理。
D 项ranged 意为涉及的“范围延伸”。
与后面的from…to…搭配合理。
本句句意是：价格上涨的原因涉及从……到……，固定搭配range from A to B。
因此，选项D 正确。
3.【答案】D【解析】本题的解答要根据上下文来推理，四个选项中 A 项intensity 强度；B 项infinity；无穷大；C 项insecurity不安全；D 项instability 不安定，不稳定性。
后面说到了“伊拉克与尼日利亚的三角洲地区”，我们知道这两个地区的局势长期不稳定。
所以D 答案与此相符。
4.【答案】B【解析】本题考核的重点是与名词的搭配的相关动词，后面的宾语是一个名词结构，the economic and political做map 的定语，而of the world 做了map 的后置定语，所以中心词是map。
考研英语2009年阅读真题翻译
2009年Text 1习惯是件有趣的事情。
我们无意识间养成了一些习惯，我们的大脑是自动运转的，轻松进入熟知套路所带来的不自觉舒适状态。
“这并非选择，而是习惯控制了那些没有思想的人”，这是威廉·华兹华斯（William Wordsworth）19世纪时说的话。
在现在这个日新月异的21世纪，甚至习惯这个词本身也带有负面涵义。
因此，在创造和革新的背景下来谈论习惯，似乎显得有点矛盾。
但大脑研究人员发现，当我们有意识地培养新的习惯的时候，我们创建了平行路径，甚至是全新的脑细胞，可以让我们的思路跳转到新的创新轨道上来。
我们不要把自己看成是不可改变的习惯动物，相反，我们可以通过有意识的培养新的习惯来引导自身的改变。
事实上，我们对新事物尝试得越多——就会越远地走出自己的舒适地带——我们在工作场所及个人生活中就会变得越有创造性，但是，不必费心试图摈弃各种旧习惯；一旦这些程序惯例融进大脑，它们就会留在那里。
相反，我们刻意培养的新习惯会创建平行路径能避开原来那些老路。
《开放思想》一书的作者Dawna Markova说：“革新所需要的第一样东西，就是一种对好奇的着迷。
然而我们被教导去做‘决定’，就像我们的总裁称呼自己为‘决策者’那样。
”她补充道，“但是，决定意味着否决一切可能性而只保留一种。
一个优秀的具有革新精神的思想者总是在探寻许多其它的可能。
”她说，我们都是通过一些自己没有意识到的方法解决问题的。
研究人员在20世纪60年代末发现人类天生主要用四种方法应对挑战。
这四种方法是分析法，程序法，关联（或合作）法和创新法。
但是在青春期结束的时候，大脑关闭一半的能力，仅仅保留了那些大约在生命最开始的十几年时间里似乎是最有价值的思维方式。
目前标准化测试主要强调分析和程序的能力，也就是说，我们中很少有人会本能地使用创新和合作的思维方式。
M.J.Ryan是2006年出版的著作《今年我将......》一书的作者以及Markova女士的商业合作伙伴，她解释说：“这打破了美国信念体系里的主要规则——任何人都可以做任何事。
09年翻译key
Keys (Translation 2009):1. We’d better ask our teacher for advice.2. Could you do me a favor to collect some information about this?3. If only you had reminded me earlier.4. I t’s quite necessary to do some physical exercise outdoors for about half an hourevery day.5. Would you please make a brief introduction about yourself?6. He’s good/ expert at repairing computers and you can ask him for help.7. The reason why he is often late for school is that he gets up late.8. To be honest/ Honestly speaking, I am not quite confident about success this time.9. If you think your view/ point of view is correct, you should stick to it.10. Judging from his accent, he comes from northern China.11. Of all the sports programs, I like watching basketball matches (the) best.12. I hope to become a famous/ well-known fashion designer in the future.13. It will be three years before our maths teacher retires.14. As/ Being shop assistants, we must be polite to every customer.15. He seems to be interested in anything new.(It seems that he is interested in anything new.)16. It is said that fruits are on sale in the supermarket at/ on the corner of the street.17. She is wearing many clothes for fear that she will catch cold.18. I regret rejecting/ having rejected his invitation at that time.19. It is no use complaining (about it), and you should face the reality.20. Once there is further information, I will inform you of it immediately.21. If you love a child, it doesn’t mean you should meet/satisfy all his demands.(Loving a child doesn’t mean meeting all his demands.)22. He has formed a good habit of brushing his teeth after a meal.23. Do you believe that my father’s bicycle has been used for over twenty years?24. Nowadays/ Today green food is becoming more and more popular.25. I wish the prices of food would not keep going up/ rising any longer.26. I didn’t realize (that) I had done something silly until then.(Not until then did I realize that I had done a silly thing.)27. The clock is out of order. Why not buy a new one?28. The flight to Paris has been/ was delayed due to the weather.29. Never before has China been so powerful.30. It needs some courage to admit mistakes.31. Many primary and middle school students complain that they lack enough sleep.32. What moved me was that she donated most of her pocket money to the disaster-hitarea.33. Children should eat as little food like fried chicken as possible.34. I didn’t catch what you had said. Would you please say it again？35. I am grateful to him for arranging the trip for me.36. Do you find it worthwhile to buy houses while the house prices are so high?37. It is hard to believe that the twins are completely different in character.38. Y ou should catch this opportunity, or you will regret about it.39. The impression which a person makes on the others at first time is very important.40. I believe he is sure to keep his promise/ word.41. He has a strong sense of responsibility and we should learn from him.42. The teacher suggested that I should give up the unpractical idea.43. It is reported that more than eighty leaders from foreign countries attended theopening ceremony of Beijing Olympic Games.44. It was a great honor for my brother to be a volunteer of the Olympics.(My brother had a great honor to be a volunteer of the Olympics.)45. It is possible that the Chinese astronauts will land on the moon in the near future.46. It is natural for a person to suffer from failure in his life.47. Be sure to take some measures to prevent anything like this from happening.48. During the meeting he made a lot of friends with the people from different parts ofthe country.49. In the matches of the Olympic Games, we should cheer to the athletes for theirexcellent performance.50. If you want to learn a foreign language well, it is far from enough just to learnsome new words by heart.51. The last one to leave the classroom must shut all the doors and windows.52. Please leave me alone and I’d like to think about it carefully.53. The digital camera I bought two years ago is out of date now.54. The police warn that personal information mustn’t be revealed to strangers.(The police warn us not to reveal our personal information to strangers.)55. Let what has happened pass, so you needn’t worry about it.56. I am to blame for it as I was mistaken about the time.57. The workers have made/ done/ performed/ created one wonder/ miracle afteranother by their wisdom.58. The real situation is much more complicated than people imagine.59. It is up to him to decide and after all he is no longer a child.(Let him decide by himself, and he is no longer a child.)60. I have a little headache, and I am afraid I can’t attend the party tonight.61. The bigger a city is, the more problems will occur.62. This kind of animal used to exist one and a half million years ago.63. To protect/ In order to protect the earth, we should use as few plastic bags aspossible.64. That child was so brave that he saved three of his classmates in the earthquake.(It was really brave of that child to save three of his classmates in the earthquake.)65. The people whom I admire most are those who have won great honor for ourcountry.66. To be frank/ honest, what I really care for is my parents’ health.67. During the lessons/ In class the students should be encouraged to give differentviews/ points of view/ opinions.68. Every time our national flag/ the five-star red flag is being raised, all of us areproud of being Chinese ourselves.69. It’s hard to imagine that water melons are 50 times more expensive in Japan thanin China.70. The Chinese government was determined to make the Beijing Olympics the mostsuccessful one in history.71. The rise of oil prices has made many people cancel their plans to buy cars.72. No matter what/ Whatever you do, it will be all right if you make an effort.73. Who will do physical work if everybody wants to undertake mental work?74. Hardly had the stamps about the Beijing Olympics been issued when they weresold out.75. All the tourists to Beijing intend to taste Beijing roasted ducks.76. That company accepted the price (that) we had offered without preconditions.77. What matters is how to apply what we have learned to our daily life.78. Finally the whole truth came out that he had nothing to do with it.79. Free education enables the children who can’t afford to go to school to haveopportunities to receive education.80. I wonder why some slim girls still want to lose weight.81. He was quite familiar with the area around here and offered to be our guide.82. Whatever great difficulties I meet, I will never give up halfway.83. Don’t waste time, or you will accomplish nothing.84. If you want to study abroad, you should get ready to depend entirely on yourself.85. The school called on every student to take an active part in different kinds ofsocial activities.86. What should be done today must be finished today, and never put it off tilltomorrow.87. Don’t be too selfish and you can’t always take other people’s help for granted.88. The difference between them lies in their lack of communication.89. In the earthquake which occurred in Sichuan Province, the Chinese people showedgreat courage and unity to the whole world.90. Tibet belongs to China, which is the fact nobody can deny.91. Lingling had no sooner got home than she couldn’t wait to tell her mother that shehad been praised by the teacher.92. Whoever/ Anyone who breaks the law should be punished however high theposition he holds.93. In some cases what is important is not the result but whether you have enjoyed theprocess.94. The result of the survey indicates that the vast majority of people in China preferto deposit their money in the banks.95. Y ou should make full use of your strong points and avoid your weak points.96. Whatever you do, you should ask why more often, and thus you can make rapidprogress.97. We must bear/ keep in mind that human life is the most precious in any cases.98. In Japan everybody, including children, knows what to do in case earthquakeshappen/ occur.99. To catch up with the most developed countries, China still has a long way to go. 100. Only those who face up to the challenges will win the final victory.(Only the people who face the challenges bravely will win the final victory.)。
美赛一等奖论文中文翻译版
目录问题回顾 (3)问题分析： (4)模型假设： (6)符号定义 (6)4.1---------- (7)4.2 有热水输入的温度变化模型 (15)4.2.1模型假设与定义 (15)4.2.2 模型的建立The establishment of the model (16)4.2.3 模型求解 (18)4.3 有人存在的温度变化模型Temperature model of human presence (19)4.3.1 模型影响因素的讨论Discussion influencing factors of the model (19)4.3.2模型的建立 (22)4.3.3 Solving model (26)5.1 优化目标的确定 (26)5.2 约束条件的确定 (28)5.3模型的求解 (29)5.4 泡泡剂的影响 (32)5.5 灵敏度的分析 (32)8 non-technical explanation of the bathtub (34)Summary人们经常在充满热水的浴缸里得到清洁和放松。
本文针对只有一个简单的热水龙头的浴缸，建立一个多目标优化模型，通过调整水龙头流量大小和流入水的温度来使整个泡澡过程浴缸内水温维持基本恒定且不会浪费太多水。
首先分析浴缸中水温度变化的具体情况。
根据能量转移的特点将浴缸中的热量损失分为两类情况：沿浴缸四壁和底面向空气中丧失的热量根据傅里叶导热定律求出；沿水面丧失的热量根据水由液态变为气态的焓变求出。
因涉及的参数过多，将系数进行回归分析的得到一个一元二次函数。
结合两类热量建立了温度关于时间的微分方程。
加入阻滞因子考虑环境温湿度升高对水温的影响，最后得到水温度随时间的变化规律（见图**）。
优化模型考虑保持水龙头匀速流入热水的情况。
将过程分为浴缸未加满和浴缸加满而水从排水口溢出的两种情况，根据能量守恒定律优化上述微分方程，建立一个有热源的情况下水的温度随时间变化的分段模型，（见图**）接下来考虑人在浴缸中对水温的影响。
2009年美赛真题论文
环岛交通的优化设计Optimal Design for Traffic CircleAbstract欧仁艾纳尔（Ez-gene Herlerd ）受到19世纪艺术形式的影响首创了“环岛式交通枢纽”的道路交叉口的概念。
时至今日，由此产生的环岛式交通在世界各地广泛存在。
一些城市主干道上现有的环形交叉口由于通行能力不足，经常出现拥挤、混乱及堵塞的现象，往往是各向车辆争相进交叉口，却很难顺畅驶出。
面对这种状况，我们以六车道入口环岛为例建立了三个模型：1、通过对六车道环岛模型的分析，考虑不加任何控制设施建立模型，并推导出环岛的交通能力表达式（考虑到交织段长度影响和车辆分布不均匀的影响及非机动车干扰）：22()3600132()(11/6)(11/6)(11/6)230A A Z i Q Q Q A l Q Q p p t p l βββ''''-∆•=•=•=•-∆•••---+ 以某一环岛为例，代入上式求出此种情况下的通行能力。
2、建立指示牌控制通行能力的计算与信号灯控制通行能力计算的模型，并以上面提到的环岛为例计算出两种模式下通行能力，同时与上面模型比较，从而对交通工程师提出指导性建议。
3、信号灯控制模型, 根据交通状况的实际需求,以延误最小、停车最少和通行能力最大作为目标函数,利用可随交通需求实时变化的加权系数把这3个目标统一为单目标函数, 建立交叉口信号配时非线性优化模型如下:224(25/)1/321[(1.0)]min (,)2(2)0.65()2(1.0)2(1)0.9(1.0/)/(1.0)2(/3600)(/)2i x c i i i i i i i i i i c x c y c Z x c Y y y q y q c x c y c Y x c s +=-=-⋅+-+--⋅⋅---⋅⋅⋅∑ 在引入算例的情况下，将算例所提供的数据代入优化得到的模型，采用基于精英蚂蚁寻优策略进行求解。
2009年国际建模A题O奖论文One Ring to Rule Them All
One Ring to Rule Them All:The Optimization of Traffic CirclesAaron Abromowitz AndreaLevyRussell MelickHarvey Mudd College Claremont, CAAdvisor: Susan E. MartonosiSummaryOur goal is a model that can account for the dynamics of vehicles in a trafficcircle. Wemainlyfocusontherateofentryintothecircletodetermine the best way to regulate traffic. We assume that vehicles circulate in a single lane and that only incomingtraffic can be regulated(that is, incomingtraffic never has the right-of-way).For our model, the adjustable parameters are the rate of entry into the queue, the rate of entry into the circle (service rate), the maximum capacity of the circle, and the rate of departure from the circle (departure rate). We use a compartment model with the queue and the traffic circle as compartments. Vehicles first enter the queue from the outside world, then enter the traffic circle from the queue, and lastly exit the traffic circle to the outside world. We model both the service rate and the departure rate as dependent on the number of vehicles inside the traffic circle.Inaddition,weruncomputersimulationstohaveavisualrepresentation of what happens in a traffic circle during different situations. These allow us to examine different cases, such as unequal traffic flow coming from the different queues or some intersections having a higher probability of being a vehicle destination than others. The simulation also implements several life-like effects, such as how vehicles accelerate on an empty road but decelerate when another vehicle is in front of them.In many cases, we find that a high service rate is the optimal way to maintain traffic flow, signifying that a yield sign for incoming traffic is most effective. However, when the circle becomes more heavily trafficked,TheUMAPJournal30(3)(2009)247–260. !c Copyright2009byCOMAP,Inc. Allrightsreserved. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without feeprovided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights for components of this work owned by others than COMAP must be honored. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP.Figure 1. A simple traffic circle. Traffic circles may have more than one lane and may have a different number of intersections.a lower service rate better accommodates traffic, indicating that a traffic light should be used. Thus, a light should be installed in most circle implementations, with variable timing depending on the expected amount of traffic.The main advantage of our approach is that the model is simple and allows us to see clearly the dynamics of the system. Also, the computer simulations provide more in-depth information about traffic flow under conditions that the model could not easily show, as well as enabling visual observation of the traffic. Some disadvantages to our approach are that we do not analyze the effects of multiple lanes nor stop lights to control the flow of traffic within the circle. In addition, we have no way of analyzing singular situations, such as vehicles that drive faster or slower than the rest of the traffic circle, or pedestrians.IntroductionTraffic circles, often called rotaries, are used to control vehicle flow through an intersection. Depending on the goal, a traffic circle may take different forms; Figure 1 shows a simple model. A circle can have one or more lanes; vehicles that enter a traffic circle can be met by a stop sign, a traffic light, or a yield sign; a circle can have a large or small radius; a circle can confront roads containing different amounts of traffic. These features affect the cost of the circle to build, the congestion that a vehicle confronts as it circles, the travel time of a vehicle in the circle, and the size of the queue of vehicles waiting to enter. Each of these variables could be a metric for evaluating the efficacy a traffic circle.Our goal is to determine how best to control traffic entering, exiting, and traversing a traffic circle. We take as given the traffic circle capacity, the arrival and departure rates at each of the roads, and the initial number of vehicles circulating in the rotary. Our metric is the queue length, or buildup, at eachoftheenteringroads. Wetrytominimizethequeuelengthbyallowingthe rate of entry from the queue into the circle to vary. For a vehicle to traverse the rotary efficiently, its time spent in the queue should be minimized. We make the following assumptions:•We assume a certain time of day, so that the parameters are constant.•There is a single lane of circulating traffic (all moving in the same direction).•Nothing impedes the exit of traffic from the rotary.•There are no singularities, such as pedestrians trying to cross.•The circulating speed is constant (i.e., a vehicle does not accelerate or decelerate to enter or exit the rotary).•Any traffic light in place regulates only traffic coming into the circle.The ModelsA SimplifiedModelWe model the system as being continuous; our approach can be thought of as modeling the vehicle mass dynamics of a traffic circle. The simplest model assumes that the rate of arrival to the back of the entering queue and the rate of departure from the queue into the traffic circle are independent of time. Thus, the rate of change in the length of the queue is, (1) where Q i is the number of cars in the queue coming in from the i th road, a i is the rate of arrival of vehicles into the i th queue, and s i is the rate of removal, alsocalledtheservicerate, fromthe i thqueueintothetrafficcircle.We introduce the parameter d i, the rate at which vehicles exit the traffic circle. We let C be the number of vehicles traveling in the circle. Then we model the change in traffic in the rotary by the difference between the influx and outflux of vehicles, where the outflux of vehicles depends on the amount of traffic in the rotary:. (2)An IntermediateModelThe model above simplifies the dynamics of a traffic circle. The mostglaring simplifications are that there is no way to indicate that the circle has a maximum capacity and that the flow rate into the traffic circle s i does not depend on the amount of traffic already circulating. These are both corrected by proposing that the traffic circle has a maximum capacity C max. As the number of vehicles circling approaches this maximum capacity, it should become more difficult for another vehicle to merge into the circle. At the extreme, when the traffic circle is operating at capacity, no more vehicles should be able to be added. Now, the s i in the previous model can be represented logistically as,where r i is how fast vehicles would join the circle if there were no traffic slowing them down. Thus, the equation governing the rate at which the i th queue length changes becomes, (3)and the equation for the number of vehicles in the traffic circle becomes(4)A CongestionModelThe previous two models still fail to take into account congestion, which alters the circulation speed, which in turn affects the departure rate d i of vehicles from the circle. Equation (3) still holds, but we need to vary d i. The vehicles will travelfaster if there is no congestion, so they will be able to depart at their fastest rate d i,max. When the circle is operating at maximum capacity, the departure rate will decrease to be d i,min. Thus, the number of vehicles present in the circle is affectedpositively in the same manner as in (4),butthe lessening factor changes to the weighted average of theExtendingthe Model Using ComputerSimulationWe create a computer simulation in Matlab to account for variables that would be too complicated to use in the mathematical model. The mathematical model does not address the vehicles’ speeds while inside the traffic circle, so the computersimulationfocuses mostly on areas related to vehicle speed:•enablingspeed), drivers to accelerate to fill gaps in the traffic (with a maximum•forcing drivers to decelerate to maintain distance between vehicles,•requiringing the circle,that drivers accelerate and decelerate when entering and exit-•giving probabilistic weights to the different directions of travel, • keeping track of time spent within the traffic circle for each vehicle, and•giving each intersection a different vehicle introduction rate.Figure 2 on p. 250 shows an outline of the program flow and design.SimulationAssumptionsThis model makes several key assumptions about the vehicles and the circle:•Allandvehiclesdecelerateareatthethesamesamesize,rate.have the same top speed, and accelerate•The circle has four intersections and a single lane of traffic.•All drivers have the same spatial tolerance.•There are no pedestrians trying to cross the circle.LimitationsThe assumption of one lane is not a key factor, because we assume that vehicles travel at the same speed. Hence, we do not need to put the slow vehicles in one lane and vehicles passing them in another lane. However, in reality there will indeed be slower vehicles, and vehicles decelerating to exit would offer opportunities for other vehicles to use a different lane to maintain a faster speed. Additionally, we cannot let emergency vehicles through the circle if there is only one lane; for a more detailed discussion of emergency vehicles and traffic circles, see Mundell [ n.d. ].By not allowing control devices inside the circle, we restrict possible configurations. We also limit the effectiveness of our stoplight model; it preventsvehiclesfromenteringthecirclebutdoesnotinhibitthemovement of vehicles within in the circle.Figure 2. Program flow. Each intersection is modeled as a queue of vehicles with a traffic control device. Vehicles are added to the queue at a constant rate. For a vehicle to leave the queue and enter the traffic circle, the area in the circle must be clear of other vehicles. Additionally, if the queue has a traffic light, the light must be active.Since we do not allow for different vehicle properties (size, acceleration, top speed, etc.), we cannot model the effects of large trucks, motorcycles, or other nonstandard vehicles (such as large and unwieldy emergency vehicles) on the flow of traffic.Givingallofthevehiclesthesameaccelerationandtopspeed,alongwith forcing all drivers to have the same spatial tolerance, prevents modeling aggressivedriversandtheirinteractionwithtimidones. Additionally, since cars in the simulation decelerate before exiting, even if they are already moving slowly, we generate a small proportion of false traffic backups.Limitingthe size and numberof intersectionsof the circle does not really limit our ability to model real-world traffic circles. Since we are mostly looking at driver behavior with the computer simulation, we should see the same behaviors as wescale up the circle and its corresponding traffic.Analyzingthe ModelsThe Simplest ModelIn all of the above models, the rate r i is indicative of the regulation imposed atthe i th intersection. A near-zero r i indicates that a traffic light is in use; a larger r i indicates that a yield sign, regulating only the incoming traffic, is in place.For the simplest model, we can use (1) and (2) to find explicit formulae for the queue length and the number of vehicles in the rotary by integrating with respect to time:.Therefore, given the inputs of the system, we can predict the queue length. To minimize the queue length, we solve (1) for when the queue length is decreasing (dQ i/dt < 0) and find that the s i term should be maximized.IntermediateModelFor the model with a carrying capacity, again we find explicit formulae for the queue length and the number of vehicles in the rotary:.We can also solve for where (3) is less than zero to find the service rates for which the queue lengths are decreasing:.CongestionModelIn modeling congestion, the model is too complex to intuit what conditions would minimize the queue length. The differential equation (5) is quadratic:Figure 3. The relationship between dC/dt and C for the congestion model using sample parameters values r1 = r2 = r3 = r4 = 60, d1,max = d2,max = d3,max = d4,max = 2, d1,min = d2,min = d3,min = d4,min =0.5, and C max =30. where.Since d i,max > d i,min, it will always be the case that A > 0. In addi-tion, B <P0 and D >P0. This meansthat the curvefor dC/dt is a concave-up quadratic curve with a positive y-intercept and a global minimum at some C > 0. Furthermore, for C = C max, we have,which is always negative for d i,min > 0. Thus, the global minimum for the curve must be in the fourth quadrant. Figure 3 shows an example of such a curve, using sample parameters.We notice from Figure 3 that there are two equilibrium points for the differential equation:is a stable equilibrium point, andis an unstable equilibrium point.Also, since for C = C max, we have dC/dt < 0, the number of vehicles will eventuallydecrease to an equilibrium value less than C limit < C max.Since our metric for how well a traffic circle operates depends on how many vehicles are in the queues, we would like the queue flow (a i −s i) to be as small as possible. In other words, we would like s i to be as large as possible. In the congestion model, the queue flow is given by (3).Without loss of generality, we analyze queue 1. The equations for each queue differ only by their a i and r i, and we keep these the same for each queues in the simulations. Since the only changing variable in (3) is C, when C = C limit the queue length Q1 will also be at its equilibrium.Using this fact, we can evaluate whether to use a traffic light or not and how long the light should be red. We compare different values for the servicerateconstant r1 andthevalueof dQ1/dt at C = C limit. Theresultscan be seen inFigure 4, which shows that when r1 increases, dQ1/dt decreases.Figure 4. The relationship between r1 and dC/dt for the congestion model withC = C limit. The parameter values are d1,max = d2,max = d3,max = d4,max = 2, d1,min = d2,min = d3,min = d4,min =0.5, C max =30, and r1 changed from 1 to 60.A real-life situation is congestion of the traffic circle. Decreasing d1,min would cause vehicles to exit the circle more slowly when there is more congestion. Using lower departure rates to approximate slower vehicle speedsinsidethecircle,wecanexaminewhathappensfordecreasingvalues of d1,min.The results are shown in Figure 5. For values of d1,min < 0.5, the smallest value for dQ1/dt is not at r1 = 60 but at a smaller value.Another situation that the congestion model can approximate is additional lanes. A crude approximation is that each lane adds C max to the capacity. Figure6 shows the results of plotting r1 versusthe C max for different numbers of lanes. As in the previous plots, the correlation is negative.SimulationResultsAn interesting effect that we see in our simulation is the buildup of vehicles in front of each exit. As vehicles decelerate to exit, they force vehiclesbehindthemtodeceleratetomaintainasafedistance. Thisbuildup creates a longer queue at the intersection before the exit, since the buildup prevents those vehicles from entering the circle. In Figure 7, we see a large number of vehicles in the fourth queue and a buildup in the fourth quadrant.Figure 5. The relationship between r1 and dC/dt for the congestion model with C = C limit, with parameter values d1,max = d2,max = d3,max = d4,max =2, and C max =30. The values of r1 range from 1 to 60 for different values of d1,min.Figure 6. The relationship between r1 and dC/dt for the congestion model withC = C limit. The parameter values are d1,max = d2,max = d3,max = d4,max = 2, d1,min = d2,min = d3,min = d4,min =0.5,C max =30, and r1 changed from 1 to 60.Figure 7. Vehicles build up before the first intersection as vehicles slow down to exit. Additionally, the queue at the fourth intersection is quite long, because vehicles cannot enter the traffic circle.Another interesting element of real life that the simulation shows is the bunching and expanding effect that vehicles experience. Because vehicles can decelerate more quickly than they accelerate, the vehicles bunch up behind a slow movingvehicle, then expand again as that vehicle accelerates into the freespace ahead. Figure 8 shows an example of this compaction.Figure 8. The arrow in the second quadrant points out a real-life effect, bunching, which happens because drivers decelerate faster than they accelerate.Wetestseveralrotaryandvehiclesetupstoexploreoptimalcircledesign:•A single intersection with high arrival and service rates creates a large traffic buildup in the quadrant immediately following it, even though the vehicles have random destinations. Figure 9 shows the buildup in quadrant 1 when the first intersection (at angle 0) has a high arrival and service rate. However, queue 1 is not appreciably longer than the others.Figure9. Thefirstintersectionhasbothhigharrivalandservicerates,whichcreatesatrafficbuildup before the next intersection. However, the queue for the first intersection does not increase, since there is limited traffic coming from the intersection behind it.•One intersection having a much higher chance of being a destination creates the expected buildup in front of the likely exit (Figure 10). However, it also creates a substantial buildup in front of the previous exit and a severe increase in that intersection’s queue as vehicles are prevented from entering the circle.The buildup in the adjacent road must be taken into account when constructing a traffic circle at a high-volume intersection.•If one intersection has a high service rate and the standard arrival rate, and another intersectionhas a high arrival rate and standard service rate, the traffic distribution is mostly random, with a slight tendency towards backupsinthequadrantfollowingtheintersectionwithhighservicerate. We expectthis result, since the intersectionwith high servicerate can add only as many vehicles as in its queue, which is limited by its low arrival rate. Also, the intersection with high arrival rate and low service rate has a much longer queue than the other intersections, entirely as expected.ConclusionWe model the dynamics of a traffic circle to determine how best to regulate traffic into the circle. As shown in Figure6 on p. 256, increased capacity decreases the queue flow, which leads to a decrease in queue length. This result indicates that a multiple-lane traffic circle might better accommodate more cars by decreasing the length of the queue in which they wait. However, as shown in the same figure, the marginal utility of increasing the maximum capacity does decrease. When applying a cost function ( with cost proportional to the space that the circle occupies), there would exist anFigure 10. The first intersection has a higher probability of being chosen as a destination. This creates a buildup in front of that intersection and a smaller buildup in front of the previous intersection. It also creates a very large increase in the queue of the previous intersection since those vehicles cannot enter the full circle.optimum size of the traffic circle.Althoughthesimplermodelsindicatethatlettingvehiclesintotherotary as fast as possible would be optimum, analysis of the congestion model shows that if d i,min is sufficiently small, then the highest service rate is no longer optimal. The implication of this result is that traffic lights could make travel through the rotary more efficient. When many vehicles use the traffic circle, such as during the morning and evening commutes, there could be enough vehicles so that the C limit is reached. In this case, using traffic lights would help ease congestion. However, the duration of the red light should be adjusted according to the d i,min for the specific traffic circle.In addition to the mathematical models, we create a computer simulation that tracks individual vehicles’ progress through the traffic circle, and their effect on other vehicles. Our simulation shows several traffic effects that can be observed in real life, namely a buildup of vehicles in front of the exits and vehicles bunching together and expanding apart as drivers brake and accelerate. We also test several traffic circle configurations.RecommendationsBased on both our mathematicaland computer models, we recommend:•Yield signs should be the standard traffic control device. Most of the time, letting vehicles enter the circle as quickly as possible is optimal.•For a high-traffic rotary, traffic lights should be used. With high traffic, slowing the rate of entry into the circle helps prevent congestion.•If any single road has high traffic, its vehicles should be given preference in entering the circle. Doing so helps prevent a large queue.•Introduce separate exit lanes. Traffic can build up in front of each intersection as cars exit, so a separate exit lane could help keep traffic moving.ReferencesMundell, Jim. n.d. Constructing and maintaining traffic calming devices. Seattle Department of Transportation. http://www.seattle. gov/Transportation/docs/TORONTO4.pdf.。
2009年美赛论文翻译翻译
2009 Contest ProblemsMCM PROBLEMSPROBLEM A: Designing a Traffic Circle问题A：设计一个道路的圆形交叉路口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.很多城市和社区有一些道路的圆形交叉路口----大的有很多路口（例如巴黎的Arc de Triomphe和Bangkok的Victory Monument），小的有一两个路口。
一些圆形交叉路口在每个进口处设置停止或让路标识，使已经在环形交叉路口的车辆拥有优先权；有的在进口处只设置停止标识（在红灯时不允许右转）。
2009美赛A类试题翻译
2009美赛试题
问题A：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。
数模1998-2016年历年美赛题目(中文)
2016 年美赛题目翻译Program A一个人用热水从一个水龙头里灌满一个浴缸，然后安顿在浴缸中，清洗和放松。
不幸的是，浴缸不是一个温泉式浴缸，一个二次加热系统和循环射流，而是一个简单的水容器。
过了一会儿，洗澡就明显地凉快，所以人增加了一个恒定滴热水从水龙头加热洗浴用水。
该浴缸的设计是在这样一种方式，当浴缸达到容量，多余的水通过溢流泄流。
在空间和时间上开发一个浴缸的水的温度模型，以确定最佳的策略，在浴缸的人可以采取保持温度，即使在整个浴缸和尽可能接近的初始温度，没有浪费太多的水。
使用你的模型来确定你的策略取决于浴缸的形状和体积，浴缸的形状/体积/温度，浴缸中的人的运动。
如果这个人用了一个泡泡浴剂，而最初填充浴缸，以协助清洗，这会影响你的模型的结果？除了要求的一页摘要MCM提交，你的报告必须包括一一页的非技术性解释的浴缸，描述你的策略，解释为什么它是如此难以在洗澡水温度得到均匀地保持用户Program B小碎片在轨道上绕地球金额已日益受到关注。
据估计，超过50万件的空间碎片，也被称为轨道碎片，目前都正在跟踪的潜在危害飞船。
这个问题本身在新闻媒体上变得更广泛的讨论时，俄罗斯卫星的Kosmos-2251和美国铱卫星-33 2009年2月10日，上相撞。
已经提出许多方法以除去碎屑。
这些方法包括小的，基于空间的水射流，并用于针对碎片的特定部分高能激光器和大型卫星，旨在清扫杂物，等等。
碎片的大小和质量范围从漆片的废弃卫星。
碎片“高速轨道捕获做出困难。
开发时间依赖模型来确定一个私人公司可以采取作为一个商业机会，以解决空间碎片问题的替代品的最佳替代品或组合。
您的模型应该包括成本，风险，收益定量和/或定性的估计，以及其他的重要因素。
您的模型应该能够评估独立的替代方案以及替代品的组合，并能够探索各种重要的“如果什么？”的情景。
使用你的模型，确定经济上有吸引力的机会是否存在没有这样的机会是可能的。
如果可行的商业机会的存在作为替代的解决方案，提供了用于去除碎屑的不同选项的比较，并包括特定建议作为对碎片应如何除去。
09年英汉互译(附参考译文)
09年英汉互译The Texas Ruffian(无赖)他是个精力充分的人，雄心勃勃，永不安分。
从来没有他干得完的事，因为事业每有成就，他都鼓励自己更加奋进；他是本世纪罕见的政坛怪客，身跨美国社会两个截然不同的时代。
朴实开拓观决定了他早期的人身轨迹和处事哲学。
迟暮之年，他身任一国元首，带我们一行前往月球探索尽头；他为人强势，干劲十足而且头脑精明，令人印象深刻。
同样让人难忘的是他的不平安感。
内心的恐惧固然首先成就了他，可尽管已是大有建树，他的恐惧却从不见淡——在这个意义上讲，他倒是政坛里最为感性的角色了。
在林德约翰逊身上，有一处惹人注目的特质——他越是努力掩饰弱点，弱点暴露的就越明显。
属下衷心不二，是条重要原那么：毕竟华盛顿这座城市，是一片四面受敌的海域，鲨鱼们一等到猎物放下戒心，便会游窜出来展开攻击。
鉴于这点，核心圈子务必得确保平安，得确保绝对平安才行。
尤其是那些对自身缺点弱点格外在意的人，好比林德约翰逊这样的，巴不得前后左右都部署着亲信。
“那家伙有多可靠？〞林德约翰逊向一名白宫工作人员问起某位准副手的为人。
“这个啊…回总统先生，他看起来相当可靠。
〞那名工作人员答道。
“我要的不是可靠！是可操！他得有本领在大庭广众下舔老子的屁股，还不忘夸它闻起来喷香喷香的味道好！〞林德约翰逊对属下求衷假设渴，几乎到了歇斯底里的地步。
如果他的不平安感是枚硬币，那这只是这枚硬币的一面。
作为一名伟大的杰出人物,，成就斐然之士兼华盛顿典型公民，他觉察自己与华盛顿众多重要场合格格不入——夹在一群打了香水、有着东部血统的城市宠儿面前，自己成了德州土生土长的流氓胚子, 匪气逼人。
疏离感和对自己的偏见深深烙在他心上，从未减淡。
〔1964年10月，正逢乔治鲍尔递交自己的备忘录首次陈述“反越〞政见，约翰逊就对一名副手说道，“你得留神这些来自东部的律师，不然让他们抓住把柄，他们会整死你！〞〕区域歧视统领了他的观念，即便是担任了总统一职后，这份歧视感依旧是那么强烈。
美国大学生数学建模竞赛优秀论文翻译
优化和评价的收费亭的数量景区简介由於公路出来的第一千九百三十，至今发展十分迅速在全世界逐渐成为骨架的运输系统，以其高速度，承载能力大，运输成本低，具有吸引力的旅游方便，减少交通堵塞。
以下的快速传播的公路，相应的管理收费站设置支付和公路条件的改善公路和收费广场。
然而，随着越来越多的人口密度和产业基地，公路如花园州公园大道的经验严重交通挤塞收费广场在高峰时间。
事实上，这是共同经历长时间的延误甚至在非赶这两小时收费广场。
在进入收费广场的车流量，球迷的较大的收费亭的数量，而当离开收费广场，川流不息的车辆需挤缩到的车道数的数量相等的车道收费广场前。
因此，当交通繁忙时，拥堵现象发生在从收费广场。
当交通非常拥挤，阻塞也会在进入收费广场因为所需要的时间为每个车辆付通行费。
因此，这是可取的，以尽量减少车辆烦恼限制数额收费广场引起的交通混乱。
良好的设计，这些系统可以产生重大影响的有效利用的基础设施，并有助于提高居民的生活水平。
通常，一个更大的收费亭的数量提供的数量比进入收费广场的道路。
事实上，高速公路收费广场和停车场出入口广场构成了一个独特的类型的运输系统，需要具体分析时，试图了解他们的工作和他们之间的互动与其他巷道组成部分。
一方面，这些设施是一个最有效的手段收集用户收费或者停车服务或对道路，桥梁，隧道。
另一方面，收费广场产生不利影响的吞吐量或设施的服务能力。
收费广场的不利影响是特别明显时，通常是重交通。
其目标模式是保证收费广场可以处理交通流没有任何问题。
车辆安全通行费广场也是一个重要的问题，如无障碍的收费广场。
封锁交通流应尽量避免。
模型的目标是确定最优的收费亭的数量的基础上进行合理的优化准则。
主要原因是拥挤的随着经济的发展，交通系统逐渐形成和完善自己。
不同种类的车辆已迅速改善的数量，质量，速度，和类型。
为了支付维修费用的高速公路，收费站系统的建立。
然而，费时费给我们带来的拥塞，高度增加烦恼的司机。
一般来说，在收费亭的数量大于数量的车道。
2009年美国大学生数学建模竞赛B题特等奖文章翻译
美国的新呼叫by作者Stephen R. Foster, J. Thomas Rogers, Robert S. Potter 斯蒂芬·福斯特，J.托马斯·罗杰斯，罗伯特·S·波特Southwestern University 西南大学Georgetown, TX 德克萨斯州乔治敦，Adviser:导师：Rick Denm里克·登曼摘要正在进行的手机革命值得检查其对过去，present, and futu现在和未来的能源影响。
Thus, our model adheres to two requirements: it can evaluate energy 因此，我们的模型坚持两个条件：它可以评估自1990年以来能源的使用情况；它能足够灵活的预测未来的能源需求。
数学上讲，我们的模型把家庭作为状态机，并使用实际人口数据以指导状态转变。
我们保持灵活的自下而上的方法，使得我们：1）model energy consumption for the current United States, 2) determine efficient ph模拟目前美国的能源消耗，2）在新兴市场国家确定有效的手机adoption schemes in emerging nations, 3) assess the impact of wasteful practices, and 采用计划，3）评估浪费行为的影响，4）预测未来的能源需求。
我们发现，新兴国家独家采用的固定电话会比独家采用手机高效两倍。
然而，我们也发现在国家层面上消除某些浪费做法可以使手机的采用高于175%的效率。
此外，我们针对目前的美国给出两种预测，揭示出在未来的50年，手机用户和制造商之间的合作可以节省超过3.9亿桶的原油。
问题背景在1990年，不到3％的美国人拥有手机[ITU]。
从那时起，越来越多的家庭选择抛弃他们的座机电话支持为每个家庭成员购买手机。
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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。
标题：一个环来控制一切:优化交通圈。
安德里亚•利维亚伦安德烈娅•利维拉塞尔•梅里克哈维姆德学院顾问:苏珊摘要我们的目的是利用车辆动力学考虑在圆形交叉路口的道路情况。
我们主要根据进入圆形道路的速度决定最好的方式来控制车流量。
我们假设在一个车道通过圆形道路循环，这样交通输入量能够被调节。
（也就是，不会有优先的交通输入量）对于我们的模型，可改变的参数是排队等候进入的速率，进入圆形道路的速率（服务速率），这个圆形道路最大的容量和离开这个道路的速率。
我们使用带有队列和交通圈的隔室模型作为隔间。
来自外界的车辆首先进行排队等候，然后进入圆环交叉路口，最后离开到外界。
我们把服务速率和离开速率作为在圆环交叉路口的车辆数量参考。
另外，我们利用计算机来拟态一个可见表示，发生在不同情形下的圆环交叉路口。
允许我们检验不同的情况，例如不平等的交通流量由于不同的队列，一些十字路口比其他车辆有一个更高的概率。
这个拟态模仿实施栩栩如生，例如如何当前面是空道路时进行加速，而当前面有其他车辆时进行减速。
大多数情况下，我们发现：一个高服务效率能够保持交通顺畅的最佳方式，这意味着对于进入交通的效率是最有效的。
然而，当交通变得拥堵时，较低的服务率更好的适应了交通，这指示应该使用一个红绿灯。
所以，在不同时间段，依靠预测中的交通流量，一个信号灯应该被安装进行循环实现。
图1注：一个简单的交通圈，交通圈可能有一个以上的车道,并可能有不同数量的十字路口。
我们方法的主要优势是，模型简单，能够清楚的看到动态系统。
而且，在模型不容易展现的情况下，关于交通流量，电脑的拟态仿效提供了非常深入的信息，也确保了交通的可视化观察。
我们方法的一些缺点是没有分析多个车道的影响，也没有红灯控制这个循环道路的交通流动。
另外，我们没有方法分析一些意外的情形，例如比起其他交通圈或者行人，车辆有时驱动快，有时慢。
前言交通圈，也叫旋转圈，通过十字交叉路口来控制车辆流动。
根据这个目标，一个交通圈可能要采取不同的形式。
图一战士了一个简单的模型。
一个圈可以有一个或者多个车道；进入交通圈的车辆会见到停车标志，或者一个让车标志；一个交通圈可以有一个大的或者小的半径。
一个交通圈包含不同数量的道路交通。
这些特性影响了交通圈修建的成本，当循环流动，车辆会面对拥堵，所需时间就会增加，队列的大小车辆就会等待进入。
这些每个变量可以作为一个度量评估交通圈的标准。
我们的目标是决定如何最好的控制车辆交通的进口，出口，以及遍历一个交通圈。
我们需要考虑交通循环能力，每个路口的到达和离开速率，以及最初循环下的车辆数。
在每个进入路口，我们的指标是队列的长度。
我们试图根据队列进入循环的变化，通过进入速率，减少队列长度。
对于一个车辆有效地穿过交通圈，在队列中所花费的时间应该最小。
我们做出这样的假设：1.我们假设一天特定的时间，所以参数是常数。
2.有一个简单的交通流通车道（都朝一个方向流动）3.在这个交通圈里，没有什么阻止交通出口处。
4.没有意外情况，比如行人突然穿过。
5.循环速度是常数（没有车辆加速或者减速，或者推出交通圈）6.只有在进入交通循环，任何交通灯在一些位置可以调节。
模型：一个简化的模型我们认为这个系统是连续的。
这个模型假设了，进入队列后面的到达速率和从这个队列进入交通圈的速率在时间上是相互独立的。
所以这个队列长度的变化速率是i i i dQ a s dt=- （1） i Q 表示从这个队列中车的数量，a i 表示进入这个队列车辆到达的速率，s i 表示移动的速率，也叫做从这个队列进入交通圈的速率。
我们引入di 这个参数，表示车辆离开交通圈的速率。
C 表示在这个交通圈里车辆行驶的数量。
通过车辆流入流出，我们去刻画这个交通圈中的改变，其中车辆的流出根据交通圈中通行的数量。
i dc s c di dt=-∑∑ （2） 模型二：上面的模型简化了交通圈的动力装置。
最显著的简化是没有指出这个圈有一个最大的容量，在交通圈中的流动速率并不依赖于已经积累的通行数量。
通过进一步的改进，交通圈有了最大的容纳量max C ，当车辆的循环数量到达最大的容纳量，对于另一个车辆进入这个交通圈里将非常困难。
最大程度下，交通圈在最大容量下运行，不在会有车辆进入。
这时，在最初的模型中si 可以被表示为：maxC s (1)C i i r =- 其中ri 表示在没有车辆减速时，加入这个交通圈的速率。
所以，这个等式控制着队列长度的变化速率maxd (1)i i i Q C a r dt C =-- （3） 在这个交通圈中车辆数量的等式是maxd (1)i i C C r d C dt C =--∑∑ （4） 拥挤模型的建立以上两种模型仍没有考虑到拥挤状况，对流通速度的影响，以及对车辆离开速率di 的影响。
方程式（3）依然成立，但是我们需要改变di 。
如果没有拥挤，车辆行驶会更快，因此他们能够以最快的速度di.max 离开。
当这个交通圈以最大容量运作，离开的速度将会减少到最小di.max ，所以，目前在这个交通圈中车辆的数量必将影响等式（4），但减少因素的改变可以取最大值和最小值的平均数。
,max ,min max max maxd (1)[(1)()]i i i C C C C r C d d dt C C C =---+∑∑∑（5） 利用计算机仿真进行宽展模型我们用matlab 创建了一个电脑模拟，目的是解释在数学模型中复杂的参量。
当在交通圈里时，数学模型不能解决车辆的速度，所以电脑模拟主要关注车辆速度。
最大的速度，确保司机加快速度填补交通差距。
迫使司机减速来保持车辆之间的距离。
当进入和退出交通圈时，要求司机加速和减速。
对于不同的同行方向，给出概率权重。
对于每一个车辆，保持跟踪时间花费在交通圈内对每个十字路口，给说不同的车辆速度图2在252页。
显示了一个轮廓的程序流程和设计。
模拟假设这个模型对车辆和交通圈做了许多关键的假设。
所有车辆都是相同的大小，相同的最高速率和以同样的速度加速和减速交通圈有四个十字路口和一个单一的交通车道。
所有司机有相同的容忍限制没有行人横穿这个交通圈图2 程序流注：每个路口被建模为一个队列的车辆交通控制装置。
车辆被添加到队列以恒定速率。
车辆离开队列,进入交通圈,在圈中的该区域必须清除其他的交通工具。
另外,如果队列有一个红绿灯,灯必须是可以使用的。
因为我们不考虑不同的车辆属性(大小、加速度、最大速度等),所以我们在交通流量中不以大卡车、摩托车、或其他非标准工具(如大型和笨拙的紧急车辆)做模型。
给所有的车辆相同的加速度和最高速度,以及迫使所有的驱动程序都必须有相同的空间公差,防止好斗的的司机和胆小的司机发生摩擦。
此外,由于模拟中汽车在出口前已经减速,即使他们已经缓慢的移动,我们生成一个小比例的虚假流量备份。
限制大小和十字路口的数量的圈子并不真正限制我们来模拟现实世界中的交通圈。
因为我们主要是看计算机模拟中司机的行为,我们将按照相同的行为和相应的交通来扩大交通圈的规模。
分析模型最简单的模型在所有上述模型,在第i 路口强制限定速度r 。
一个接近于零的r 表明一个交通灯正在使用当中;一个更大的r 表明一个让车标志,调节只有适当的传入车辆。
[]0i i i i Q t s a Q +-= t d e d s C d sC i i i i i∑∑∑∑∑-⎪⎪⎭⎫ ⎝⎛-+=0 因此,考虑到系统的输入,我们可以预测队列长度。
为了使队列长度最小化,当队列长度逐渐减到(dQildt < 0)时我们解决(1),发现si 术语应该最大化。
中级模型因为模型有一定的承载力,我们又找到明确的公式计算队列长度和汽车的数量。
0max 1i i i i Q i C C r a Q +⎥⎦⎤⎢⎣⎡⎪⎪⎭⎫ ⎝⎛--= i d C r e d C r r C d C r r C i mzx i i i i i i i ⎪⎪⎭⎫ ⎝⎛+-⎪⎪⎪⎪⎪⎭⎫ ⎝⎛+-++=∑∑∑∑∑∑∑∑max 0max我们也可以解决在（3）小于零的时候找到维修费用。
当队列长度减少:max 1C C a r i i -> 拥塞模型在建立拥堵模型时,模型太过于复杂，很难凭直觉知道什么条件下会使队列长度最小化。
把微分方程(5)乘二次方:,2D BC AC dtdC ++=图 3dt dC /和C 之间的关系在拥堵模型中实用简单的参数数值：604321====r r r r 5.0,2min ,4min ,3min ,2min ,1max ,4max ,2max ,1=======d d d d d d d ,30max =C此时∑∑∑∑∑=⎪⎪⎭⎫ ⎝⎛+-=-=i i i i i r D d C r B C d C d A ,,max ,max max min ,max max , 因为∑∑>min ,max ,i i d d ，它将永远是A>0，此外，B<0和D>0。
这意味着dt dC /的曲线是一个y 轴截距在一些C > 0的点是整体最小值的上凹的二次曲线。
此外，对于max C C =，有,maxmin ,C d dt dC i -= 对于0min ,>i d 总是负面的。
因此,全局最低的曲线必须在第四象限。
图3展示了这样一个使用样本参数的曲线。
从图3中,我们注意到有两个平衡积分微分方程：AAD B B C 242---=是一个稳定的平衡点，并且 AAD B B C 242-+-=是一个不稳定的平衡点。
而且因为max C C =，我们有dt dC / <0,汽车的数量最终会减少到一个平衡值小于max lim C C it <的值。