美赛数学建模比赛论文模板
美赛数模论文格式
美赛数模论文格式篇一:2015年数学建模美赛论文格式2015年美国数学建模要求1( 文章标题居中用宋体142( 第一/第二/第三作者宋体143( 第一作者详细地址，包括国家，电子邮件(宋体11)，第二第三作者一样4( 关键词:文章涵盖你论文中的关键词。
这些关键词也会被使用的出版商制作一个关键字索引。
(使用宋体11)5( 对于本文的其余部分，请用宋体126( 摘要:本文档介绍并演示了如何准备你的相机准备手稿跨技术出版物。
最好的是阅读这些说明，并按照该文的轮廓。
7( 文本区为你的稿件必须是宽17厘米，高25厘米(6.7和9.8英寸，RESP)。
请勿超过本区域以外。
使用质量好，约21 X 29 cm或8×11英寸白纸。
您的原稿将约20,减少由出版商。
当设计你的数字和表格等时，请铭记你的原稿将由出版商进行20%的删减。
8( 介绍:所有稿件必须是英文(包括表格和数字)。
请保持您的稿件的第二个副本在你的办公室，以防丢失。
9( 使用斜体强调一个词或短语。
不要用粗体字打字或大写字母除外，对于章节标题(见备注一节的标题，下同)。
使用一台激光打印机，而不是一个矩阵点打印机。
10(文本组织:标题:标题用粗体，首字母大写，其他字母小写。
二级标题作为接下来段落的一部分页码:不要打印页码:请在底部(打字区外)附近的左上角用淡蓝色的铅笔轻轻编号在每一张纸上。
, 脚注:脚注应该是单倍行距和文字分开。
理想地，脚注出现的其参考的页面上，并且被放置在文本的下方，由一个水平线从文本分离。
表格:(参考:表格1，表格2…)应该作为文本的一部分，(用1,2注明)这样做可以避免文档的混淆。
描述性的标题应该置于每个表格之上。
标题应该是自包含的，在表格的下面或者旁边放着。
表格的单位应该用方括号【】注视。
如果方括号无法使用，则用大括号{}或普通括号()图形:(参考图形1，图形2…)也作为文本的一部分，要留下足够的空间让图形的说明不会和文本混淆。
建模美赛获奖范文
建模美赛获奖范文全文共四篇示例，供读者参考第一篇示例：近日，我校数学建模团队在全国大学生数学建模竞赛中荣获一等奖的喜讯传来，这是我校首次在该比赛中获得如此优异的成绩。
本文将从建模过程、团队合作、参赛经验等方面进行详细介绍，希望能为更多热爱数学建模的同学提供一些借鉴和参考。
让我们来了解一下比赛的背景和要求。
全国大学生数学建模竞赛是由中国工程院主办，旨在促进大学生对数学建模的兴趣和掌握数学建模的基本方法和技巧。
比赛通常会设置一些实际问题，参赛队伍需要在规定时间内通过建立数学模型、分析问题、提出解决方案等步骤来完成任务。
最终评选出的优胜队伍将获得一等奖、二等奖等不同级别的奖项。
在本次比赛中，我们团队选择了一道关于城市交通拥堵研究的题目，并从交通流理论、路网优化等角度进行建模和分析。
通过对城市交通流量、拥堵原因、路段限制等方面的研究，我们提出了一种基于智能交通系统的解决方案，有效缓解了城市交通拥堵问题。
在展示环节，我们通过图表、数据分析等方式清晰地呈现了我们的建模过程和成果，最终赢得了评委的认可。
在整个建模过程中，团队合作起着至关重要的作用。
每个成员都发挥了自己的专长和优势，在分析问题、建模求解、撰写报告等方面各司其职。
团队内部的沟通和协作非常顺畅，大家都能积极提出自己的想法和看法，达成共识后再进行实际操作。
通过团队合作，我们不仅完成了比赛的任务，也培养了团队精神和合作能力，这对我们日后的学习和工作都具有重要意义。
参加数学建模竞赛是一次非常宝贵的经历，不仅能提升自己的数学建模能力，也能锻炼自己的解决问题的能力和团队协作能力。
在比赛的过程中，我们学会了如何快速建立数学模型、如何分析和解决实际问题、如何展示自己的成果等，这些能力对我们未来的学习和工作都将大有裨益。
在未来，我们将继续努力，在数学建模领域不断学习和提升自己的能力，为更多的实际问题提供有效的数学解决方案。
我们也希望通过自己的经验和教训，为更多热爱数学建模的同学提供一些指导和帮助，共同进步，共同成长。
优秀的数学建模论文范文(通用8篇)
优秀的数学建模论文范文第1篇摘要：将数学建模思想融入高等数学的教学中来，是目前大学数学教育的重要教学方式。
建模思想的有效应用，不仅显著提高了学生应用数学模式解决实际问题的能力，还在培养大学生发散思维能力和综合素质方面起到重要作用。
本文试从当前高等数学教学现状着手，分析在高等数学中融入建模思想的重要性，并从教学实践中给出相应的教学方法，以期能给同行教师们一些帮助。
关键词：数学建模；高等数学；教学研究一、引言建模思想使高等数学教育的基础与本质。
从目前情况来看，将数学建模思想融入高等教学中的趋势越来越明显。
但是在实际的教学过程中，大部分高校的数学教育仍处在传统的理论知识简单传授阶段。
其教学成果与社会实践还是有脱节的现象存在，难以让学生学以致用，感受到应用数学在现实生活中的魅力，这种教学方式需要亟待改善。
二、高等数学教学现状高等数学是现在大学数学教育中的基础课程，也是一门必修的课程。
他能为其他理工科专业的学生提供很多种解题方式与解题思路，是很多专业，如自动化工程、机械工程、计算机、电气化等必不可少的基础课程。
同时，现实生活中也有很多方面都涉及高数的运算，如，银行理财基金的使用问题、彩票的概率计算问题等，从这些方面都可以看出人们不能仅仅把高数看成是一门学科而已，它还与日常生活各个方面有重要的联系。
但现在很多学校仍以应试教育为主，采取填鸭式教学方式，加上高数的教材并没有与时俱进，将其与生活的关系融入教材内，使学生无法意识到高数的重要性以及高数在日常生活中的魅力，因此产生排斥甚至对抗的心理，只是在临考前突击而已。
因此，对高数进行教学改革是十分有必要的，而且怎么改，怎么让学生发现高数的魅力，并积极主动学习高数也是作为教师所面临的一个重大问题。
三、将数学建模思想融入高等数学的重要性第一，能够激发学生学习高数的兴趣。
建模思想实际上是使用数学语言来对生活中的实际现象进行描述的过程。
把建模思想应用到高等数学的学习中，能够让学生们在日常生活中理解数学的实际应用状况与解决日常生活问题的方便性，让学生们了解到高数并不只是一门课程，而是整个日常生活的基础。
数学建模美赛论文格式中文版Word版
你的论文需要从此开始请居中使用Arial14字体第一作者，第二作者和其他（使用Arial14字体）1.第一作者的详细地址，包括国籍和email(使用Arial11)2.第二作者的详细地址，包括国籍和email(使用Arial11)3.将所有的详细信息标记为相同格式关键词列出文章的关键词。
这些关键词会被出版方用作关键词索引(使用Arial11字体）论文正文使用Times New Roman12字体摘要这一部分阐述说明了如何为TransTechPublications.准备手稿。
最好阅读这些用法说明并且整篇论文都是遵照这个提纲。
手稿的正文部分应该是17cm*25cm（宽*高）的格式（或者是6.7*9.8英尺）。
请不要在这个区域以外书写。
请使用21*29厘米或8*11英尺的质量较好的白纸。
你的手稿可能会被出版商缩减20%。
在制图和绘表格时候请特别注意这些准则。
引言所有的语言都应该是英语。
请备份你的手稿（以防在邮寄过程中丢失）我们收到手稿即默认为原作者允许我们在期刊和书报出版。
如果作者在论文中使用了其他刊物中的图表，他们需要联系原作者，获取使用权。
将单词或词组倾斜以示强调。
除了每一部分的标题（标记部分的标题），不要加粗正文或大写首字母。
使用激光打印机，而不是点阵打印机正文的组织：小标题小标题应该加粗并注意字母的大小写。
第二等级的小标题被视为后面段落的一部分（就像这一大段的一小部分的开头）页码不要打印页码。
请用淡蓝色铅笔在每一张纸的左下角（在打印区域以外）标注数字。
脚注脚注应该单独放置并且和正文分开理想地情况下，脚注应该出现在参考文献页，并且放在文章的末尾，和正文用分割线分开。
表格表格（如表一，表二，...）应该放在正文当中，是正文的一部分，但是，要避免文本混乱。
一个描述性的表格标题要放在图表的下方。
标题应该独立的放在表格的下方或旁边。
表中的单位应放在中括号中[兆伏]如果中括号不可用，需使用大括号{兆}或小括号（兆)。
美国大学生数学建赛论文模板【范文】
For office use onlyT1________________ T2________________ T3________________ T4________________Team Control Number21432Problem ChosenCFor office use onlyF1________________F2________________F3________________F4________________2012 Mathematical Contest in Modeling (MCM) Summary SheetTwo models to make conspirators nowhere to hide in social network With the development of high-technology, the number of white collar, high-tech crimes grow by more than 4% a year [1]. Bec ause of conspirators’ high IQ and professional knowledge, they are hard to be tracked down. Thus, we need use some special data mining and analytical methods to analyze social networks’ inherent law and finally offer help for litigating criminal suspect.M odel I is used for calculating everyone’s criminal possibility by the following 4 procedures: 1) Derive topics’ danger coefficient by Ana lytic Hierarchy Process (AHP);2) Set the discriminate line by Support Vector Machine (SVM); 3) Use the weight sum to c alculate everyone’s criminal possibility; 4) Provide a nomination form about conspiracy leaders by the Pagerank algorithm.Model II is an improved text analysis, used for more accurately analyzing the content and context of relevant information. The model includes four steps as follows: 1) Ascertain keywords and topics by counting their arisen times; 2) Syncopate me ssages’ sentence; 3) Match intelligently between messages and topics; 4) Get results by model I at last.We utilize models to evaluate requirement 1 and 2. The results show the fault of rates are 8.33% and 12.5%, which is acceptable.Table1. The results of requirement 1 and 2.conspirators criminal possibility leaders rankRequirement1Seeri 0.494 Julia 0.137 Sherri 0.366 Beth 0.099 Dolores 0.323 Jerome 0.095Requirement2 Sherri 0.326 Alex 0.098 Paige 0.306 Paige 0.094 Melia 0.284 Sherri 0.092To verify our two models and describe the ideas for requirement 3, we use models to analyze the 10 people’s example. The results of model II sho w our topics contain 78.8% initial information, better than the former 5 topics’ 57.7%. The results of model I can identify two shadowy conspirators, Bob and Inez. Thus, the models are more accurate and effective.According to the requirement4, we specifically discuss the effect of the thorough network analysis to our models. Meanwhile, we try to extend our models in distinguishing the safe page and unsafe page in Internet and the results derived from our models are reasonable.Two models to make conspirators nowhere to hideTeam #13373February 14th ,2012ContentIntroduction (3)The Description of the Problem (3)Analysis (3)What is the goal of the Modeling effort? (4)Flow chart (4)Assumptions (5)Terms, Definitions and Symbols (5)Model I (6)Overview (6)Model Built (6)Solution and Result (9)Analysis of the Result (10)Model II (11)Overview (11)Model Built (11)Result and Analysis (12)Conclusions (13)Technical summary (13)Strengths and Weaknesses (13)Extension (14)Reference (14)Appendix (16)IntroductionWith the development of our society, more and more high-tech conspiracy crimes and white-collar crimes take place in business and government professionals. Unlike simple violent crime, it is a kind of bran-new crime style, would gradually create big fraud schemes to hurt others’ benefit and destroy business companies.In order to track down the culprits and stop scams before they start, we must make full use of effective simulation model and methodology to search their criminal information. We create a Criminal Priority Model (CPM) to evaluate every suspect’s criminal possibility by analyzing text message and get a priority line which is helpful to ICM’s investigation.In addition, using semantic network analysis to search is one of the most effective ways nowadays; it will also be helpful we obtain and analysis semantic information by automatically extract networks using co-occurrence, grammatical analysis, and sentiment analysis. [1]During searching useful information and data, we develop a whole model about how to effective search and analysis data in network. In fact, not only did the coalescent of text analysis and disaggregated model make a contribution on tracking down culprits, but also provide an effective way for analyzing other subjects. For example, we can utilize our models to do the classification of pages.In fact, the conditions of pages’classification are similar to criminological analysis. First, according to the unsafe page we use the network crawler and Hyperlink to find the pages’ content and the connection between each pages. Second, extract the messages and the relationships between pages by Model II. Third, according to the available information, we can obtain the pages’priority list about security and the discriminate line separating safe pages and the unsafe pages by Model I. Finally we use the pages’ relationships to adjust the result.The Description of the ProblemAnalysisAfter reading the whole ICM problem, we make a depth analysis about the conspiracy and related information. In fact, the goal of ICM leads us to research how to take advantage of the thorough network, semantic, and text analyses of the message contents to work out personal criminal possibility.At first, we must develop a simulation model to analysis the current case’s data, and visualize the discriminate line of separating conspirator and non-conspirator.Then, by increasing text analyses to research the possible useful information from “Topic.xls”, we can optimize our model and develop an integral process of automatically extract and operate database.At last, use a new subject and database to verify our improved model.What is the goal of the Modeling effort?●Making a priority list for crime to present the most likely conspirators●Put forward some criteria to discriminate conspirator and non-conspirator, createa discriminate line.●Nominate the possible conspiracy leaders●Improve the model’s accuracy and the credit of ICM●Study the principle and steps of semantic network analysis●Describe how the semantic network analysis could empower our model.Flow chartFigure 1Assumptions●The messages have no serious error.●These messages and text can present what they truly mean.●Ignore special people, such as spy.●This information provided by ICM is reasonable and reliable.Terms, Definitions and SymbolsTable 2. Model parametersParameter MeaningThe rate of sending message to conspirators to total sending messageThe rate of receiving message to conspirators to total receiving messageThe dangerous possibility of one’s total messagesThe rate of messages with known non-conformist to total messagesDanger coefficient of topicsThe number of one’s sending messagesThe number of one’s receiving messagesThe number of one’s sending messages from criminalThe number of one’s receiving messages from criminalThe number of one’s sending messages from non-conspiratorThe number of one’s receiving messages from non-conspiratorDanger coefficient of peopleModel IOverviewModel I is used for calculating and analyzing everyone’s criminal possibility. In fact, the criminal possibility is the most important parameter to build a priority list and a discriminate line. The model I is made up of the following 4 procedures: (1) Derive topics’danger coefficient by Analytic Hierarchy Process (AHP); (2) Set the discriminate line by Support Vector Machine (SVM); (3) Use the weight sum to calculate everyone’s criminal possibility; (4) Provide a nomination form about conspiracy leaders by the Pagerank algorithm.Model BuiltStep.1PretreatmentIn order to decide the priority list and discriminate line, we must sufficiently study the data and factors in the ICM.For the first, we focus on the estimation about the phenomena of repeated names. In the name.xls, there are three pair phenomena of repeated names. Node#7 and node#37 both call Elsie, node#16 and node#34 both call Jerome, node#4 and node#32 both calls Gretchen. Thus, before develop simulation models; we must evaluate who are the real Elsie, Jerome and Gretchen.To decide which one accord with what information the problem submitsFirst we study the data in message.xls ，determine to analysis the number of messages of Elsie, Jerome and Gretchen. Table1 presents the correlation measure of their messages with criminal topic.Figure2By studying these data and figures, we can calculate the rate of messages about criminal topic to total messages; node#7 is 0.45455, while node#37 is 0.27273. Furthermore node#7 is higher than node#37 in the number of messages.Thus, we evaluate that node #7 is more likely Elsie what the ICM points out.In like manner, we think node#34, node#32 are those senior managers the ICM points out. In the following model and deduction, we assume node#7 is Elsie, node#34 is Jerome and node #32 is Gretchen.Step.2Derive topics’ danger coefficient by Analytic Hierarchy ProcessUse analytic hierarchy process to calculate the danger every topic’s coefficient. During the research, we decide use four factors’ effects to evaluate ：● Aim ：Evaluate the danger coefficient of every topic.[2]● Standard ：The correlation with dangerous keywordsThe importance of the topic itselfThe relationship of the topic and known conspiratorsThe relationship of the topic and known non-conspirators● Scheme ： The topics (1,2,3……15)Figure3According to previous research, we decide the weight of The Standard to Aim ：These weights can be evaluated by paired comparison algorithm, and build a matrix about each part.For example, build a matrix about Standard and Aim, the equation is followingij j i a C C ⇒:ijji ij n n ij a a a a A 1,0)(=>=⨯ The other matrix can be evaluated by the similar ways. At last, we make a consistency check to matrix A and find it is reasonable.The result shows in the table, and we can use the data to continue the next model. Step.3 Use the weight sum to calculate everyone ’s criminal possibilityWe will start to study every one’s danger coefficient by using four factors,, and .[3]100-第一份工作开始时间）（第一份工作结束时间第一份工作持续时间=The first factor means calculate the rate of someone’s sending criminal messages to total sending messages.The second factors means calculate the rate of someone’s receivingcriminal messages to total receiving messages.=The third factormeans calculate the dangerous possibility of someone’stotal messages.The four factorthe rate of someone’s messages with non-conspirators tototal messages.At last, we use an equation to calculate every one’s criticality, namely thepossibility of someone attending crime. ( Shows every factors’weighing parameter)After calculating these equations abov e, we derive everyone’s criminal possibilityand a priority list. (See appendix for complete table about who are the most likely conspirators) We instead use a cratering technique first described by Rossmo [1999]. The two-dimensional crime points xi are mapped to their radius from the anchor point ai, that is, we have f : xi → ri, where f(xi) = j i i a a (a shifted modulus). The set ri isthen used to generate a crater around the anchor point.There are two dominatingStep.4 Provide a nomination form about conspiracy leaders by the Pagerankalgorithm.At last, we will find out the possible important leaders by pagerank model, and combined with priority list to build a prior conspiracy leaders list.[4]The essential idea from Page Rank is that if node u has a link to node v, then the author of u is an implicitly conferring some importance to node v. Meanwhile it means node v has a important chance. Thus, using B (u) to show the aggregation of links to node u, and using F (u) to show the aggregation of received links of node u, The C is Normalization factor. In each iteration, propagate the ranks as follows: The next equation shows page rank of node u:Using the results of Page Rank and priority list, we can know those possiblecriminal conspiracy leaders.Solution and ResultRequirement 1:According to Model I above, we calculate these data offered by requirement 1 and build two lists. The following shows the result of requirement 1.By running model I step2, we derive danger coefficient of topics, the known conspiracy topic 7, 11 and 13 are high danger coefficient (see appendix Table4. for complete information).After running model step3, we get a list of every one’s criticality .By comparing these criticality, we can build a priority list about criminal suspects. In fact, we find out criminal suspects are comparatively centralized, who are highly different from those known non-conspirators. This illuminates our model is relative reasonable. Thus we decide use SVM to get the discriminate line, namely to separate criminal suspects and possible non-conspirators (see appendix Table5. for complete information). Finally, we utilize Page rank to calculate criminal suspects’ Rank and status, table4 shows the result. Thus, we nominate 5 most likely criminal leaders according the results of table4.They are Julia, Beth, Jerome, Stephanie and Neal.According to the requirement of problem1, we underscore the situations of three senior managers Jerome, Delores and Gretchen. Because the SVM model makes a depth analysis about conspirators, Jerome is chosen as important conspirator, Delores and Gretchen both has high danger coefficient. We think Jerome could be a conspirator, while Delores and Gretchen are regarded as important criminal suspects. Using the software Ucinet, we derive a social network of criminal suspects.The blue nodes represent non-conspirators. The red nodes represent conspirators. The yellow nodes represent conspiracy leaders.Figure 4Requirement 2:Using the similar model above, we can continue analyzing the results though theconditions change.We derive three new tables (4, 5 and 6): danger coefficient of topics, every one’s criticality and the probability of nominated. At last, we get a new priority list (table6) and 5 most likely criminal leaders: Alex, Sherri, Yao, Elsie and Jerome.We sincerely wish that our analysis can be helpful to ICM’s investigation. We figure out a new figure, which shows the social network of criminal suspects for requirement 2.Figure 5Analysis of the Result1)AnalysisIn the requirement 1, we find out 24 possible criminal suspects. All of 7 known conspirators are in the 24 suspects and their danger coefficients are also pretty high. However, there are 2 known non-conspirators are in these suspects.Thus, the rate of making mistakes is 8.33%. In all, we still have enough reasons to think the model is reasonable.In addition, we find 5 suspects who are likely conspirators by Support Vector Machine (SVM).In the requirement 2, we also choose 24 the most likely conspirators after run our CPM. All of 8 known conspirators are also in the 24 suspects and their danger coefficients are pretty high. Because 3 known non-conspirators are in these suspects, the rate of making mistakes is 12.5%, which is higher to the result of requirement 1.2)ComparisonTo research the effect of changing the number of criminal topics and conspirators to results, we decide to do an additional research about their effect.We separate the change of topics and crimes’numbers, analysis result’s changes of only one factor:In order to analyze the change between requirement 1 and 2, we choose those people whose rank has a big change over 30.Reference: the node.1st result: the part of the requirement1’s priority list.2nd result: the part of the requirement2’s priority list.3rd result: the priority’s changes of requirement 1 and 2.After investigate these people, we find out the topics about them isn’t close connected with node#0. Thus, the change of node#0 does not make a great effect on their change.However, there are more than a half of people who talk about topic1. According to the analysis, we find the topic1 has a great effect on their change. The topic1 is more important to node#0.Thus; we can do an assumption that the decision of topics has bigger effect on the decision of the personal identity and decide to do a research in the following content.Model IIOverviewAccording to requirement3, we will take the text analysis into account to enhance our model. In the paper, text analysis is presented as a paradigm for syntactic-semantic analysis of natural language. The main characteristics of this approach are: the vectors of messages about keywords, semanteme and question formation. In like manner, we need get three vectors of topics. Then, we utilize similarity to separate every message to corresponding topics. Finally, we evaluate these effects of text analysis by model I.Model BuiltStep.1PretreatmentIn this step, we need conclude relatively accurate topics by keywords in messages. Not only builds a database about topics, but also builds a small database for adjusting the topic classification of messages. The small database for adjusting is used for studying possible interpersonal relation between criminal suspects, i. e. Bob always use positive and supportive words to comment topics and things about Jerry, and then we think Bob’s messages are closely connected with topics about Jerry. [5] At first, we need to count up how many keywords in the whole messages.Text analysis is word-oriented, i.e., the word plays the central role in language understanding. So we avoid stipulating a grammar in the traditional sense and focus on the concept of word. During the analysis of all words in messages, we ignore punctuation, some simple word such as “is” and “the”, and extract relative importantwords.Then, a statistics will be completed about how many times every important word occurs. We will make a priority list and choose the top part of these words.Finally, according to some messages, we will turn these keywords into relatively complete topics.Step.2Syncopate sentenceWe will make a depth research to every sentence in messages by running program In the beginning, we can utilize the same way in step1 to syncopate sentence, deriving every message’s keywords. We decide create a vector about keywords: = () (m is the number keywords in everymessage)For improving the accuracy and relativity of our keywords, we decide to build a vector that shows every keyword’s synonyms, antonym.= () (1<k<m, p is the number of correlative words)According to primary analysis, we can find some important interpersonal relations between criminal suspects, i.e. Bob is closely connected with Jerry, then we can build a vector about interpersonal relation.= () (n is the number of relationships in one sentence )Step.3Intelligent matchingIn order to improve the accuracy of our disaggregated model, we use three vectors to do intelligent matching.Every message has three vectors:. Similarly, every topic alsohas three vectors.At last, we can do an intelligent matching to classify. [6]Step.4Using CPMAfter deriving new the classification of messages, we will make full use of new topics to calculate every one’s criticality.Result and AnalysisAfter calculating the 10 people example, we derive new topics. By verifying the topics’ contained initial information, we can evaluate the effect of models.The results of model II show our topics contain 78.8% initial information, better than former 5 topics’ 57.7%.T hus, new topics contain more initial information. Meanwhile, we build a database about interpersonal relation, and using it to optimize the results of everyone’s criminal possibility.Table 3#node primary new #node primary new1 0 0.065 6 0.342 0.2652 0.342 0.693 7 0.891 0.9123 0.713 0.562 8 0.423 0.354 1 1 9 0.334 0.7235 0.823 0.853 10 0.125 0.15 The results of model I can identify the two shadowy conspirators, Bob and Inez. In the table, the rate of fault is becoming smaller.According to Table11, we can derive some information:1.Analysis the danger coefficient of two people, Bob and Inez. Bob is theperson who self-admitted his involvement in a plan bargain for a reducedsentence. His data changes from 0.342 to 0.693. And Inez is the person whogot off, his data changes from 0.334 to 0.723. The models can identify thetwo shadowy people.2.Carol, the person who was later dropped his data changes from 0.713 to0.562. Although it still has a relatively high danger coefficient, the resultsare enhancing by our models.3.The distance between high degree people and low degree become bigger, itpresents the models would more distinctly identify conspirators andnon-conspirators.Thus, the models are more accurate and effective.ConclusionsTechnical summaryWe bring out a whole model about how to extract and analysis plentiful network information, and finally solve the classification problems. Four steps are used to make the classification problem easier.1)According known conspirators and correlative information, use resemblingnetwork crawler to extract what we may need information and messages.[7]2)Using the second model to analysis and classify these messages and text, getimportant topics.3)Using the first model to calculate everyone’s criminal possibility.4)Using an interpersonal relation database derived by step2 to optimize theresults. [8]Strengths and WeaknessesStrengths:1）We analyze the danger coefficient of topics and people by using different characteristics to describe them. Its results have a margin of error of 10percentage points. That the Models work well.2）In the semantic analysis, in addition to obtain topics from messages in social network, we also extract the relationships of people and adjust the final resultimprove the model.3）We use 4 characteristics to describe people’s danger coefficient. SVM has a great advantage in classification by small characteristics. Using SVM to classify the unknown people and its result is good.Weakness：1）For the special people, such as spy and criminal researcher, the model works not so well.2）We can determine some criminals by topics; at the same time we can also use the new criminals to adjust the topics. The two react upon each other. We canexpect to cycle through several times until the topics and criminals are stable.However we only finish the first cycle.3）For the semantic analysis model we have established, we just test and verify in the example (social network of 10 people). In the condition of large social network, the computational complexity will become greater, so the classify result is still further to be surveyed.ExtensionAccording to our analysis, not only can our model be applied to analyze criminal gangs, but also applied to similar network models, such as cells in a biological network, safe pages in Internet and so on. For the pages’ classification in Internet, our model would make a contribution. In the following, we will talk about how to utilize [9] Our model in pages’ classification.First, according to the unsafe page we use the network crawler and Hyperlink to find the pages’content and the connection between each page. Second, extract the messages and the relationships between pages by Model II. Third, according to the available information, we can obtain the pages’priority list about security and the discriminate line separating safe pages and the unsafe pages by Model I. Finally we use the pages’ relationships to adjust the result.Reference1. http://books.google.pl/books?id=CURaAAAAYAAJ&hl=zh-CN2012.2. AHP./wiki/%E5%B1%82%E6%AC%A1%E5%88%86%E6%9E%90%E6%B 3%95.3. Schaller, J. and J.M.S. Valente, Minimizing the weighted sum of squared tardiness on a singlemachine. Computers & Operations Research, 2012. 39(5): p. 919-928.4. Frahm, K.M., B. Georgeot, and D.L. Shepelyansky, Universal emergence of PageRank.Journal of Physics a-Mathematical and Theoretical, 2011. 44(46).5. Park, S.-B., J.-G. Jung, and D. Lee, Semantic Social Network Analysis for HierarchicalStructured Multimedia Browsing. Information-an International Interdisciplinary Journal, 2011.14(11): p. 3843-3856.6. Yi, J., S. Tang, and H. Li, Data Recovery Based on Intelligent Pattern Matching.ChinaCommunications, 2010. 7(6): p. 107-111.7. Nath, R. and S. Bal, A Novel Mobile Crawler System Based on Filtering off Non-ModifiedPages for Reducing Load on the Network.International Arab Journal of Information Technology, 2011. 8(3): p. 272-279.8. Xiong, F., Y. Liu, and Y. Li, Research on Focused Crawler Based upon Network Topology.Journal of Internet Technology, 2008. 9(5): p. 377-380.9. Huang, D., et al., MyBioNet: interactively visualize, edit and merge biological networks on theWeb. Bioinformatics, 2011. 27(23): p. 3321-3322.AppendixTable 4requirement 1topic danger topic danger topic danger topic danger7 1.65 4 0.78 5 0.47 8 0.1713 1.61 10 0.77 15 0.46 14 0.1711 1.60 12 0.47 9 0.19 6 0.141 0.812 0.473 0.18requirement 2topic danger topic danger topic danger topic danger1 0.402 0.26 15 0.15 14 0.117 0.37 9 0.23 8 0.15 3 0.0913 0.37 10 0.21 5 0.14 6 0.0611 0.30 12 0.18 4 0.12Table 5requirement 1#node danger #node danger #node danger #node danger 21 0.74 22 0.19 0 0.13 23 0.03 67 0.69 4 0.19 40 0.13 72 0.03 54 0.61 33 0.19 36 0.13 62 0.03 81 0.49 47 0.19 11 0.12 51 0.02 7 0.47 41 0.19 69 0.12 57 0.02 3 0.37 28 0.18 29 0.12 64 0.02 49 0.36 16 0.18 12 0.11 71 0.02 43 0.36 31 0.17 25 0.11 74 0.01 10 0.32 37 0.17 82 0.11 58 0.01 18 0.29 27 0.16 60 0.10 59 0.01 34 0.29 45 0.16 42 0.10 70 0.00 48 0.28 50 0.16 65 0.09 53 0.00 20 0.27 24 0.16 9 0.09 76 0.00 15 0.27 44 0.16 5 0.09 61 0.00 17 0.26 38 0.16 66 0.09 75 -0.01 2 0.23 13 0.16 26 0.08 77 -0.01 32 0.23 35 0.15 39 0.06 55 -0.02 30 0.20 1 0.15 80 0.04 68 -0.02 73 0.20 46 0.15 78 0.04 52 -0.0319 0.20 8 0.14 56 0.03 63 -0.03 14 0.19 6 0.14 79 0.03requirement 2#node danger #node danger #node danger #node danger 0 0.39881137 75 0.1757106 47 0.1090439 11 0.0692506 21 0.447777778 52 0.1749354 71 0.1089147 4 0.0682171 67 0.399047158 38 0.1738223 82 0.1088594 42 0.0483204 54 0.353754153 10 0.1656977 14 0.1079734 65 0.046124 81 0.325736434 19 0.1559173 27 0.1060724 60 0.0459948 2 0.306054289 40 0.1547065 23 0.105814 39 0.0286822 18 0.303178295 30 0.1517626 5 0.1039406 62 0.0245478 66 0.28372093 80 0.145155 8 0.10228 78 0.0162791 7 0.279870801 24 0.1447674 73 0.1 56 0.0160207 63 0.261886305 70 0.1425711 50 0.0981395 64 0.0118863 68 0.248514212 29 0.1425562 26 0.097213 72 0.011369548 0.239668277 45 0.1374667 1 0.0952381 79 0.009302349 0.238076781 37 0.1367959 69 0.0917313 51 0.0056848 34 0.232614868 17 0.1303064 33 0.0906977 57 0.0056848 3 0.225507567 6 0.1236221 31 0.0905131 74 0.0054264 35 0.222435188 22 0.1226934 36 0.0875452 76 0.005168 77 0.214470284 13 0.1222868 41 0.0822997 53 0.0028424 20 0.213718162 44 0.115007 46 0.0749354 58 0.0015504 43 0.204328165 12 0.1121447 28 0.0748708 59 0.0015504 32 0.193311469 15 0.1121447 16 0.074234 61 0.0007752 55 0.182687339 9 0.1117571 25 0.0701292Table 6requirement 1#node leader #node leader #node leader #node leader 15 0.1368 49 0.0481 7 0.0373 19 0.0089 14 0.0988 4 0.0423 21 0.0357 32 0.0073 34 0.0951 10 0.0422 18 0.029 22 0.0059 30 0.0828 67 0.0421 48 0.0236 81 0.0053 17 0.0824 54 0.0377 20 0.0232 73 043 0.0596 3 0.0377 2 0.0181 33 0requirement 2#node leader #node leader #node leader #node leader 21 0.0981309 7 0.0714406 54 0.0526831 43 0.01401872 0.0942899 34 0.0707246 32 0.0464614 81 0.00977763 0.0916127 0 0.0706746 18 0.041114248 0.0855984 20 0.0658119 68 0.028532867 0.0782211 49 0.0561665 35 0.024741。
美赛论文模版
摘要：第一段：写论文解决什么问题1．问题的重述a. 介绍重点词开头：例1：“Hand move” irrigation, a cheap but labor-intensive system used on small farms, consists of a movable pipe with sprinkler on top that can be attached to a stationary main.例2:……is a real-life common phenomenon with many complexi t ies.例3：An (effective plan) is crucial to………b. 直接指出问题：例1：We find the optimal number of tollbooths in a highway toll-plaza for a given number of highway lanes: the number of tollbooths that minimizes average delay experienced by cars.例2：A brand-new university needs to balance the cost of information technology security measures wi t h the potential cost of attacks on its systems.例3：We determine the number of sprinklers to use by analyzing the energy and motion of water in the pipe and examining the engineering parameters of sprinklers available in the market.例4: After mathematically analyzing the …… problem, our modeling group would like to present our conclusions, strategies, (and recommendations )to the …….例5：Our goal is... that (mini mizes the time )……….2．解决这个问题的伟大意义反面说明。
美赛数学建模模板
摘要：第一段：写论文解决什么问题1．问题的重述a. 介绍重点词开头：例1：“Hand move” irrigation, a cheap but labor-intensive system used on small farms, consists of a movable pipe with sprinkler on top that can be attached to a stationary main.例2:……is a real-life common phenomenon with many complexities.例3：An (effective plan) is crucial to………b. 直接指出问题：例 1：We find the optimal number of tollbooths in a highway toll-plaza for a given number of highway lanes: the number of tollbooths that minimizes average delay experienced by cars.例2：A brand-new university needs to balance the cost of information technology security measures with the potential cost of attacks on its systems.例3：We determine the number of sprinklers to use by analyzing the energy and motion of water in the pipe and examining the engineering parameters of sprinklers available in the market.例4: After mathematically analyzing the …… problem, our modeling group would like to present our conclusions, strategies, (and recommendations )to the …….例5：Our goa l is... that (minimizes the time )……….2．解决这个问题的伟大意义反面说明。
美国数学建模论文格式
Journal Citation(to be inserted by the publisher)Copyright by Trans Tech PublicationsYour Paper's Title Starts Here:Please Centeruse Arial14First Author1,Second Author2and Others3(use Arial14)1Full address of first author,including country,email(use Arial11)2Full address of second author,including country,email3List all distinct addresses in the same wayKeywords::List the keywords covered in your paper.These keywords will also be used by the Keywordspublisher to produce a keyword index.(use Arial11)For the rest of the paper,please use Times New Roman12Abstract.This document explains and demonstrates how to prepare your camera-ready manuscript for Trans Tech Publications.The best is to read these instructions and follow the outline of this text. The text area for your manuscript must be17cm wide and25cm high(6.7and9.8inches,resp.). Do not place any text outside this e good quality,white paper of approximately21x29cm or8x11inches.Your manuscript will be reduced by approximately20%by the publisher.Please keep this in mind when designing your figures and tables etc.IntroductionAll manuscripts must be in English.Please keep a second copy of your manuscript in your office (just in case anything gets lost in the mail).When receiving the manuscript,we assume that the corresponding authors grant us the copyright to use the manuscript for the book or journal in question.Should authors use tables or figures from other Publications,they must ask the corresponding publishers to grant them the right to publish this material in their paper.Use italic for emphasizing a word or phrase.Do not use boldface typing or capital letters except for section headings(cf.remarks on section headings,below).Use a laser printer,not a matrix dot printer.Organization of the TextSection Headings.The section headings are in boldface capital and lowercase letters.Second level headings are typed as part of the succeeding paragraph(like the subsection heading of this paragraph).Page Numbers.Do not print page numbers:Please number each sheet slightly in the left corner near the bottom(outside the typing area)with a light blue pencil.Footnotes.Footnotes1should be single spaced and separated from the text.Ideally,footnotes appear on the page of their reference,and are placed at the foot of the text,separated from the text by a horizontal line.Tables.Tables(refer with:Table1,Table2,...)should be presented as part of the text,but in such a way as to avoid confusion with the text.A descriptive title should be placed above each table. The caption should be self-contained and placed below or beside the table.Units in tables should be given in square brackets[meV].If square brackets are not available,use curly{meV}or standard brackets(meV).1This is a footnote2Title of Publication(to be inserted by the publisher)Figures.Figures(refer with:Fig.1,Fig.2,...)also should be presented as part of the text, leaving enough space so that the capt-ion will not be confused with the text.The caption should be self-contained and placed below or beside the figure.Generally,only original drawings or photographic reproductions are acceptable.Only very good photocopies are acceptable.Utmost care must be taken to insert the figures in correct alignment with the text.Half-tone pictures should be in the form of glossy prints.If possible,please include your figures as graphic images in the electronic version.If TTP is required to scan and insert images,please keep the following points in mind:(a)the allotted space(for inserting illustrations)must exactly match the space made available inthe camera-ready version,so that the electronic version is identical to the hard copy with regard to page and line breaks.(b)the required positioning of any high-quality separate illustration must be clearly indicated onits reverse side.The size of the illustrations must exactly match the space left in the camera-ready manuscript.Equations.Equations(refer with:Eq.1,Eq.2,...)should be indented5mm(0.2").There should be one line of space above the equation and one line of space below it before the text continues.The equations have to be numbered sequentially,and the number put in parentheses at the right-hand edge of the text.Equations should be punctuated as if they were an ordinary part of the text.Punctuation appears after the equation but before the equation number,e.g.c2=a2+b2.(1)Literature ReferencesReferences are cited in the text just by square brackets[1].(If square brackets are not available, slashes may be used instead,e.g./2/.)Two or more references at a time may be put in one set of brackets[3,4].The references are to be numbered in the order in which they are cited in the text and are to be listed at the end of the contribution under a heading References,see our example below.SummaryOn your floppy disk,please indicate the format and word processor used.Please also provide your phone number,fax number and e_mail address for rapid communication with the publisher(will not be published).Please always send your disk along with a hard copy that must match the disk's content exactly.If you follow the foregoing,your paper will conform to the requirements of the publisher and facilitate a problem-free publication process.References[1]Dj.M.Maric,P.F.Meier and S.K.Estreicher:Mater.Sci.Forum Vol.83-87(1992),p.119[2]M.A.Green:High Efficiency Silicon Solar Cells(Trans Tech Publications,Switzerland1987).This document is available on the web at /download **Please submit your paper in hardcopy and also electronically to the conference editor.。
美赛论文优秀模版
For office use onlyT1________________ T2________________ T3________________ T4________________ Team Control Number11111Problem ChosenABCDFor office use onlyF1________________F2________________F3________________F4________________ 2015Mathematical Contest in Modeling (MCM/ICM) Summary Sheet In order to evaluate the performance of a coach, we describe metrics in five aspects: historical record, game gold content, playoff performance, honors and contribution to the sports. Moreover, each aspect is subdivided into several secondary metrics. Take playoff performance as example, we collect postseason result (Sweet Sixteen, Final Four, etc.) per year from NCAA official website, Wikimedia and so on.First, ****grade.To eval*** , in turn, are John Wooden, Mike Krzyzewski, Adolph Rupp, Dean Smith and Bob Knight.Time line horizon does make a difference. According to turning points in NCAA history, we divide the previous century into six periods with different time weights which lead to the change of ranking.We conduct sensitivity analysis on FSE to find best membership function and calculation rule. Sensitivity analysis on aggregation weight is also performed. It proves AM performs better than single model. As a creative use, top 3 presidents (U.S.) are picked out: Abraham Lincoln, George Washington, Franklin D. Roosevelt.At last, the strength and weakness of our mode are discussed, non-technical explanation is presented and the future work is pointed as well.Key words: Ebola virus disease; Epidemiology; West Africa; ******ContentsI. Introduction (2)1.1 (2)1.2 (2)1.3 (2)1.4 (2)1.5 (2)1.6 (2)II. The Description of the Problem (2)2.1 How do we approximate the whole course of paying toll? (2)2.2 How do we define the optimal configuration? (2)2.3 The local optimization and the overall optimization (3)2.4 The differences in weights and sizes of vehicles (3)2.5 What if there is no data available? (3)III. Models (3)3.1 Basic Model (3)3.1.1 Terms, Definitions and Symbols (3)3.1.2 Assumptions (3)3.1.3 The Foundation of Model (4)3.1.4 Solution and Result (4)3.1.5 Analysis of the Result (4)3.1.6 Strength and Weakness (4)3.2 Improved Model (4)3.2.1 Extra Symbols (4)3.2.2 Additional Assumptions (5)3.2.3 The Foundation of Model (5)3.2.4 Solution and Result (5)3.2.5 Analysis of the Result (5)3.2.6 Strength and Weakness (6)IV. Conclusions (6)4.1 Conclusions of the problem (6)4.2 Methods used in our models (6)4.3 Applications of our models (6)V. Future Work (6)5.1 Another model (6)5.1.1 The limitations of queuing theory (6)5.1.2 (6)5.1.3 (7)5.1.4 (7)5.2 Another layout of toll plaza (7)5.3 The newly- adopted charging methods (7)VI. References (7)VII. Appendix (8)I. IntroductionIn order to indicate the origin of the toll way problems, the following background is worth mentioning.1.11.21.31.41.51.6II. The Description of the Problem2.1 How d o we approximate the whole course of paying toll?●●●●1) From the perspective of motorist:2) From the perspective of the toll plaza:3) Compromise:2.3 The l ocal optimization and the overall optimization●●●Virtually:2.4 The differences in weights and sizes of vehicl es2.5 What if there is no data availabl e?III. Models3.1 Basic Model3.1.1 Terms, Definitions and SymbolsThe signs and definitions are mostly generated from queuing theory.●●●●●3.1.2 Assumptions●●●●3.1.3 The Foundation of Model1) The utility function●The cost of toll plaza:●The loss of motorist:●The weight of each aspect:●Compromise:2) The integer programmingAccording to queuing theory, we can calculate the statistical properties as follows.3)The overall optimization and the local optimization●The overall optimization:●The local optimization:●The optimal number of tollbooths:3.1.4 Solution and Result1) The solution of the integer programming:2) Results:3.1.5 Analysis of the Result●Local optimization and overall optimization:●Sensitivity: The result is quite sensitive to the change of the three parameters●Trend:●Comparison:3.1.6 Strength and Weakness●Strength: In despite of this, the model has proved that . Moreover, we have drawnsome useful conclusions about . T he model is fit for, such as●Weakness: This model just applies to . As we have stated, .That’s just whatwe should do in the improved model.3.2 Improved Model3.2.1 Extra Symbols●●●●3.2.2 Additional Assumptions●●●Assumptions concerning the anterior process are the same as the Basic Model.3.2.3 The Foundation of Model1) How do we determine the optimal number?As we have concluded from the Basic Model,3.2.4 Solution and Result1) Simulation algorithmBased on the analysis above, we design our simulation arithmetic as follows.●Step1:●Step2:●Step3:●Step4:●Step5:●Step6:●Step7:●Step8:●Step9:2) Flow chartThe figure below is the flow chart of the simulation.3) Solution3.2.5 Analysis of the Result3.2.6 Strength and Weakness●Strength: The Improved Model aims to make up for the neglect of . The resultseems to declare that this model is more reasonable than the Basic Model and much more effective than the existing design.●Weakness: . Thus the model is still an approximate on a large scale. This hasdoomed to limit the applications of it.IV. Conclusions4.1 Conclusions of the probl em●●●4.2 Methods used in our mod els●●●4.3 Applications of our mod els●●●V. Future Work5.1 Another model5.1.1 The limitations of queuing theory5.1.25.1.41)●●●●2)●●●3)●●●4)5.2 Another layout of toll plaza5.3 The newly- ad opted charging methodsVI. References[1][2][4]VII. Appendix。
建模美赛获奖范文
建模美赛获奖范文标题：《探索与创新：建模美赛获奖作品范文解析》建模美赛（MCM/ICM）是全球大学生数学建模竞赛的盛事，每年都吸引了众多优秀的学生参与。
在这个舞台上，获奖作品往往展现了卓越的数学建模能力、创新思维和问题解决技巧。
本文将解析一份获奖范文，带您领略建模美赛获奖作品的风采。
一、背景与问题阐述（此处详细描述范文所针对的问题背景、研究目的和意义，以及问题的具体阐述。
）二、模型建立与假设1.模型分类与选择：根据问题特点，范文选择了适当的模型进行研究和分析。
2.假设条件：明确列出建模过程中所做的主要假设，并解释其合理性。
三、模型求解与结果分析1.数据收集与处理：介绍范文中所用数据来源、处理方法及有效性验证。
2.模型求解：详细阐述模型的求解过程，包括算法选择、计算步骤等。
3.结果分析：对求解结果进行详细分析，包括图表展示、敏感性分析等。
四、模型优化与拓展1.模型优化：针对原模型存在的问题，范文提出了相应的优化方案。
2.拓展研究：对模型进行拓展，探讨其在其他领域的应用和推广价值。
五、结论与建议1.结论总结：概括范文的研究成果，强调其创新点和贡献。
2.实践意义：分析建模结果在实际问题中的应用价值和意义。
3.建议：针对问题解决，提出具体的建议和措施。
六、获奖亮点与启示1.创新思维：范文在模型选择、求解方法等方面展现出创新性。
2.严谨论证：文章结构清晰，逻辑严密，数据充分，论证有力。
3.团队合作：建模美赛强调团队协作，范文体现了成员间的紧密配合和分工合作。
总结：通过分析这份建模美赛获奖范文，我们可以学到如何从问题背景出发，建立合理的模型，进行严谨的求解和分析，以及如何优化和拓展模型。
同时，也要注重创新思维和团队合作，才能在建模美赛中脱颖而出。
美赛数学建模比赛论文资料材料模板
The Keep-Right-Except-To-Pass RuleSummaryAs for the first question, it provides a traffic rule of keep right except to pass, requiring us to verify its effectiveness. Firstly, we define one kind of traffic rule different from the rule of the keep right in order to solve the problem clearly; then, we build a Cellular automaton model and a Nasch model by collecting massive data; next, we make full use of the numerical simulation according to several influence factors of traffic flow; At last, by lots of analysis of graph we obtain, we indicate a conclusion as follow: when vehicle density is lower than 0.15, the rule of lane speed control is more effective in terms of the factor of safe in the light traffic; when vehicle density is greater than 0.15, so the rule of keep right except passing is more effective In the heavy traffic.As for the second question, it requires us to testify that whether the conclusion we obtain in the first question is the same apply to the keep left rule. First of all, we build a stochastic multi-lane traffic model; from the view of the vehicle flow stress, we propose that the probability of moving to the right is 0.7and to the left otherwise by making full use of the Bernoulli process from the view of the ping-pong effect, the conclusion is that the choice of the changing lane is random. On the whole, the fundamental reason is the formation of the driving habit, so the conclusion is effective under the rule of keep left.As for the third question, it requires us to demonstrate the effectiveness of the result advised in the first question under the intelligent vehicle control system. Firstly, taking the speed limits into consideration, we build a microscopic traffic simulator model for traffic simulation purposes. Then, we implement a METANET model for prediction state with the use of the MPC traffic controller. Afterwards, we certify that the dynamic speed control measure can improve the traffic flow .Lastly neglecting the safe factor, combining the rule of keep right with the rule of dynamical speed control is the best solution to accelerate the traffic flow overall.Key words：Cellular automaton model Bernoulli process Microscopic traffic simulator model The MPC traffic controlContentContent (2)1. Introduction (3)2. Analysis of the problem (3)3. Assumption (3)4. Symbol Definition (3)5. Models (3)5.1 Building of the Cellular automaton model (3)5.1.1 Verify the effectiveness of the keep right except to pass rule (4)5.1.2 Numerical simulation results and discussion (5)5.1.3 Conclusion (8)5.2 The solving of second question (8)5.2.1 The building of the stochastic multi-lane traffic model (8)5.2.2 Conclusion (8)5.3 Taking the an intelligent vehicle system into a account (8)5.3.1 Introduction of the Intelligent Vehicle Highway Systems (9)5.3.2 Control problem (9)5.3.3 Results and analysis (9)5.3.4 The comprehensive analysis of the result (9)6. Improvement of the model (10)6.1 strength and weakness (10)6.1.1 Strength (10)6.1.2 Weakness (10)6.2 Improvement of the model (10)7. Reference (12)1. IntroductionAs is known to all, it ’s essential for us to drive automobiles, thus the driving rules is crucial important. In many countries like USA, China, drivers obey the rules which called “The Keep-Right-Except-To-Pass (that is, when driving automobiles, the rule requires drivers to drive in the right-most unless they are passing another vehicle)”.2. Analysis of the problemFor the first question, we decide to use the Cellular automaton to build models, then analyze the performance of this rule in light and heavy traffic. Firstly, we mainly use the vehicle density to distinguish the light and heavy traffic; secondly, we consider the traffic flow and safe as the represent variable which denotes the light or heavy traffic; thirdly, we build and analyze a Cellular automaton model; finally, we judge the rule through two different driving rules, and then draw conclusions.3. AssumptionIn order to streamline our model we have made several key assumptions● The highway of double row three lanes that we study can representmulti-lane freeways.● The data that we refer to has certain representativeness and descriptive● Operation condition of the highway not be influenced by blizzard or accidental factors ● Ignore the driver's own abnormal factors, such as drunk driving and fatigue driving ● The operation form of highway intelligent system that our analysis can reflectintelligent system● In the intelligent vehicle system, the result of the sampling data has high accuracy.4. Symbol Definitioni The number of vehiclest The time5. ModelsBy analyzing the problem, we decided to propose a solution with building a cellular automaton model.5.1 Building of the Cellular automaton modelThanks to its simple rules and convenience for computer simulation, cellular automaton model has been widely used in the study of traffic flow in recent years.Let )(t x i be the position of vehicle i at time t , )(t v i be the speed of vehicle i at time t ,p be the random slowing down probability, and R be the proportion of trucks and buses, the distance between vehicle i and the front vehicle at time t is:1)()(1--=-t x t x gap i i i , if the front vehicle is a small vehicle.3)()(1--=-t x t x gap i i i , if the front vehicle is a truck or bus.5.1.1 Verify the effectiveness of the keep right except to pass ruleIn addition, according to the keep right except to pass rule, we define a new rule called: Control rules based on lane speed. The concrete explanation of the new rule as follow:There is no special passing lane under this rule. The speed of the first lane (the far left lane) is 120–100km/h (including 100 km/h)；the speed of the second lane (the middle lane) is 100–80km8/h (including80km/h)；the speed of the third lane (the far right lane) is below 80km/ h. The speeds of lanes decrease from left to right.● Lane changing rules based lane speed controlIf vehicle on the high-speed lane meets control v v <, ),1)(min()(max v t v t gap i f i +≥, safe b i gap t gap ≥)(, the vehicle will turn into the adjacent right lane, and the speed of the vehicle after lane changing remains unchanged, where control v is the minimum speed of the corresponding lane.● The application of the Nasch model evolutionLet d P be the lane changing probability (taking into account the actual situation that some drivers like driving in a certain lane, and will not take the initiative to change lanes), )(t gap f i indicates the distance between the vehicle and the nearest front vehicle, )(t gap b i indicates the distance between the vehicle and the nearest following vehicle. In this article, we assume that the minimum safe distance gap safe of lane changing equals to the maximum speed of the following vehicle in the adjacent lanes.● Lane changing rules based on keeping right except to passIn general, traffic flow going through a passing zone (Fig. 5.1.1) involves three processes: the diverging process (one traffic flow diverging into two flows), interacting process (interacting between the two flows), and merging process (the two flows merging into one)[4].Fig.5.1.1 Control plan of overtaking process(1) If vehicle on the first lane (passing lane) meets ),1)(min()(max v t v t gap i f i +≥ and safe b i gap t gap ≥)(, the vehicle will turn into the second lane, the speed of the vehicle after lane changing remains unchanged.5.1.2 Numerical simulation results and discussionIn order to facilitate the subsequent discussions, we define the space occupation rate as L N N p truck CAR ⨯⨯+=3/)3(, where CAR N indicates the number of small vehicles on the driveway,truck N indicates the number of trucks and buses on the driveway, and L indicates the total length of the road. The vehicle flow volume Q is the number of vehicles passing a fixed point per unit time,T N Q T /=, where T N is the number of vehicles observed in time duration T .The average speed ∑∑⨯=T it i a v T N V 11)/1(, t i v is the speed of vehicle i at time t . Take overtaking ratio f p as the evaluation indicator of the safety of traffic flow, which is the ratio of the total number of overtaking and the number of vehicles observed. After 20,000 evolution steps, and averaging the last 2000 steps based on time, we have obtained the following experimental results. In order to eliminate the effect of randomicity, we take the systemic average of 20 samples [5].Overtaking ratio of different control rule conditionsBecause different control conditions of road will produce different overtaking ratio, so we first observe relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions.(a) Based on passing lane control (b) Based on speed controlFig.5.1.3Fig.5.1.3Relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions.It can be seen from Fig. 5.1.3:(1) when the vehicle density is less than 0.05, the overtaking ratio will continue to rise with the increase of vehicle density; when the vehicle density is larger than 0.05, the overtaking ratio will decrease with the increase of vehicle density; when density is greater than 0.12, due to the crowding, it will become difficult to overtake, so the overtaking ratio is almost 0.(2) when the proportion of large vehicles is less than 0.5, the overtaking ratio will rise with the increase of large vehicles; when the proportion of large vehicles is about 0.5, the overtaking ratio will reach its peak value; when the proportion of large vehicles is larger than 0.5, the overtaking ratio will decrease with the increase of large vehicles, especially under lane-based control condition s the decline is very clear.Concrete impact of under different control rules on overtaking ratioFig.5.1.4Fig.5.1.4 Relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions. (Figures in left-hand indicate the passing lane control, figures in right-hand indicate thespeed control. 1f P is the overtaking ratio of small vehicles over large vehicles, 2f P is the overtaking ratio ofsmall vehicles over small vehicles, 3f P is the overtaking ratio of large vehicles over small vehicles, 4f P is the overtaking ratio of large vehicles over large vehicles.).It can be seen from Fig. 5.1.4:(1) The overtaking ratio of small vehicles over large vehicles under passing lane control is much higher than that under speed control condition, which is because, under passing lane control condition, high-speed small vehicles have to surpass low-speed large vehicles by the passing lane, while under speed control condition, small vehicles are designed to travel on the high-speed lane, there is no low- speed vehicle in front, thus there is no need to overtake. ● Impact of different control rules on vehicle speedFig. 5.1.5 Relationships among vehicle density, proportion of large vehicles and average speed under different control conditions. (Figures in left-hand indicates passing lane control, figures in right-hand indicates speed control. a X is the average speed of all the vehicles, 1a X is the average speed of all the small vehicles, 2a X is the average speed of all the buses and trucks.).It can be seen from Fig. 5.1.5:(1) The average speed will reduce with the increase of vehicle density and proportion of large vehicles.(2) When vehicle density is less than 0.15,a X ,1a X and 2a X are almost the same under both control conditions.● Effect of different control conditions on traffic flowFig.5.1.6Fig. 5.1.6Relationships among vehicle density, proportion of large vehicles and traffic flow under different control conditions. (Figure a1 indicates passing lane control, figure a2 indicates speed control, and figure b indicates the traffic flow difference between the two conditions.It can be seen from Fig. 5.1.6：(1) When vehicle density is lower than 0.15 and the proportion of large vehicles is from 0.4 to 1, the traffic flow of the two control conditions are basically the same.(2) Except that, the traffic flow under passing lane control condition is slightly larger than that of speed control condition.5.1.3 ConclusionIn this paper, we have established three-lane model of different control conditions, studied the overtaking ratio, speed and traffic flow under different control conditions, vehicle density and proportion of large vehicles.5.2 The solving of second question5.2.1 The building of the stochastic multi-lane traffic model5.2.2 ConclusionOn one hand, from the analysis of the model, in the case the stress is positive, we also consider the jam situation while making the decision. More specifically, if a driver is in a jam BP(situation, applying ))results with a tendency of moving to the right lane for this,2(xRdriver. However in reality, drivers tend to find an emptier lane in a jam situation. For this reason, we apply a Bernoulli process )7.0,2(B where the probability of moving to the right is 0.7and to the left otherwise, and the conclusion is under the rule of keep left except to pass, So, the fundamental reason is the formation of the driving habit.5.3 Taking the an intelligent vehicle system into a accountFor the third question, if vehicle transportation on the same roadway was fully under the control of an intelligent system, we make some improvements for the solution proposed by usto perfect the performance of the freeway by lots of analysis.5.3.1 Introduction of the Intelligent Vehicle Highway SystemsWe will use the microscopic traffic simulator model for traffic simulation purposes. The MPC traffic controller that is implemented in the Matlab needs a traffic model to predict the states when the speed limits are applied in Fig.5.3.1. We implement a METANET model for prediction purpose[14].5.3.2 Control problemAs a constraint, the dynamic speed limits are given a maximum and minimum allowed value. The upper bound for the speed limits is 120 km/h, and the lower bound value is 40 km/h. For the calculation of the optimal control values, all speed limits are constrained to this range. When the optimal values are found, they are rounded to a multiplicity of 10 km/h, since this is more clear for human drivers, and also technically feasible without large investments.5.3.3 Results and analysisWhen the density is high, it is more difficult to control the traffic, since the mean speed might already be below the control speed. Therefore, simulations are done using densities at which the shock wave can dissolve without using control, and at densities where the shock wave remains. For each scenario, five simulations for three different cases are done, each with a duration of one hour. The results of the simulations are reported in Table5.1, 5.2, 5.3.●Enforced speed limits●Intelligent speed adaptationFor the ISA scenario, the desired free-flow speed is about 100% of the speed limit. The desired free-flow speed is modeled as a Gaussian distribution, with a mean value of 100% of the speed limit, and a standard deviation of 5% of the speed limit. Based on this percentage, the influence of the dynamic speed limits is expected to be good[19].5.3.4 The comprehensive analysis of the resultFrom the analysis above, we indicate that adopting the intelligent speed control system can effectively decrease the travel times under the control of an intelligent system, in other words, the measures of dynamic speed control can improve the traffic flow.Evidently, under the intelligent speed control system, the effect of the dynamic speed control measure is better than that under the lane speed control mentioned in the first problem. Becauseof the application of the intelligent speed control system, it can provide the optimal speed limit in time. In addition, it can guarantee the safe condition with all kinds of detection device and the sensor under the intelligent speed system.On the whole, taking all the analysis from the first problem to the end into a account, when it is in light traffic, we can neglect the factor of safe with the help of the intelligent speed control system.Thus, under the state of the light traffic, we propose a new conclusion different from that in the first problem: the rule of keep right except to pass is more effective than that of lane speed control.And when it is in the heavy traffic, for sparing no effort to improve the operation efficiency of the freeway, we combine the dynamical speed control measure with the rule of keep right except to pass, drawing a conclusion that the application of the dynamical speed control can improve the performance of the freeway.What we should highlight is that we can make some different speed limit as for different section of road or different size of vehicle with the application of the Intelligent Vehicle Highway Systems.In fact, that how the freeway traffic operate is extremely complex, thereby, with the application of the Intelligent Vehicle Highway Systems, by adjusting our solution originally, we make it still effective to freeway traffic.6. Improvement of the model6.1 strength and weakness6.1.1 Strength●it is easy for computer simulating and can be modified flexibly to consider actual trafficconditions ,moreover a large number of images make the model more visual.●The result is effectively achieved all of the goals we set initially, meantime the conclusion ismore persuasive because of we used the Bernoulli equation.●We can get more accurate result as we apply Matlab.6.1.2 Weakness●The relationship between traffic flow and safety is not comprehensively analysis.●Due to there are many traffic factors, we are only studied some of the factors, thus ourmodel need further improved.6.2 Improvement of the modelWhile we compare models under two kinds of traffic rules, thereby we come to the efficiency of driving on the right to improve traffic flow in some circumstance. Due to the rules of comparing is too less, the conclusion is inadequate. In order to improve the accuracy, Wefurther put forward a kinds of traffic rules: speed limit on different type of cars.The possibility of happening traffic accident for some vehicles is larger, and it also brings hidden safe troubles. So we need to consider separately about different or specific vehicle types from the angle of the speed limiting in order to reduce the occurrence of traffic accidents, the highway speed limit signs is in Fig.6.1.Fig.6.1Advantages of the improving model are that it is useful to improve the running condition safety of specific type of vehicle while considering the difference of different types of vehicles. However, we found that the rules may be reduce the road traffic flow through the analysis. In the implementation it should be at the85V speed of each model as the main reference basis. Inrecent years, the85V of some researchers for the typical countries from Table 6.1[ 21]:Author Country ModelOttesen andKrammes2000America LCDCLDCVC⨯---=01.0012.057.144.10285Andueza2000 Venezuela].[308.9486.7)/894()/2795(25.9885curvehorizontalLDCRaRVT++--=].[tan819.27)/3032(69.10085gentLRVT+-=Jessen2001 America][00239.0614.0279.080.86185LSDADTGVVP--+=][00212.0432.010.7285NLSDADTVVP-+=Donnell2001 America22)2(8500724.040.10140.04.78TLGRV--+=22)3(85008369.048.10176.01.75TLGRV--+=22)4(8500810.069.10176.05.74TLGRV--+=22)5(8500934.008.21.83TLGV--=BucchiA.BiasuzziK.And SimoneA.2005 ItalyDCV124.0164.6685-=DCEV4.046.3366.5585--=Meanwhile, there are other vehicles driving rules such as speed limit in adverse weather conditions. This rule can improve the safety factor of the vehicle to some extent. At the same time, it limits the speed at the different levels.7. Reference[1] M. Rickert, K. Nagel, M. Schreckenberg, A. Latour, Two lane traffic simulations usingcellular automata, Physica A 231 (1996) 534–550.[20] J.T. Fokkema, Lakshmi Dhevi, Tamil Nadu Traffic Management and Control inIntelligent Vehicle Highway Systems,18(2009).[21] Yang Li, New Variable Speed Control Approach for Freeway. (2011) 1-66。
数学建模论文模板(10篇)
数学建模论文模板(10篇)创新是知识经济的灵魂，创新能力培养是本科教育的根本目的之一、大学数学作为本科基础教学课程，在培养学生创新思维和创新能力方面具有举足轻重的作用，而数学建模能力的培养正是实现这一目的的最好途径。
2.数学教学中渗透数学建模思想是大学数学教学的必然要求。
目前，高校中高等数学教学普遍存在内容多、课时少的问题，教师在教学中往往只注重理论知识的教学，忽视了知识的应用；只注重数学学科本身知识的讲解，不注重学科之间的结合，这样使学生体会不到数学的真正用处。
为了克服这一教学中的不足，应将数学建模思想融入大学数学教学中去，使学生具备扎实的数学理论基本功和数学技能的同时，更具备运用数学思想解决实际问题的创新能力和应用能力。
3.数学建模有助于提高学生的多方面能力数学建模是将数学知识应用到实际问题中的一种创造性实践活动，它能增强学生将数学理论应用到实际问题中的社会实践意识。
数学建模具有思维的灵活性和结论的不确定性，在解决实际问题时可以从不同的角度，采用不同的数学方法建立数学模型，因此，可以激发学生的想象力、观察力和创造力。
另外,在建模时往往需要查阅相关文献资料，从中吸取有用的信息用于建模，这无形之中拓宽了学生的知识面，培养了学生的科研能力。
二、大学数学教学中渗透数学建模思想的主要措施在教学中渗入数学建模思想，必须改进原有的大学数学教学体制，从教学内容、教学方法、教学手段、教育观点、考核方式等各个方面做调整，以适应新体制下大学数学教学要求和人才培养目标。
1.从教学内容上改进以促进数学建模思想的普及和深入。
科学合理地修订教学大纲和调整教学内容，适当增加数学建模以及数学实验的教学环节势在必行。
为了让学生了解数学和数学建模的思想和理念，我校主要从课堂上和课外两方面采取了一些措施，并取得了一定的成效。
（1）在不改变现行课程主体结构下，教师从概念引入、定理证明、例题编排、课后练习各个教学环节都融入数学建模的思想和方法，这需要教师挖掘数学课程中能通过构建数学模型来解决的数学问题，合理地将数学建模的思想方法穿去，从而展示数学思想的形成过程。
【完整解析】美赛-数学建模-写作模版(各部分)
Summary：clearly describe your approach to the problem and,most prominently,your most important conclusions.●Restatement and clarification of the problem:State in your own words what you aregoing to do.●Explain assumptions and rationale（principle）/justification:Emphasize the assumptionsthat bear on the problem.Clearly list all variables used in your model.●Include your model design and justification for type model used or developed.●Describe model testing and sensitivity analysis,including error analysis,etc.●Discuss the strengths and weaknesses of your model or approach摘要第一段：写论文解决什么问题.1．问题的重述a.介绍重点词开头：例1：“Hand move”irrigation,a cheap but labor-intensive system used on small farms,consists of a movable pipe with sprinkler on top that can be attached to a stationary main.例2:……is a real-life common phenomenon with many complexities.例3：An(effective plan)is crucial to………b.直接指出问题：例1：We find the optimal number of tollbooths in a highway toll-plaza for a given number of highway lanes:the number of tollbooths that minimizes average delay experienced by cars.我们找到了在给定XX的情况下最佳的……例2：A brand-new university needs to balance the cost of information technology security measures with the potential cost of attacks on its systems.XX需要具有B性能的C例3：We determine the number of sprinklers to use by analyzing the energy and motion of water in the pipe and examining the engineering parameters of sprinklers available in the market.我们通过分析参数B确定A，并且检验了现实情况C例4:After mathematically analyzing the……problem,our modeling group would like to present our conclusions,strategies,(and recommendations)to the…….在数学分析B后，我们的模型组将呈现了我们的结论和建议We begin by considering only the rigid recoil effects of the bat–ball col-LisionOur main goal is to understand the sweet spot.A secondary goal is tounderstand the differences between the sweet spots of different bat types.Because the collision happens on such a short time-scale(around1ms),we treat the bat as a free body.That is to say,we are not concerned with the batter’s hands exerting force on the bat that may be transferred to the ball....Our paper is organized as follows....例5：Our goal is...that(minimizes the time)……….2．解决这个问题的伟大意义反面说明。
美国大学生数学建模比赛的论文格式
ContentsⅠIntroduction (1)1.1Problem Background (1)1.2Previous Research (2)1.3Our Work (2)ⅡGeneral Assumptions (3)ⅢNotations and Symbol Description (3)3.1 Notations (4)3.2 Symbol Description (4)ⅣSpread of Ebola (5)4.1 Traditional Epidemic Model (5)4.1.1.The SEIR Model (5)4.1.2 (6)4.1.3 (6)4.2 Improved Model (7)4.2.1.The SEIHCR Model (8)4.2.2 (9)ⅤPharmaceutical Intervention (9)5.1 Total Quantity of the Medicine (10)5.1.1.Results from WHO Statistics (10)5.1.2.Results from SEIHCR Model (11)5.2 Delivery System (12)5.2.1.Locations of Delivery (13)5.2.2 (14)5.3 Speed of Manufacturing (15)ⅥOther Important Interventions (16)6.1 Safer Treatment of Corpses (17)6.2 Conclusion (18)ⅦControl and Eradication of Ebola (19)7.1 How Ebola Can Be Controlled (20)7.2 When Ebola Will Be Eradicated (21)ⅧSensitivity Analysis (22)8.1 Impact of Transmission Rate (23)8.2 Impact of the Incubation Priod (24)ⅨStrengths and Weaknesses (25)9.1 Strengths (26)9.2 Weaknesses (27)9.3 Future Work (28)Letter to the World Medical Association (30)References (31)ⅠIntroduction1.1.Promblem Background1.2.Previous Research1.3.Our WorkⅡGeneral Assumptions●●ⅢNotations and Symbol Description3.1. Notataions3.2. Symbol DescriptionSymbol DescriptionⅣSpread of Ebola4.1. Traditional Epidemic Model4.1.1. The SEIR Model4.1.2. Outbreak Data4.1.3. Reslts of the SEIR Model4.2. Improved Model4.2.1. The SEIHCR Model4.2.2. Choosing paametersⅤPharmaceutical Intervention 5.1. Total Quantity of the Medicine 5.1.1. Results from WHO Statistics5.2. Delivery System5.2.1. Locations of Delivery5.2.2. Amount of Delivery5.3. Speed of Manufacturong5.4. Medicine EfficacyⅥOther Important Interventions 6.1. Safer Treatment of Corpses6.2. ConclusionⅦControl and Eradication of Ebola 7.1. How Ebola Can Be Controlled7.2. When Ebola Will Be EradicatedⅧSensitivity Analysis8.1. Impact of Transmission Rate8.2. Impact of Incubation PeriodⅨStrengths and Weaknesses 9.1. Strengths●●●9.2. Weaknesses●●●9.3.Future WorkLetter to the World Medical AssociationTo whom it may concern,Best regards,Team #32150References ［1］［2］［3］［4］。
美国大学生数学建模竞赛 二等奖论文
The P roblem of R epeater C oordination SummaryThis paper mainly focuses on exploring an optimization scheme to serve all the users in a certain area with the least repeaters.The model is optimized better through changing the power of a repeater and distributing PL tones,frequency pairs ing symmetry principle of Graph Theory and maximum coverage principle,we get the most reasonable scheme.This scheme can help us solve the problem that where we should put the repeaters in general cases.It can be suitable for the problem of irrigation,the location of lights in a square and so on.We construct two mathematical models(a basic model and an improve model)to get the scheme based on the relationship between variables.In the basic model,we set a function model to solve the problem under a condition that assumed.There are two variables:‘p’(standing for the power of the signals that a repeater transmits)and‘μ’(standing for the density of users of the area)in the function model.Assume‘p’fixed in the basic one.And in this situation,we change the function model to a geometric one to solve this problem.Based on the basic model,considering the two variables in the improve model is more reasonable to most situations.Then the conclusion can be drawn through calculation and MATLAB programming.We analysis and discuss what we can do if we build repeaters in mountainous areas further.Finally,we discuss strengths and weaknesses of our models and make necessary recommendations.Key words:repeater maximum coverage density PL tones MATLABContents1.Introduction (3)2.The Description of the Problem (3)2.1What problems we are confronting (3)2.2What we do to solve these problems (3)3.Models (4)3.1Basic model (4)3.1.1Terms,Definitions,and Symbols (4)3.1.2Assumptions (4)3.1.3The Foundation of Model (4)3.1.4Solution and Result (5)3.1.5Analysis of the Result (8)3.1.6Strength and Weakness (8)3.1.7Some Improvement (9)3.2Improve Model (9)3.2.1Extra Symbols (10)Assumptions (10)3.2.2AdditionalAdditionalAssumptions3.2.3The Foundation of Model (10)3.2.4Solution and Result (10)3.2.5Analysis of the Result (13)3.2.6Strength and Weakness (14)4.Conclusions (14)4.1Conclusions of the problem (14)4.2Methods used in our models (14)4.3Application of our models (14)5.Future Work (14)6.References (17)7.Appendix (17)Ⅰ.IntroductionIn order to indicate the origin of the repeater coordination problem,the following background is worth mentioning.With the development of technology and society,communications technology has become much more important,more and more people are involved in this.In order to ensure the quality of the signals of communication,we need to build repeaters which pick up weak signals,amplify them,and retransmit them on a different frequency.But the price of a repeater is very high.And the unnecessary repeaters will cause not only the waste of money and resources,but also the difficulty of maintenance.So there comes a problem that how to reduce the number of unnecessary repeaters in a region.We try to explore an optimized model in this paper.Ⅱ.The Description of the Problem2.1What problems we are confrontingThe signals transmit in the way of line-of-sight as a result of reducing the loss of the energy. As a result of the obstacles they meet and the natural attenuation itself,the signals will become unavailable.So a repeater which just picks up weak signals,amplifies them,and retransmits them on a different frequency is needed.However,repeaters can interfere with one another unless they are far enough apart or transmit on sufficiently separated frequencies.In addition to geographical separation,the“continuous tone-coded squelch system”(CTCSS),sometimes nicknamed“private line”(PL),technology can be used to mitigate interference.This system associates to each repeater a separate PL tone that is transmitted by all users who wish to communicate through that repeater. The PL tone is like a kind of password.Then determine a user according to the so called password and the specific frequency,in other words a user corresponds a PL tone(password)and a specific frequency.Defects in line-of-sight propagation caused by mountainous areas can also influence the radius.2.2What we do to solve these problemsConsidering the problem we are confronting,the spectrum available is145to148MHz,the transmitter frequency in a repeater is either600kHz above or600kHz below the receiver frequency.That is only5users can communicate with others without interferences when there’s noPL.The situation will be much better once we have PL.However the number of users that a repeater can serve is limited.In addition,in a flat area ,the obstacles such as mountains ,buildings don’t need to be taken into account.Taking the natural attenuation itself is reasonable.Now the most important is the radius that the signals transmit.Reducing the radius is a good way once there are more users.With MATLAB and the method of the coverage in Graph Theory,we solve this problem as follows in this paper.Ⅲ.Models3.1Basic model3.1.1Terms,Definitions,and Symbols3.1.2Assumptions●A user corresponds a PLz tone (password)and a specific frequency.●The users in the area are fixed and they are uniform distribution.●The area that a repeater covers is a regular hexagon.The repeater is in the center of the regular hexagon.●In a flat area ,the obstacles such as mountains ,buildings don’t need to be taken into account.We just take the natural attenuation itself into account.●The power of a repeater is fixed.3.1.3The Foundation of ModelAs the number of PLz tones (password)and frequencies is fixed,and a user corresponds a PLz tone (password)and a specific frequency,we can draw the conclusion that a repeater can serve the limited number of users.Thus it is clear that the number of repeaters we need relates to the density symboldescriptionLfsdfminrpμloss of transmission the distance of transmission operating frequency the number of repeaters that we need the power of the signals that a repeater transmits the density of users of the areaof users of the area.The radius of the area that a repeater covers is also related to the ratio of d and the radius of the circular area.And d is related to the power of a repeater.So we get the model of function()min ,r f p µ=If we ignore the density of users,we can get a Geometric model as follows:In a plane which is extended by regular hexagons whose side length are determined,we move a circle until it covers the least regular hexagons.3.1.4Solution and ResultCalculating the relationship between the radius of the circle and the side length of the regular hexagon.[]()()32.4420lg ()20lg Lfs dB d km f MHz =++In the above formula the unit of ’’is .Lfs dB The unit of ’’is .d Km The unit of ‘‘is .f MHz We can conclude that the loss of transmission of radio is decided by operating frequency and the distance of transmission.When or is as times as its former data,will increase f d 2[]Lfs .6dB Then we will solve the problem by using the formula mentioned above.We have already known the operating frequency is to .According to the 145MHz 148MHz actual situation and some authority material ,we assume a system whose transmit power is and receiver sensitivity is .Thus we can conclude that ()1010dBm mW +106.85dBm −=.Substituting and to the above formula,we can get the Lfs 106.85dBm −145MHz 148MHz average distance of transmission .()6.4d km =4mile We can learn the radius of the circle is 40mile .So we can conclude the relationship between the circle and the side length of regular hexagon isR=10d.1)The solution of the modelIn order to cover a certain plane with the least regular hexagons,we connect each regular hexagon as the honeycomb.We use A(standing for a figure)covers B(standing for another figure), only when As don’t overlap each other,the number of As we use is the smallest.Figure1According to the Principle of maximum flow of Graph Theory,the better of the symmetry ofthe honeycomb,the bigger area that it covers(Fig1).When the geometric centers of the circle andthe honeycomb which can extend are at one point,extend the honeycomb.Then we can get Fig2,Fig4:Figure2Fig3demos the evenly distribution of users.Figure4Now prove the circle covers the least regular hexagons.Look at Fig5.If we move the circle slightly as the picture,you can see three more regularhexagons are needed.Figure 52)ResultsThe average distance of transmission of the signals that a repeater transmit is 4miles.1000users can be satisfied with 37repeaters founded.3.1.5Analysis of the Result1)The largest number of users that a repeater can serveA user corresponds a PL and a specific frequency.There are 5wave bands and 54different PL tones available.If we call a code include a PL and a specific frequency,there are 54*5=270codes.However each code in two adjacent regular hexagons shouldn’t be the same in case of interfering with each other.In order to have more code available ,we can distribute every 3adjacent regular hexagons 90codes each.And that’s the most optimized,because once any of the three regular hexagons have more codes,it will interfere another one in other regular hexagon.2)Identify the rationality of the basic modelNow we considering the influence of the density of users,according to 1),90*37=3330>1000,so here the number of users have no influence on our model.Our model is rationality.3.1.6Strength and Weakness●Strength:In this paper,we use the model of honeycomb-hexagon structure can maximize the use of resources,avoiding some unnecessary interference effectively.It is much more intuitive once we change the function model to the geometric model.●Weakness:Since each hexagon get too close to another one.Once there are somebuildingsor terrain fluctuations between two repeaters,it can lead to the phenomenon that certain areas will have no signals.In addition,users are distributed evenly is not reasonable.The users are moving,for example some people may get a party.3.1.7Some ImprovementAs we all know,the absolute evenly distribution is not exist.So it is necessary to say something about the normal distribution model.The maximum accommodate number of a repeater is 5*54=270.As for the first model,it is impossible that 270users are communicating in a same repeater.Look at Fig 6.If there are N people in the area 1,the maximum number of the area 2to area 7is 3*(270-N).As 37*90=3330is much larger than 1000,our solution is still reasonable to this model.Figure 63.2Improve Model3.2.1Extra SymbolsSigns and definitions indicated above are still valid.Here are some extra signs and definitions.symboldescription Ra the radius of the circular flat area the side length of a regular hexagon3.2.2Additional AdditionalAssumptionsAssumptions ●The radius that of a repeater covers is adjustable here.●In some limited situations,curved shape is equal to straight line.●Assumptions concerning the anterior process are the same as the Basic Model3.2.3The Foundation of ModelThe same as the Basic Model except that:We only consider one variable(p)in the function model of the basic model ;In this model,we consider two varibles(p and μ)of the function model.3.2.4Solution and Result1)SolutionIf there are 10,000users,the number of regular hexagons that we need is at least ,thus according to the the Principle of maximum flow of Graph Theory,the 10000111.1190=result that we draw needed to be extended further.When the side length of the figure is equal to 7Figure 7regular hexagons,there are 127regular hexagons (Fig 7).Assuming the side length of a regular hexagon is ,then the area of a regular hexagon is a .The area of regular hexagons is equal to a circlewhose radiusis 22a =1000090R.Then according to the formula below:.221000090a R π=We can get.9.5858R a =Mapping with MATLAB as below (Fig 8):Figure 82）Improve the model appropriatelyEnlarge two part of the figure above,we can get two figures below (Fig 9and Fig 10):Figure 9AREAFigure 10Look at the figure above,approximatingAREA a rectangle,then obtaining its area to getthe number of users..The length of the rectangle is approximately equal to the side length of the regular hexagon ,athe width of the rectangle is ,thus the area of AREA is ,then R −*R a ⎛⎞−⎜⎟⎜⎟⎝⎠we can get the number of users in AREA is()，2**10000 2.06R a R π⎡⎤⎛⎞−⎢⎥⎜⎟⎢⎥⎝⎠=⎢⎥⎢⎥⎢⎥⎣⎦9.5858R a =As 2.06<<10,000,2.06can be ignored ,so there is no need to set up a repeater in.There are 6such areas(92,98,104,110,116,122)that can be ignored.At last,the number of repeaters we should set up is,1276121−=2)Get the side length of the regular hexagon of the improved modelThus we can getmile=km 40 4.1729.5858a == 1.6* 6.675a =3)Calculate the power of a repeaterAccording to the formula[]()()32.4420lg ()20lg Lfs dB d km f MHz =++We get32.4420lg 6.67520lg14592.156Los =++=32.4420lg 6.67520lg14892.334Los =++=So we get106.85-92.156=14.694106.85-92.334=14.516As the result in the basic model,we can get the conclusion the power of a repeater is from 14.694mW to 14.516mW.3.2.5Analysis of the ResultAs 10,000users are much more than 1000users,the distribution of the users is more close toevenly distribution.Thus the model is more reasonable than the basic one.More repeaters are built,the utilization of the outside regular hexagon are higher than the former one.3.2.6Strength and Weakness●Strength:The model is more reasonable than the basic one.●Weakness:Repeaters don’t cover all the area,some places may not receive signals.And thefoundation of this model is based on the evenly distribution of the users in the area,if the situation couldn’t be satisfied,the interference of signals will come out.Ⅳ.Conclusions4.1Conclusions of the problem●Generally speaking,the radius of the area that a repeater covers is4miles in our basic model.●Using the model of honeycomb-hexagon structure can maximize the use of resources,avoiding some unnecessary interference effectively.●The minimum number of repeaters necessary to accommodate1,000simultaneous users is37.The minimum number of repeaters necessary to accommodate10,000simultaneoususers is121.●A repeater's coverage radius relates to external environment such as the density of users andobstacles,and it is also determined by the power of the repeater.4.2Methods used in our models●Analysis the problem with MATLAB●the method of the coverage in Graph Theory4.3Application of our models●Choose the ideal address where we set repeater of the mobile phones.●How to irrigate reasonably in agriculture.●How to distribute the lights and the speakers in squares more reasonably.Ⅴ.Future WorkHow we will do if the area is mountainous?5.1The best position of a repeater is the top of the mountain.As the signals are line-of-sight transmission and reception.We must find a place where the signals can transmit from the repeater to users directly.So the top of the mountain is a good place.5.2In mountainous areas,we must increase the number of repeaters.There are three reasons for this problem.One reason is that there will be more obstacles in the mountainous areas. The signals will be attenuated much more quickly than they transmit in flat area.Another reason is that the signals are line-of-sight transmission and reception,we need more repeaters to satisfy this condition.Then look at Fig11and Fig12,and you will know the third reason.It can be clearly seen that hypotenuse is larger than right-angleFig11edge(R>r).Thus the radius will become smaller.In this case more repeaters are needed.Fig125.3In mountainous areas,people may mainly settle in the flat area,so the distribution of users isn’t uniform.5.4There are different altitudes in the mountainous areas.So in order to increase the rate of resources utilization,we can set up the repeaters in different altitudes.5.5However,if there are more repeaters,and some of them are on mountains,more money will be munication companies will need a lot of money to build them,repair them when they don’t work well and so on.As a result,the communication costs will be high.What’s worse,there are places where there are many mountains but few persons. Communication companies reluctant to build repeaters there.But unexpected things often happen in these places.When people are in trouble,they couldn’t communicate well with the outside.So in my opinion,the government should take some measures to solve this problem.5.6Another new method is described as follows(Fig13):since the repeater on high mountains can beFig13Seen easily by people,so the tower which used to transmit and receive signals can be shorter.That is to say,the tower on flat areas can be a little taller..Ⅵ.References[1]YU Fei,YANG Lv-xi,"Effective cooperative scheme based on relay selection",SoutheastUniversity,Nanjing,210096,China[2]YANG Ming,ZHAO Xiao-bo,DI Wei-guo,NAN Bing-xin,"Call Admission Control Policy based on Microcellular",College of Electical and Electronic Engineering,Shijiazhuang Railway Institute,Shijiazhuang Heibei050043,China[3]TIAN Zhisheng,"Analysis of Mechanism of CTCSS Modulation",Shenzhen HYT Co,Shenzhen,518057,China[4]SHANGGUAN Shi-qing,XIN Hao-ran,"Mathematical Modeling in Bass Station Site Selectionwith Lingo Software",China University of Mining And Technology SRES,Xuzhou;Shandong Finance Institute,Jinan Shandon,250014[5]Leif J.Harcke,Kenneth S.Dueker,and David B.Leeson,"Frequency Coordination in the AmateurRadio Emergency ServiceⅦ.AppendixWe use MATLAB to get these pictures,the code is as follows:1-clc;clear all;2-r=1;3-rc=0.7;4-figure;5-axis square6-hold on;7-A=pi/3*[0:6];8-aa=linspace(0,pi*2,80);9-plot(r*exp(i*A),'k','linewidth',2);10-g1=fill(real(r*exp(i*A)),imag(r*exp(i*A)),'k');11-set(g1,'FaceColor',[1,0.5,0])12-g2=fill(real(rc*exp(i*aa)),imag(rc*exp(i*aa)),'k');13-set(g2,'FaceColor',[1,0.5,0],'edgecolor',[1,0.5,0],'EraseMode','x0r')14-text(0,0,'1','fontsize',10);15-Z=0;16-At=pi/6;17-RA=-pi/2;18-N=1;At=-pi/2-pi/3*[0:6];19-for k=1:2;20-Z=Z+sqrt(3)*r*exp(i*pi/6);21-for pp=1:6;22-for p=1:k;23-N=N+1;24-zp=Z+r*exp(i*A);25-zr=Z+rc*exp(i*aa);26-g1=fill(real(zp),imag(zp),'k');27-set(g1,'FaceColor',[1,0.5,0],'edgecolor',[1,0,0]);28-g2=fill(real(zr),imag(zr),'k');29-set(g2,'FaceColor',[1,0.5,0],'edgecolor',[1,0.5,0],'EraseMode',xor';30-text(real(Z),imag(Z),num2str(N),'fontsize',10);31-Z=Z+sqrt(3)*r*exp(i*At(pp));32-end33-end34-end35-ezplot('x^2+y^2=25',[-5,5]);%This is the circular flat area of radius40miles radius 36-xlim([-6,6]*r)37-ylim([-6.1,6.1]*r)38-axis off;Then change number19”for k=1:2;”to“for k=1:3;”,then we get another picture:Change the original programme number19“for k=1:2;”to“for k=1:4;”,then we get another picture:Change the original programme number19“for k=1:2;”to“for k=1:1;”,and delete number 35“ezplot('x^2+y^2=25',[-5,5]);”then we get another picture:Change the original programme number19“for k=1:2;”to“for k=1:6;”,and change number 35“ezplot('x^2+y^2=25',[-5,5]);”to”ezplot('x^2+y^2=6*sqrt(3)*10000/360/pi',[-20,20]);”Change number36,37“36-xlim([-6,6]*r)37-ylim([-6.1,6.1]*r)”To“xlim([-20,20]*r)ylim([-20.1,20.1]*r)”,then we getTeam#8921Page21of21Delete“36-xlim([-6,6]*r)37-ylim([-6.1,6.1]*r)”We get。
数学建模美赛写作模版(包含摘要、格式、总结、表格、公式、图表、假设)
论文reference 格式中文解说版总体要求1 正文中引用的文献与文后的文献列表要完全一致.ν文中引用的文献可以在正文后的文献列表中找到；文献列表的文献必须在正文中引用。
2 文献列表中的文献著录必须准确和完备。
3 文献列表的顺序文献列表按著者姓氏字母顺序排列；姓相同,按名的字母顺序排列；著者姓和名相同，按出版年排列。
νν相同著者，相同出版年的不同文献，需在出版年后面加a、b、c、d……来区分，按文题的字母顺序排列。
如: Wang, M. Y。
（2008a). Emotional……Wang, M。
Y。
(2008b). Monitor……Wang，M。
Y. (2008c). Weakness……4 缩写chap. chapter 章ed。
edition 版Rev. ed。
revised edition 修订版2nd ed. second edition 第2版Ed. (Eds。
）Editor （Editors）编Trans. Translator（s) 译n.d. No date 无日期p。
(pp。
）page （pages）页Vol. Volume (as in Vol。
4) 卷vols。
volumes （as in 4 vols.）卷No。
Number 第Pt。
Part 部分Tech. Rep. Technical Report 技术报告Suppl. Supplement 增刊5 元分析报告中的文献引用ν元分析中用到的研究报告直接放在文献列表中，但要在文献前面加星号＊。
并在文献列表的开头就注明*表示元分析用到的的文献。
正文中的文献引用标志在著者—出版年制中，文献引用的标志就是“著者”和“出版年”，主要有两种形式：（1）正文中的文献引用标志可以作为句子的一个成分，如：Dell（1986）基于语误分析的结果提出了音韵编码模型，…….汉语词汇研究有庄捷和周晓林（2001）的研究。
（2)也可放在引用句尾的括号中，如:在语言学上，音节是语音结构的基本单位，也是人们自然感到的最小语音片段。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
The Keep-Right-Except-To-Pass RuleSummaryAs for the first question, it provides a traffic rule of keep right except to pass, requiring us to verify its effectiveness. Firstly, we define one kind of traffic rule different from the rule of the keep right in order to solve the problem clearly; then, we build a Cellular automaton model and a Nasch model by collecting massive data; next, we make full use of the numerical simulation according to several influence factors of traffic flow; At last, by lots of analysis of graph we obtain, we indicate a conclusion as follow: when vehicle density is lower than 0.15, the rule of lane speed control is more effective in terms of the factor of safe in the light traffic; when vehicle density is greater than 0.15, so the rule of keep right except passing is more effective In the heavy traffic.As for the second question, it requires us to testify that whether the conclusion we obtain in the first question is the same apply to the keep left rule. First of all, we build a stochastic multi-lane traffic model; from the view of the vehicle flow stress, we propose that the probability of moving to the right is 0.7and to the left otherwise by making full use of the Bernoulli process from the view of the ping-pong effect, the conclusion is that the choice of the changing lane is random. On the whole, the fundamental reason is the formation of the driving habit, so the conclusion is effective under the rule of keep left.As for the third question, it requires us to demonstrate the effectiveness of the result advised in the first question under the intelligent vehicle control system. Firstly, taking the speed limits into consideration, we build a microscopic traffic simulator model for traffic simulation purposes. Then, we implement a METANET model for prediction state with the use of the MPC traffic controller. Afterwards, we certify that the dynamic speed control measure can improve the traffic flow .Lastly neglecting the safe factor, combining the rule of keep right with the rule of dynamical speed control is the best solution to accelerate the traffic flow overall.Key words：Cellular automaton model Bernoulli process Microscopic traffic simulator model The MPC traffic controlContentContent (2)1. Introduction (3)2. Analysis of the problem (3)3. Assumption (3)4. Symbol Definition (3)5. Models (4)5.1 Building of the Cellular automaton model (4)5.1.1 Verify the effectiveness of the keep right except to pass rule (4)5.1.2 Numerical simulation results and discussion (5)5.1.3 Conclusion (8)5.2 The solving of second question (8)5.2.1 The building of the stochastic multi-lane traffic model (9)5.2.2 Conclusion (9)5.3 Taking the an intelligent vehicle system into a account (9)5.3.1 Introduction of the Intelligent Vehicle Highway Systems (9)5.3.2 Control problem (9)5.3.3 Results and analysis (9)5.3.4 The comprehensive analysis of the result (10)6. Improvement of the model (11)6.1 strength and weakness (11)6.1.1 Strength (11)6.1.2 Weakness (11)6.2 Improvement of the model (11)7. Reference (13)1. IntroductionAs is known to all, it’s essential for us to drive automobiles, thus the driving rules is crucial important. In many countries like USA, China, drivers obey the rules which called “The Keep-Right-Except-To-Pass (that is, when driving automobiles, the rule requires drivers to drive in the right-most unless theyare passing another vehicle)”.2. Analysis of the problemFor the first question, we decide to use the Cellular automaton to build models,then analyze the performance of this rule in light and heavy traffic. Firstly,we mainly use the vehicle density to distinguish the light and heavy traffic; secondly, we consider the traffic flow and safe as the represent variable which denotes the light or heavy traffic; thirdly, we build and analyze a Cellular automaton model; finally, we judge the rule through two different driving rules,and then draw conclusions.3. AssumptionIn order to streamline our model we have made several key assumptions●The highway of double row three lanes that we study can representmulti-lane freeways.●The data that we refer to has certain representativeness and descriptive●Operation condition of the highway not be influenced by blizzard oraccidental factors●Ignore the driver's own abnormal factors, such as drunk driving andfatigue driving●The operation form of highway intelligent system that our analysis canreflect intelligent system●In the intelligent vehicle system, the result of the sampling data hashigh accuracy.4. Symbol Definitioni The number of vehiclest The time5. ModelsBy analyzing the problem, we decided to propose a solution with building a cellular automaton model.5.1 Building of the Cellular automaton modelThanks to its simple rules and convenience for computer simulation, cellular automaton model has been widely used in the study of traffic flow in recent years. Let )(t x i be the position of vehicle i at time t , )(t v i be the speed of vehicle i at time t , p be the random slowing down probability, and R be the proportion of trucks and buses, the distance between vehicle i and the front vehicle at time t is:1)()(1--=-t x t x gap i i i , if the front vehicle is a small vehicle.3)()(1--=-t x t x gap i i i , if the front vehicle is a truck or bus.5.1.1 Verify the effectiveness of the keep right except to pass ruleIn addition, according to the keep right except to pass rule, we define a new rule called: Control rules based on lane speed. The concrete explanation of the new rule as follow:There is no special passing lane under this rule. The speed of the first lane (the far left lane) is 120–100km/h (including 100 km/h)；the speed of the second lane (the middle lane) is 100–80km8/h (including80km/h)；the speed of the third lane (the far right lane) is below 80km/ h. The speeds of lanes decrease from left to right.● Lane changing rules based lane speed controlIf vehicle on the high-speed lane meets control v v <, ),1)(min()(max v t v t gap i f i +≥, safe b i gap t gap ≥)(, the vehicle will turn into the adjacent right lane, and the speed of the vehicle after lane changing remains unchanged, where control v is the minimum speed of the corresponding lane.● The application of the Nasch model evolutionLet d P be the lane changing probability (taking into account the actual situation that some drivers like driving in a certain lane, and will not takethe initiative to change lanes), )(t gap f i indicates the distance between the vehicle and the nearest front vehicle, )(t gap b i indicates the distance between the vehicle and the nearest following vehicle. In this article, we assume that the minimum safe distance gap safe of lane changing equals to the maximum speed of the following vehicle in the adjacent lanes.Lane changing rules based on keeping right except to passIn general, traffic flow going through a passing zone (Fig. 5.1.1) involves three processes: the diverging process (one traffic flow diverging into two flows), interacting process (interacting between the two flows), and merging process (the two flows merging into one) [4].Fig.5.1.1 Control plan of overtaking process(1) If vehicle on the first lane (passing lane) meets ),1)(min()(max v t v t gap i f i +≥ and safe b i gap t gap ≥)(, the vehicle will turn into the second lane, the speed of the vehicle after lane changing remains unchanged.5.1.2 Numerical simulation results and discussionIn order to facilitate the subsequent discussions, we define the space occupation rate as L N N p truck CAR ⨯⨯+=3/)3(, where CAR N indicates the number ofsmall vehicles on the driveway,truck N indicates the number of trucks and buses on the driveway, and L indicates the total length of the road. The vehicle flow volume Q is the number of vehicles passing a fixed point per unit time,T N Q T /=, where T N is the number of vehicles observed in time duration T .The average speed ∑∑⨯=T it i a v T N V 11)/1(, t i v is the speed of vehicle i at time t . Take overtaking ratio f p as the evaluation indicator of the safety of traffic flow, which is the ratio of the total number of overtaking and the number of vehicles observed. After 20,000 evolution steps, and averaging the last 2000 steps based on time, we have obtained the following experimental results. In order to eliminate the effect of randomicity, we take the systemic average of 20 samples [5].Overtaking ratio of different control rule conditionsBecause different control conditions of road will produce different overtaking ratio, so we first observe relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions.(a) Based on passing lane control (b) Based on speed control Fig.5.1.3Fig.5.1.3 Relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions.It can be seen from Fig. 5.1.3:(1) when the vehicle density is less than 0.05, the overtaking ratio will continue to rise with the increase of vehicle density; when the vehicle density is larger than 0.05, the overtaking ratio will decrease with the increase of vehicle density; when density is greater than 0.12, due to the crowding, it willbecome difficult to overtake, so the overtaking ratio is almost 0.(2) when the proportion of large vehicles is less than 0.5, the overtaking ratio will rise with the increase of large vehicles; when the proportion of large vehicles is about 0.5, the overtaking ratio will reach its peak value; when the proportion of large vehicles is larger than 0.5, the overtaking ratio will decrease with the increase of large vehicles, especially under lane-based control condition s the decline is very clear.● Concrete impact of under different control rules on overtaking ratioFig.5.1.4Fig.5.1.4 Relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions. (Figures in left-hand indicate the passing lane control, figures in right-hand indicate the speed control. 1f P is the overtaking ratio of small vehicles over large vehicles, 2f P is the overtaking ratio of small vehicles over small vehicles, 3f P is the overtaking ratio of large vehicles over small vehicles, 4f P is the overtaking ratio of large vehicles over large vehicles.). It can be seen from Fig. 5.1.4:(1) The overtaking ratio of small vehicles over large vehicles under passing lane control is much higher than that under speed control condition, which is because, under passing lane control condition, high-speed small vehicles have to surpass low-speed large vehicles by the passing lane, while under speed control condition, small vehicles are designed to travel on the high-speed lane, there is no low- speed vehicle in front, thus there is no need to overtake. ● Impact of different control rules on vehicle speedFig. 5.1.5 Relationships among vehicle density, proportion of large vehicles and average speed under different control conditions. (Figures in left-hand indicates passing lane control, figures in right-hand indicates speed control.a X is the average speed of all the vehicles, 1a X is the average speed of all the small vehicles, 2a X is the average speed of all the buses and trucks.).It can be seen from Fig. 5.1.5:(1) The average speed will reduce with the increase of vehicle density and proportion of large vehicles.(2) When vehicle density is less than 0.15,a X ,1a X and 2a X are almost the same under both control conditions.Effect of different control conditions on traffic flowFig.5.1.6Fig. 5.1.6 Relationships among vehicle density, proportion of large vehicles and traffic flow under different control conditions. (Figure a1 indicates passing lane control, figure a2 indicates speed control, and figure b indicates the traffic flow difference between the two conditions.It can be seen from Fig. 5.1.6：(1) When vehicle density is lower than 0.15 and the proportion of large vehicles is from 0.4 to 1, the traffic flow of the two control conditions are basically the same.(2) Except that, the traffic flow under passing lane control condition is slightly larger than that of speed control condition.5.1.3 ConclusionIn this paper, we have established three-lane model of different control conditions, studied the overtaking ratio, speed and traffic flow under different control conditions, vehicle density and proportion of large vehicles.5.2 The solving of second question5.2.1 The building of the stochastic multi-lane traffic model5.2.2 ConclusionOn one hand, from the analysis of the model, in the case the stress is positive, we also consider the jam situation while making the decision. More specifically, if a driver is in a jam situation, applying ))(,2(x P B R results with a tendency of moving to the right lane for this driver. However in reality, drivers tend to find an emptier lane in a jam situation. For this reason, we apply a Bernoulli process )7.0,2(B where the probability of moving to the right is 0.7and to the left otherwise, and the conclusion is under the rule of keep left except to pass, So, the fundamental reason is the formation of the driving habit.5.3 Taking the an intelligent vehicle system into a accountFor the third question, if vehicle transportation on the same roadway was fully under the control of an intelligent system, we make some improvements for the solution proposed by us to perfect the performance of the freeway by lots of analysis.5.3.1 Introduction of the Intelligent Vehicle Highway SystemsWe will use the microscopic traffic simulator model for traffic simulation purposes. The MPC traffic controller that is implemented in the Matlab needs a traffic model to predict the states when the speed limits are applied in Fig.5.3.1. We implement a METANET model for prediction purpose[14].5.3.2 Control problemAs a constraint, the dynamic speed limits are given a maximum and minimum allowed value. The upper bound for the speed limits is 120 km/h, and the lower bound value is 40 km/h. For the calculation of the optimal control values, all speed limits are constrained to this range. When the optimal values are found, they are rounded to a multiplicity of 10 km/h, since this is more clear for human drivers, and also technically feasible without large investments.5.3.3 Results and analysisWhen the density is high, it is more difficult to control the traffic, since the mean speed might already be below the control speed. Therefore, simulations are done using densities at which the shock wave can dissolve without using control, and at densities where the shock wave remains. For each scenario, five simulations for three different cases are done, each with a duration of one hour. The results of the simulations are reported in Table 5.1, 5.2, 5.3.●Enforced speed limits●Intelligent speed adaptationFor the ISA scenario, the desired free-flow speed is about 100% of the speed limit. The desired free-flow speed is modeled as a Gaussian distribution, with a mean value of 100% of the speed limit, and a standard deviation of 5% of the speed limit. Based on this percentage, the influence of the dynamic speed limits is expected to be good[19].5.3.4 The comprehensive analysis of the resultFrom the analysis above, we indicate that adopting the intelligent speed control system can effectively decrease the travel times under the control of an intelligent system, in other words, the measures of dynamic speed control can improve the traffic flow.Evidently, under the intelligent speed control system, the effect of the dynamic speed control measure is better than that under the lane speed control mentioned in the first problem. Because of the application of the intelligent speed control system, it can provide the optimal speed limit in time. In addition, it can guarantee the safe condition with all kinds of detection device and the sensor under the intelligent speed system.On the whole, taking all the analysis from the first problem to the end into a account, when it is in light traffic, we can neglect the factor of safe with the help of the intelligent speed control system.Thus, under the state of the light traffic, we propose a new conclusion different from that in the first problem: the rule of keep right except to pass is more effective than that of lane speed control.And when it is in the heavy traffic, for sparing no effort to improve the operation efficiency of the freeway, we combine the dynamical speed control measure with the rule of keep right except to pass, drawing a conclusion that the application of the dynamical speed control can improve the performance of the freeway.What we should highlight is that we can make some different speed limit as for different section of road or different size of vehicle with the application of the Intelligent Vehicle Highway Systems.In fact, that how the freeway traffic operate is extremely complex, thereby,with the application of the Intelligent Vehicle Highway Systems, by adjusting our solution originally, we make it still effective to freeway traffic.6. Improvement of the model6.1 strength and weakness6.1.1 Strength●it is easy for computer simulating and can be modified flexibly to consideractual traffic conditions ,moreover a large number of images make the model more visual.●The result is effectively achieved all of the goals we set initially, meantimethe conclusion is more persuasive because of we used the Bernoulli equation.●We can get more accurate result as we apply Matlab.6.1.2 Weakness●The relationship between traffic flow and safety is not comprehensivelyanalysis.●Due to there are many traffic factors, we are only studied some of the factors,thus our model need further improved.6.2 Improvement of the modelWhile we compare models under two kinds of traffic rules, thereby we come to the efficiency of driving on the right to improve traffic flow in some circumstance. Due to the rules of comparing is too less, the conclusion is inadequate. In order to improve the accuracy, We further put forward a kinds of traffic rules: speed limit on different type of cars.The possibility of happening traffic accident for some vehicles is larger, and it also brings hidden safe troubles. So we need to consider separately about different or specific vehicle types from the angle of the speed limiting in order to reduce the occurrence of traffic accidents, the highway speed limit signs is in Fig.6.1.Fig .6.1Advantages of the improving model are that it is useful to improve the running condition safety of specific type of vehicle while considering the difference of different types of vehicles. However, we found that the rules may be reduce the road traffic flow through the analysis. In the implementation it should be at the 85V speed of each model as the main reference basis. In recent years, the85V of some researchers for the typical countries from Table 6.1[ 21]:Author Country ModelOttesen and Krammes2000 AmericaLC DC L DC V C ⨯---=01.0012.057.144.10285Andueza2000Venezuela ].[308.9486.7)/894()/2795(25.9885curve horizontal L DC Ra R V T++--=].[tan 819.27)/3032(69.10085gent L R V T +-= Jessen2001America][00239.0614.0279.080.86185LSD ADT G V V P --+=][00212.0432.010.7285NLSD ADT V V P -+=Donnell2001 America22)2(8500724.040.10140.04.78T L G R V --+=22)3(85008369.048.10176.01.75T L G R V --+=22)4(8500810.069.10176.05.74T L G R V --+=22)5(8500934.008.21.83T L G V --=BucchiA.BiasuzziK. And SimoneA.2005Italy DCV 124.0164.6685-= DCE V 4.046.3366.5585--=2855.035.1119.0745.65DC E DC V ---=FitzpatrickAmericaKV 98.17507.11185-= Meanwhile, there are other vehicles driving rules such as speed limit in adverseweather conditions. This rule can improve the safety factor of the vehicle to some extent. At the same time, it limits the speed at the different levels.7. Reference[1] M. Rickert, K. Nagel, M. Schreckenberg, A. Latour, Two lane trafficsimulations using cellular automata, Physica A 231 (1996) 534–550.[20] J.T. Fokkema, Lakshmi Dhevi, Tamil Nadu Traffi c Management and Control inIntelligent Vehicle Highway Systems,18(2009).[21] Yang Li, New Variable Speed Control Approach for Freeway. (2011) 1-66。