2015美赛预备
2015年美国数学建模竞赛第二次模拟赛题
Problem A Warmer Days or Sour Grapes ?The high quality of wines（葡萄酒）produced in the Finger Lakes Region（五指湖区）of upstate （北部）New York is widely known. Proximity（接近）to lakes tempers the climate and makes it more suitable for growing several varieties of premium（独特）grapes: R iesling（雷司令）, G ewürztraminer（琼瑶浆）,C hardonnay（霞多丽）, M erlot（梅洛）, P inot Noir（黑比诺）, and CabernetF ranc（品丽珠）. (There are many more, but we will restrict（限制）the discussion to these six to simplify（简化）the modeling.) Each variety has its own preferred “average temperature” range but is also different in its susceptibility（感受性）to diseases and ability to withstand（抵抗）short periods of unusually cold temperature.As our local climate changes, the relative suitability of these varieties will be changing as well. A forward-looking winery（酒厂）has hired your team to help with the long-term planning. You will need to recommenda) the proportion（比例）of the total vineyard（葡萄园）to be used for growing each of the above six varieties;b) and when should these changes be implemented （实施）(based on observed temperatures and/or current market prices for each type of wine).Naturally, the winery is interested in maximizing its annual profit. But since the latter （后者）is weather-dependent, it might vary a lot year-to-year. You are also asked to evaluate the trade-offs （权衡）between optimizing the expected/average case versus the worst(-realistic-)scenario（情景）.Things to keep in mind:Climate modeling is complicated（复杂）and predicting the rate of “global warming” is a hotly debated area. For the purposes of this problem, assume that the annual average temperature in Ithaca（伊萨卡）, NY will increase by no more than 4°C by the end of this century.It is not all about the average temperature – a short snap（临时）of sub- zero（零度）temperature in late Ferburay or early March (after the vines already started getting used to warmer weather) is far more damaging than the same low temperature would be in the middle of the winter.It takes at least 3 years for a newly planted vine to start producing grapes suitable for winemaking.Problem B Outlook of Car-to-Car TechSAN FRANCISCO -- After more than a decade of research into car-to-car communications, U.S. auto safety regulators took a step forward today by unveiling their plan for requiring cars to have wireless gear that will enable them to warn drivers of danger.These vehicle-to-vehicle (V2V) transmitters and software could save thousands of lives and prevent hundreds of thousands of crashes each year by providing cars with information they never will be able to gather simply from cameras and sensors. “Safety is our top priority, and V2V technology represents the next great advance in saving lives,” Transportation Secretary Anthony Foxx said in an announcement. “This technology could move us from helping people survive crashes to helping them avoid crashes altogether.”Requirement 1: Present a mathematical model to discuss the reduction of the number of traffic accidents and road fatalities/injuries in San Francisco by V2V technology. Requirement 2: Determine the maximum number of cars in San Francisco due to the V2V technology.Requirement 3: Discuss the benefits of V2V technology to alleviate road congestion. Requirement 4: Provide your recommendation to the government.Prblem C Forest FiresOne major environmental concern is the occurrence of forest fires (also called wildfires), which affect forest preservation, bring economical and ecological damage and endanger human lives. Such phenomenon is due to multiple causes (e.g. human negligence and lightnings). Despite an increasing of state expenses to control this disaster, each year millions of forest hectares (ha) are destroyed all around the world.Fast detection is an important element for successful firefighting. Traditional human surveillance is expensive and affected by subjective factors, there has been an emphasis to develop automatic solutions, such as satellite-based, infrared/smoke scanners and local sensors (e.g. meteorological). Propagation models try to describe the future evolution of the forest fire given an initial scenario and certain input parameters. Modeling the dynamical behavior of fire propagation in a forest is helpful for creating scheme to control and fight fire.Requirement 1 Describe several different metrics that could be used to evaluate the effectiveness of fire detection. Could you combine your metrics to make them even more useful for measuring quality?Requirement 2 Model the dynamical behavior of fire spread in a forest. Requirement 3 Discuss the factors to affect fire occurrence. Which factors are the most critical in causing fires. Build mathematical models to predict the burned area of fires using Meteorological Data.Requirement 4 Give y our suggestion for preventing from forest fire and fighting against it.Problem D Wearable Activity RecognitionThe percentage of EU citizens aged 65 years or over is projected to increase from 17.1% in 2008 to 30.0% in 2060. In particular, the number of 65 years old is projected to rise from 84.6 million to 151.5 million, while the number of people aged 80 or over is projected to almost triple from 21.8 million to 61.4 million (EUROSTAT: New European Population projections 2008–2060). It has been calculated that the purely demographic effect of an ageing population will push up health-care spending by between 1% and 2% of the gross domestic product (GDP) of most member states. At first sight this may not appear to be very much when extended over several decades, but on average it would in fact amount to approximately a 25% increase in spending on health care, as a share of GDP, in the next 50 years (European Economy Commission, 2006). The effective incorporation of technology into health-care systems could therefore be decisive in helping to decrease overall public spending on health. One of these emerging health-care systems is daily living physical activity recognition.Daily living physical activity recognition is currently being applied in chronic disease management (Amft & Troter, 2008; Zwartjes, Heida, van Vugt, Geelen, & Veltink, 2010), rehabilitation systems (Sazonov, Fulk, Sazonova, & Schuckers, 2009) and disease prevention (Sazonov, Fulk, Hill, Schutz, & Browning, 2011; Warren et al., 2010), as well as being a personal indicator to health status (Arcelus et al., 2009). One of the principal subjects of the health related applications being mooted is the monitoring of the elderly. For example, falls represent one of the major risks and obstacles to old people’s independence (Najafi, Aminian, Loew, Blanc, & Robert, 2002; Yu, 2008). This risk is increased when some kind of degenerative disease affects them. Most Alzheimer’s patients, for exa mple, spend a long time every day either sitting or lying down since they would otherwise need continuous vigilance and attention to avoid a fall.The registration of daily events, an important task in anticipating and/or detecting anomalous behavior patterns and a primary step towards carrying out proactive management and personalized treatment, is normally poorly accomplished by patients’ families, healthcare units or auxiliary assistants because of limitations in time and resources. Automatic activity-recognition systems could allow us to conduct a completely detailed monitoring and assessment of the individual, thus significantly reducing current human supervision requirements.Most wearable activity recognition systems assume a predefined sensor deployment that remains unchanged during runtime. However, this assumption does not reflect real-life conditions. During the normal use of such systems, users may place the sensors in a position different from the predefined sensor placement. Also, sensors may move from their original location to a different one, due to a loose attachment. Activity recognition systems trained on activity patterns characteristic of a given sensor deployment may likely fail due to sensor displacements.Your task is as follows.(1) Build models to recognize daily living activities.(2) Explore the effects of sensor displacement induced by both the intentionalmisplacement of sensors and self-placement by the user.(3) Verify your recognition models’ toleranc e to sensor displacement.Data Set Information:The REALDISP (REAListic sensor DISPlacement) dataset has been originally collected to investigate the effects of sensor displacement in the activity recognition process in real-world settings. It builds on the concept of ideal-placement, self-placement and induced- displacement. The ideal and mutual-displacement conditions represent extreme displacement variants and thus could represent boundary conditions for recognition algorithms. In contrast, self-placement reflects a users perception of how sensors could be attached, e.g., in a sports or lifestyle application. The dataset includes a wide range of physical activities (warm up, cool down and fitness exercises), sensor modalities (acceleration, rate of turn, magnetic field and quaternions) and participants (17 subjects). Apart from investigating sensor displacement, the dataset lend itself for benchmarking activity recognition techniques in ideal conditions.Dataset summary:#Activities: 33#Sensors: 9#Subjects: 17#Scenarios: 3ACTIVITY SET:A1: WalkingA2: JoggingA3: RunningA4: Jump upA5: Jump front & backA6: Jump sidewaysA7: Jump leg/arms open/closedA8: Jump ropeA9: Trunk twist (arms outstretched)A10: Trunk twist (elbows bent)A11: Waist bends forwardA12: Waist rotationA13: Waist bends (reach foot with opposite hand)A14: Reach heels backwardsA15: Lateral bend (10_ to the left + 10_ to the right)A16: Lateral bend with arm up (10_ to the left + 10_ to the right)A17: Repetitive forward stretchingA18: Upper trunk and lower body opposite twistA19: Lateral elevation of armsA20: Frontal elevation of armsA21: Frontal hand clapsA22: Frontal crossing of armsA23: Shoulders high-amplitude rotationA24: Shoulders low-amplitude rotationA25: Arms inner rotationA26: Knees (alternating) to the breastA27: Heels (alternating) to the backsideA28: Knees bending (crouching)A29: Knees (alternating) bending forwardA30: Rotation on the kneesA31: RowingA32: Elliptical bikeA33: CyclingSENSOR SETUP:Each sensor provides 3D acceleration (accX,accY,accZ), 3D gyro (gyrX,gyrY,gyrZ), 3D magnetic field orientation (magX,magY,magZ) and 4D quaternions (Q1,Q2,Q3,Q4). The sensors are identified according to the body part on which is placed respectively:。
2015年MCM美赛题目及翻译
PROBLEM A: Eradicating（根除）EbolaThe world medical association has announced that their new medication could stop Ebola and cure patients whose disease is not advanced（晚期的）. Build a realistic, sensible, and useful model that considers not only the spread of the disease, the quantity of the medicine needed, possible feasible （可行的）delivery systems, locations of delivery, speed of manufacturing of the vaccine or drug, but also any other critical factors your team considers necessary as part of the model to optimize the eradication of Ebola, or at least its current strain（压力）. In addition to your modeling approach for the contest, prepare a 1-2 page non-technical letter for the world medical association to use in their announcement.PROBLEM B: Searching for a lost planeRecall the lost Malaysian flight MH370. Build a generic（一般的）mathematical model that could assist "searchers" in planning a useful search for a lost plane feared to（恐怕） have crashed in open water such as the Atlantic, Pacific, Indian, Southern, or Arctic Ocean while flying from Point A to Point B. Assume that there are no signals from the downed （坠落的） plane. Your model should recognize that there are many different types of planes for which we might be searching and that there are many different types of search planes, often using different electronics or sensors. Additionally, prepare a 1-2 page non-technical paper for the airlines to use in their press conferences concerning their plan for future searches.。
2015美赛A题优秀论文
2.4 2.5 2.6
Model Modeling Objectives . . . . . . . . . . . . . . . . . . . . Problem Space . . . . . . . . . . . . . . . . . . . . . . . The Multi-Layer State Based Stochastic Epidemic Model 2.3.1 Individual Layer - Stochastic State Based Model . 2.3.2 Inter-Region Layer modeling . . . . . . . . . . . . 2.3.3 Human Mobility Model . . . . . . . . . . . . . . . 2.3.4 Supply Distribution Model . . . . . . . . . . . . . 2.3.5 A note on GLEAM . . . . . . . . . . . . . . . . . Implementation . . . . . . . . . . . . . . . . . . . . . . . Additional Considerations . . . . . . . . . . . . . . . . . 2.5.1 Modeling of Hospitals . . . . . . . . . . . . . . . Consequences of Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
参加美国大学生数学建模竞赛 - 知乎
1.组队
我们队 一个应用数学的学渣（就是我） 一个化学院的女森 加上一个 计算机院物联网的男生 一般组队都是 数院 电气 电信 经管 这样 我们一次模拟都没有做过，但是分析过大概10多篇08年一等奖的文章，当时觉得 他们的模型都看不懂= =
2.场地
因为学校机房有限，都给了参加过过赛的同学的队，比赛的时候 出去开了两间房，白天就在一起做题。酒店没有 桌子，就坐在地上然后把电脑放床上= =
比赛：最理想是国赛前定下美国赛队伍，拿国赛练级攒经验比较恰当。其他如教工杯之类的比赛，鉴于真实比 赛环境和练习的机会不多，建议当成美赛认真练。只要认真练，几次真赛历练之后，建模和配合方面问题就不 应该太大了。 学术论文写作：难点不是专业词汇或格式排版的问题，这些问题阅卷人可能会对外国参赛者宽容些，真正困难 是表达如何逻辑清晰严密、符合学术规范了。有条件的最好找英语国家教授或学术期刊编辑帮忙不断改，找不 到就只能是找海归教授、理工专业外国留学生将就了，再没条件的只能研读outstanding和英文经典论文了。
赛前准备程度基本决定了比赛的时间充裕度 ，赛前准备不足往往要靠比赛时不眠不休、争分夺秒拼命抢时间来 弥补，这种情况下能做出多少创造性工作就难说了。
三、练级篇：
练习：练习的时候要根据队伍的特点有针对性的训练提高——模型方面，多积累实际问题产生背景，注意培养 思考的深度，善用发散和逆向思维；实现方面，注意提升各种算法求解效率的方法，多积累算法调试、测试、 参数调整、有效性检验等方面的经验；
大家要有信心 一等奖不难 加油噢~ 编辑于 2013-07-23 9 条评论
参加美国大学生数学建模竞赛 - 知乎
改名中，我的头像更适合做知乎吉祥物 李曈、Steve Balaba、张镇麟 等人赞同 首先说一下自己的参赛经历：2013年S奖，2014年M奖，两次参赛是不同的队伍。
美赛参赛规则和注意事项
美赛参赛规则和注意事项比赛开始前：1、所有的参赛队必须在美国东部时间2014年2月6号（星期四）下午2点前完成注册。
此注册过程需要由指导老师完成。
2、缴费。
注册完成之后各个队伍需要缴纳100美元的报名费。
3、完成缴费后，每个参赛队伍会获得一个控制编号，获得控制编号意味着报名成功，同时控制编号是识别队伍的唯一标志。
4、在比赛前或比赛中希望更改参赛信息的，都需要通过指导老师进行更改。
5、指导老师需在完成注册和缴费之后确认队伍的相关资料，并打印含有队伍控制编号和摘要的页面，这会在准备邮包时用到。
选择参赛队成员：1、各队需要在美国东部时间2014年2月6日（星期四）晚上8点大赛开始以前选择好参赛队的队员。
一旦比赛开始，就不能增加或是改变任何一个参赛队队员。
2、每个参赛队伍最多只可由3名学生组成。
3、一个学生最多只能参加一个队伍。
4、参赛队成员必须与指导老师来自同一所学校。
比赛开始之后：1、美国东部时间2014年2月6日（星期四）晚上8点竞赛开始时，可以通过竞赛网站得到题目。
美国东部时间2014年2月6日晚7点50分，比赛题目也会同步发布于一下镜像网站：/mcm/index.html/mcm/index.html/mcm/index.html/mcm/index.html2、每个参赛队伍可以从三道赛题中任选一道。
3、参赛队准备解决方案。
参赛队可以利用任何非生命提供的数据和资料——包括计算机，软件，参考书目，网站，书籍等，但是所有引用的资料必须注明出处，如有参赛队未注明引用的内容的出处，将被取消参赛资格。
参赛队成员不允许向指导教师或者除了本团队成员以外的其他人寻求帮助或讨论问题。
与除本团队成员以外的人的任何形式的接触都是严格禁止的。
这包括通过E-mail联系、电话联系、私人交谈、通过网络聊天联络或是其他的任何问答系统，或者其他任何的交流方式。
论文构成：1、摘要摘要是 MCM 参赛论文的一个非常重要的部分。
在评卷过程中，摘要占据了相当大的比重，以至于有的时候获奖论文之所以能在众多论文中脱颖而出是因为其高质量的摘要。
2015数模美赛A题翻译
PROBLEM A: Eradicating EbolaThe world medical association has announced that their new medication could stop Ebola and cure patients whose diseases not advanced. Build a realistic, sensible, and useful model that considers not only the spread of the disease, the quantity of the medicine needed, possible feasible delivery systems, locations of delivery, speed of manufacturing of the vaccine or drug, but also any other critical factors your team considers necessary as part of the model to optimize the eradication of Ebola, or at least its current strain. In addition to your modeling approach for the contest, prepare a 1-2 page non-technical letter for the world medical association to use in their announcement.A消除埃博拉病毒世界医学协会已经宣布他们的新疗法可以阻止埃博拉疫情和治愈非晚期患者。
构建一个现实的、合理的和有用的模型,不仅要考虑疾病的传播,所需药物的数量,可能且可行的给药系统,给药地点,生产疫苗或药物的速度,而且还要考虑其他关键因素（你的团队认为有必要要考虑的）作为模型的一部分以优化消除埃博拉病毒，或至少是现行毒株。
美赛格式翻译
2015年美国数学建模要求Your Paper's TitleStarts Here: Please Centeruse Helvetica(Arial) 14论文的题目从这里开始：用Helvetica (Arial)14号FULL First Author1, a, FULLSecond Author2,b and Last Author3,c第一第二第三作者的全名1Fulladdress of first author, including country第一作者的地址全名，包括国家2Fulladdress of second author, including country第二作者的地址全名，包括国家3Listall distinct addresses in the same way第三作者同上aemail,bemail, cemail第一第二第三作者的邮箱地址1．文章标题居中用宋体14 2．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）。
2015年 美国(国际)大学生数学建模竞赛
美国（国际）大学生数学建模竞赛将于2015年2月5日-2月9日举行。
美国大学生数学建模竞赛（MCM/ICM），是唯一的国际性数学建模竞赛，也是世界范围内最具影响力的数学建模竞赛，为现今各类数学建模竞赛之鼻祖，目前我国已有清华大学、北京大学、浙江大学、上海交通大学、武汉大学等多所国内知名院校的学生参与了此项赛事的角逐。
2015年美国（国际）大学生数学建模竞赛比赛时间：美国东部时间：2015年2月5日（星期四）下午8点-2月9日下午8点（共4天）北京时间：2015年2月6日（星期五）上午9点-2月10日上午9点农历：十二月十八～十二月廿二重要说明：—COMAP是所有的规则和政策的最后仲裁者，对不遵循竞赛规则和程序的任何队伍，拥有唯一的自由裁量权，取消参赛资格或拒绝登记。
—评委、竞赛组织者、以及UMAP杂志的编辑拥有最终裁定权。
—如果参赛队伍违反竞赛规则，其指导老师一年内将不能指导其他团队，其所在参赛单位将被处以一年的察看处理。
—如果同一机构第二次被抓到违反规则的队伍，该学校将至少不被允许参加下一年度的赛事。
—以下所有时间都是美国东部时间EST（北京时间比美国东部时间早13个小时）—递交参赛论文后，意味参赛者同意以下条款：—论文提交后，出版权归COMAP，Inc所有；—COMAP可以使用，编辑，引用和出版论文，用于宣传或任何其他目的，包括在线展示，出版电子版，在UMAP杂志刊登或其他方式，并且没有任何形式的补偿；—COMAP可以在没有进一步的通知，许可，或补偿的情形下，使用这次比赛相关材料，团队成员、指导老师的名字，以及和他们的背景资料。
—递交参赛论文后，意味参赛者作出以下承诺：—论文中出现的所有的图像，数据，照片，图表，图画，如果未注明，都是由参赛者创建；如果引用其它资源，都在参考文献中列出，并在引用的具体位置标注来源。
—不论是直接，还是转述方式的文字引用，都在参考文献中列出，并在引用的具体位置标注来源；直接的文字引用使用引号标注。
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Automata, World Scientic, Singa-pore,1986. Nagel, Kai, and Michael Schreckenberg. A cellular automaton model for freeway traffic, Journal de Physique I 2.12 (1992): 2221-2229. Rickert, Marcus, et al., Two lane traffic simulations using cellular automata, Physica A: Statistical Mechanics and its Applications 231.4 (1996): 534550. Nagel, Kai, et al. Two-lane traffic rules for cellular automata: A systematic approach, Physical Review E 58.2 (1998): 1425.
Assumptions of the Model
• Drivers follow the rules with a specified probability. A driver might not want to change lanes even if all the conditions are satisfied. We assume that a driver changes to the left lane or to the right lane with probabilities pleft or pright, when possible. • All drivers tend to drive as fast as possible while keeping a safe following distance. Nearly every driver wants to drive faster on the freeway as long as there is enough time for him to react if the vehicle ahead decelerates. Also, the maximum speed is limited by the vehicle type and the speed limit of freeway.
元胞自动机仿真模拟模型？
2. 查阅资料
Keywords: traffic flow, : Traffic safety , Overtaking rules, :Traffic intelligent system ,… Keywords: traffic flow model, celluar automation model,…
也就是从问题的合理简化出发，达到有效
解决问题的目的，这是数学应用的特征。
通过假设，恰当地简化问题， 弥补信息数据的不足.
假设：车道数，道路限速，车的性能，车型， 驾驶习惯，… 假设：元胞大小，时间步长，换道所需时间， … 合理的假设主要作用是，简化问题以便在有 限的时间内能应用参赛者所学知识产生解决方 案、提供某些必须的而在竞赛时间内又无法采 集到的信息。
无法体现超车规则
K2 Q v f (K ) Kj
traffic flow and density 2000
Q(traffic flow)
1500
1000
500
0
0
20
40
60 80 K(traffic density)
100
120
明确目标
• Build a model that can simulate the overtaking process. • Propose mathematical criteria to determine the performance of a rule.
3. 建模计算
(1)定义 (2)假设(选择模型) (3)模型表达 (4)结果呈现
(1)定义-数学建模的切入点
数学建模用数学方法解决问题，首先要用数
学语言描述研究的对象，即给出清晰、准确 这个超车规则的效绩？ 的“定义”.
the performance of this rule in light and heavy traffic.
不必要的假设： 道路畅通，没有堵车.
对假设的合理、必要和影响进行清晰的描述， 给出某种理由，引用文献，分析它的含意.
基于已有数据资料分析做假设
基于问题的背景知识做假设 数学建模最重要的方面之一就是精致地描述假设
究竟如何被用于建立模型和如何确定模型中的参 数.
不同的假设对应不同的模型。假设与模型的一致
性。
不合理的假设：每条车道 最高和最低限速相同.
Assumptions and Justifications
• No pedestrian can affect the vehicles on freeways. Usually, pedestrians have no access to freeways, let alone crossing a freeway. • We ignore crosswinds during overtaking. This impact is negligible compared with that of the headwind. • Drivers cannot drive in the emergency lane or on the shoulder.
• The freeway is completely flat and straight, with no curves or slopes. This assumption allows us to focus on the nature of overtaking. • We assume that all drivers act based on the same set of rules. Drivers may be aggressive or not, but both groups follow the same rules.
We classify the vehicles into three groups: • Cars: Cars are small vehicles, which can have high speeds. • Buses: Buses are large vehicles, and their speeds can be relatively high. • Trucks: Trucks are large vehicles that can have only lower speeds.
讨论：
超车规则，只能用言语描述； 规则优劣要用数量指标评价： 道路通行效率：车流量？车流密度？车流速度？… 安全性：事故发生率？超车次数？…
引入变量，参量；
综合评价模型； 超车动力学模型； 评价指标(宏观数据)--车流量、超车次数、… 车流模型或车流动力学微分方程模型只能刻画宏观
Problem A, “The Keep-Right-Except-ToPass-Rule,”
asked teams to build and analyze a mathematical model to analyze the performance of this rule in light and in heavy traffic. Is this rule effective promoting greater throughput? If not, teams were to suggest and analyze alternatives that might promote greater throughput, safety, and/or other factors that they deemed important.
车流密 度大小
to examine tradeoffs between traffic flow and 车流vs.安全？ safety. the role of under- or over-posted speed
limits? other factors?
车道的最低、最高限速的作用？
问题来源：
The Keep Right Problem was contributed by
Michael Tortorella (Dept. of Industrial and Systems Engineering, Rutgers University, Piscataway, NJ). The Coach Problem was contributed byWilliam P. Fox (Dept. of Defense Analysis, Naval Postgraduate School, Monterey, CA).
数学建模基本步骤
1. 读题讨论 2. 查阅资料 3. 建模计算
4. 分析证明
5. 论文写作
1. 读题讨论
求什么？
目标是什么？ 相关因素是什么？
好的超车规则 提高道路通行效率， 保障安全性，… 车道数，道路限速，车 的性能，驾驶习惯，…
可选择的数学方法是什么？
车流模型？ 一阶偏微分方 程模型？
关于所研究问题已有的工作 关于所采用的方法已有的运用 建模所需的数据资料 检验模型所需的数据资料
车道数，道路限速，车 的性能，驾驶习惯，… 车流量，密度，速度， 超车次数，事故发生 率，…
重要的参考文献
S. Wolfram, Theory and Applications of Cellular