数学建模MCM美赛 M 奖

2024美赛数学建模题目
2024年美国大学生数学建模竞赛（MCM/ICM）赛题包括以下六道题目：
MCM A（环境类）题目：遭受旱灾的植物群落。

题目要求建立预测模型，预测植物群落未来随时间的变化。

MCM B（环境类、政策类）题目：重新想象马赛马拉。

题目难度主要在数据不好找，预测动物和人们相互作用的模型。

MCM C（数图、图论优化类知识）题目：预测单词结果。

可以采用神经网络模型，利用隶属度函数进行分类，用聚类模型转换为不同的类，再用神经网络作为输出。

ICM D 题目：联合国可持续发展目标的优先顺序。

关键在数据层面，构建
各个指标之间的关系网络，各个指标之间存在限制。

ICM E（环境类）题目：光污染。

难度系数主要还是在获取光污染的数据上。

ICM F 题目：绿色GDP。

择某个标准来计算绿色GDP，基于水资源安全的模型来构建它对全球气候变化的影响。

以上就是2024年美国大学生数学建模竞赛的六道赛题，每道题目的主题和要求均已给出。

如需更多信息，可以登录美赛官网进行查询。

美国数学建模竞赛的相关信息一．美国数学建模竞赛MCM简介MCM全称：The Mathematical Contest in Modeling（数学建模竞赛，国内称为美国国际数模竞赛）ICM全称：The Interdisciplinary Contest in Modeling（交叉学科建模竞赛，国内称为美国大学生数学建模与交叉学科竞赛）MCM始于1985年，由美国自然基金协会和美国数学应用协会共同主办，美国运筹学学会、工业与应用数学学会、数学学会等多家机构协办。

其宗旨是鼓励大学生对范围并不固定的各种实际问题予以阐明、分析并提出解法，每队在4天内对问题展开设计，要以清楚定义的格式写出解法论文。

该项比赛吸引了中国（含香港）、美国、英国、加拿大、芬兰、爱尔兰、澳大利亚、南非、新加坡等多个国家的著名大学代表队参加。

1999年COMAP推出了交叉学科建模竞赛。

其特等奖论文将刊登于同年UMAP杂志。

近年来，MCM/ICM比赛越来越具有影响力，也得到越来越多的学校和单位认可。

其获奖学生在出国留学、保送研究生、找工作时，在激烈的竞争中胜出的机会要多很多。

MCM将题目公开在网络上这种开放式的竞赛方式，竞赛环境相对而言比较自由，然而参赛选手来世界各地，竞争之激烈可想而知。

MCM/ICM其要求与国内竞赛大致相同，除了要求用英语阅读、写作水平外。

这对于中国的学生来说是一个非常大的挑战，如果成功参赛，将极大程度上提高英语水平。

总而言之，在建模期间，知识将会进一步积累，知识面也会得到提高，而英语写作能力、资料的检索能力、创新能力等都将得到训练，这些能力综合起来其实就是科研能力，将为今后的科研打下坚实的基础。

二．美国数学建模竞赛网站进入方法首先进入中国数学建模网站，点击友情链接页面，找到美国大学生数学建模竞赛，点击即可直接进入网站。

具体过程如下：全国数学建模竞赛/友情链接/html_cn/block/f104f25e0431f7882cb1ddd5be2d8a14.html美国大学生数学建模竞赛(MCM & ICM in USA)/undergraduate/contests/三．2011年美国大学生数学建模竞赛（MCM/ICM）竞赛2011年美国大学生数学建模竞赛（MCM/ICM）竞赛于（美国东部时间）2011年2月10日晚8:01~14日晚8:00举行。

For office use onlyT1________________ T2________________ T3________________ T4________________ Team Control Number70028Problem ChosenBFor office use onlyF1________________F2________________F3________________F4________________2017MCM/ICMSummary Sheet(Your team's summary should be included as the first page of your electronic submission.)Type a summary of your results on this page. Do not include the name of your school, advisor, or team members on this page.SummaryThe performance of highway toll plaza directly affects the capacity of the highway, so the design of road toll plaza is imperative.In this paper, we conduct performance analysis for a specific toll plaza in New Jersey, USA, including accident prevention, throughput and cost. First of all, we usegrey model to predict the future output of the toll plaza, and compared with the realdata, the average value of the residual value is 0.429. Then we can draw a conclusionthat the throughput performance of the toll plaza is secondary. Next, we use queuingtheory to get the service index of the toll plaza in the light and heavy traffic, and thecellular automaton model is used to consider the changing circumstances of servicelevel, uses regression model to establish a function relation between traffic accidentand four factors. Then, we find that the rate of change has the greatest influence onit and the pavement performance has the least influence . In terms of cost, weconsider the toll plaza land and road construction. And the cost of road constructionis divided into the labor cost and material cost.Next, according to the influence of road geometry on the traffic performance of Toll Plaza, we select the transition curve trajectory model to improve the toll plazatransition, which can also have an improvement on the size and shape of the toll plazaand merge mode.Finally, we do a series of performance studies for our improved toll plaza. First of all, the improvement in the square flow and car flow under the condition of servicelevel are determined respectively through simulation .Next, we draw a conclusion thatthe service performance of the toll plaza is not obvious in small car flow, but there is amarked increase in large flow. Then, due to the fact that the unmanned vehicle coulddeal with a variety of road conditions, it undoubtedly expands our improved optionalscheme. Eventually, we obtain the throughput of toll before and after the improvementunder the different proportion of mixed charge mode and find that the improvedthroughput in the toll plaza has been increased on the performance.contents1 Introduction: (1)1.1 Problem background: (1)1.2 Steps: (1)1.3 Our work: (1)2 Assumptions (2)3 Nomenclature (2)4 Throughput analysis of grey forecasting model (3)5 error analysis (4)6 Service level of toll station (5)7 Vehicle lane changing rules based on Cellular Automata (6)8 Security analysis based on multivariate statistical regression mode (8)8.1 Study on the rate of change of Toll Plaza (8)8.2 Study on the longitudinal slope of entrance section of Toll Plaza (9)8.3 Research on service level of toll station (10)8.4 Study on pavement performance of toll station (10)9 Safety performance evaluation model of toll station (11)10 Cost analysis model of toll station (11)11 Analysis of the influence of lane geometry parameters on its capacity (12)11.1 Determination of lane changing rate (12)11.2 Influence of geometric parameters on the flow of the car lane (14)11.3 Energy consumption analysis based on cellular automata model (15)Definition of energy consumption: (16)Numerical simulation and analysis of the results: (17)Influence of curvature radius on energy consumption (17)Influence of arc length on energy consumption (18)12 The effect of traffic flow on service performance based on improved queuing theory 1913 The influence of unmanned vehicles on the improved model of Toll Plaza .. 2114 The influence of charging method on improving model of Toll Plaza (21)15 Strengths and Weaknesses (22)15.1 Strengths: (22)15.2 Weaknesses: (22)15.3 Future Model Development: (22)Comprehensive improvement strategy of tollplaza1Introduction:1.1Problem background:Highway toll and toll plaza is to ensure traffic safety and unimpeded, however because of lack of unified design specification, toll station and its square construction exists many problems. Such as: low value because of the technical indicators to make square construction scale too small and cause the toll plaza opened only few years as the traffic bottleneck, and use the high value on the one hand, because of the technical indicators and make the toll station construction scale is too large, waste a lot of money and resources. Due to incorrect linear indicators, or too short, the gradual square square length is insufficient, square road centerline offset, etc., it is too difficult to use after the completion of the square.so establishing the toll gates and the toll plaza design norms, as soon as possible, has the very vital significance in standardizing the construction of the toll station, ensuring the smooth general characteristic of toll plaza and traffic safety, improving the charging efficiency and management level, reducing the land acquisition and controlling investment and so on .1.2Steps:·A performance analysis of any particular toll plaza design that may already be implemented through the following three factors: accident prevention, throughput and cost .·Determine if there are better solutions (shape, size, and merging pattern) than any in common use.·Consider the performance of your solution in light and heavy traffic.·Consider the situation where more autonomous (self-driving) vehicles are added and how the solution is affected by the proportions of conventional (human-staffed) tollbooths, exact-change (automated) tollbooths, and electronic toll collection booths (such as electronic toll collection via a transponder in the vehicle)1.3Our work:·Based on the available data ,we make a performance analysis of any particulartoll plaza design that may already be implemented .·According to the problem from the performance analysis ,we make out a better solutions (shape, size, and merging pattern) than any in common use.·Determine the performance of the solution in light and heavy traffic ,how the solution change as more autonomous (self-driving) vehicles are added to the traffic mix and how the solution is affected by the proportions of conventional (human-staffed) tollbooths, exact-change (automated) tollbooths, and electronic toll collection booths.2AssumptionsTo simplify the problem and make it convenient for us to simulate real-life conditions, we make the following basic assumptions.1. Each section of roads is one-way traffic2.Vehicles in the retention period of toll station can be neglected3.In any hour of the vehicle arrival rate is proportional to the length of time4.The probability of any vehicle arrival in one hour of time is not affected by the previous history .5. The vehicles arrive in line with the Poisson distribution, namely the headway is negative exponential distribution3Nomenclatureε(0)(t)the residual errorq(t)the relative errorc the variance ratioP the small error probabilityr the curvature of the bend radiusu the static friction coefficientl the gradual change ratiok the number of serving drivewayρ/k traffic intensityw mean time to stay at a toll stationd automotive braking distancef the tire and road surface friction coefficientY the number of traffic accidents in toll stations per year∆W Width of the gradualα1curve angle R 1the radius of convex curve points pdelay probability e(n,t) energy consumption of the first n vehicles from time t to t+14 Throughput analysis of grey forecasting modelFigure 4-0-1Schematic diagram of New Jersey toll plazaFirst of all, we chose a toll plaza on the New Jersey in the United States for a specific performance analysis of toll plaza, and it includes the accident prevention, throughput, and cost.In view of the throughput of the toll plaza, we choose the grey forecasting model GM(1,1) , to predict the throughput of the toll plaza. Due to the problem of uncertainty, so we take the grey prediction model to deal with it.Suppose x (0)(1),x (0)(2)…,x (0)(M )In order to overcome the irregular , we use accumulation processx (1)(t )=∑x (0)(i)M i<1 Such a relatively smooth new series approximation can be described by the following differential equation:dx (1)dt +ax (1)=μ Its an albino form discrete solution of differential equation is: x ̂(1)(i +1)=.x (1)−u a /e ;ai +u aThe type of the parameter a、u be determined by the least squares fitting method is as follows:（1）（2）（3）A ̂=0a u 1=(B T B);1B T Y N Among them the matrix is:B =[ −12,x (1)(1)+x (1)(2)-1−12,x (1)(2)+x (1)(3)-1⋯⋯−12,x (1)(m −1)+x (1)(m )-1] Y N =(x (0)(2),x (0)(3),⋯,x (0)(m ))TSo the original data fitting sequence is:x ̂(0)(1)=x (0)(1)x ̂(0)(i +1)=x (1)(i +1)−x (1)(i )Table 4-0-1 Traffic flow prediction table5 error analysisIn equation (11), and regulations, the original data of reducing value and its residual error and relative error between observed value is as follows{ε(0)(t )=x (0)(t )−x′(0)(t )q (t )=ε(0)(t )x (0)(t )×100%The following inspection of the accuracy: x(0)=1M ∑x (0)(t )M t<0 ε(0)=1M;1∑(ε(0)(t )−ε0M t<2)2Second, calculate the variance ratio c =s 2s 1and small error probability P =2|ε(0)(t )−ε(0)|<0.6745s 13（4）（5）（6） （7） （8） （9） （10） （11）Figure 5-0-2comparison chart of grey prediction modelWe use m、p、v max to represent quality of the vehicle, random delayprobability and maximum speed respectively, g represents the local acceleration of gravity, r represents curvature of the bend radius and u represents the static friction coefficient . With the road statistical analysis carried out on the real value and the error of predicted value, we obtain the following res ults:It shows that the GM(1,1)model prediction results have a better response to .reflect the actual situation.6 Service level of toll stationThe direct feeling of the driver to the traffic environment of the toll station is from the queue length of the toll lane, and the length of the queue depends on the service level of the toll station V/C. In this regard, we use the queuing theory model of multichannel Queuing service, in which the vehicle arrival time is in a Poisson distribution, which is the negative exponential distribution; Suppose m is random arrival rate ,c i is output rate,k is the number of serving driveway, ρ=m c .There is the probability of having no vehicle in the queuing theoryρ(0)=1,∑1n!k−1n=0p n :1k!ρk k k−ρ- Average number of vehicles in queueing theory:n =ρ+p n ρ(0)k!k n−k (1;ρk )2 （12）（13）queue length: q =n −ρ=p n ρ(0)k!k n−k (1;ρk )2 Average number of waiting vehicles per lanea =q kAverage waiting time in queue systems:d =n m =q m +1c Average waiting time in queue:W =q mMean tardinessDeceleration time of vehicle entering toll stationt 1=v 03.6a 1Mean time to stay at a toll stationw =E ,S -+W qVehicle acceleration time of leaving toll stationt 2=v 03.6a 2 In this equation, v 0 is the normal traffic flow (km/h); a 1 、a 2 are deceleration of the vehicle (m/s 2); W q is average queue time (s)； E ,S - is expected service time (s);7 Vehicle lane changing rules based on CellularAutomataWe apply the previous cellular automata model, which is now extended to multi Lane case. The main difference between multi lane and single lane is to consider the model of lane changing. In this paper, we take 4 lanes as an example.In reality, it may be possible to change lanes when the driver is found to be close to the exit and the front of the adjacent lane is empty. If you want to change lanes ,you should consider the vehicle behind the adjacent lane. When the distance （14）（15） （16） （17） （18） （19） （20）to the rear of the adjacent lane reaches to a certain length, you can change the road. Lane change scenarios can be shown in figure (), when the c car on the 1 Lane is blocked by the c 1 car, while the c 2 and c 3 cars on the 2 lanes are relatively large. in order to maintain the speed, c car will change to the road lane 2.Figure 7-0-3Schematic diagram of lane changingWhether or not the driver chooses the lane change is mainly decided by the d 0,d n,otℎer 、d n ,back three indicators, through the previous research, this paper thinks that the lane changing rule is:When d n,back >v maxC n ={1−C n d n <min{v n +1，v max } d n,otℎer >d n ,d n,back >v max c n Otℎer circumstancesWhen d n,back ≤v max ,C n ={1−C n d n <min{v n +1，v max } d n,otℎer >d nv max −θ(−∆x )α>1+min{d n,otℎer +1,v max }−min *V n +1，v max +c n Otℎer circumstancesAmong them, C n is the n car in the lane , C n =0 or 1,d n 、d n,otℎer andd n,back are the distance between the first n vehicle and the front vehicle, the distance from the adjacent lane and the distance from the vehicle in the adjacent lane, respectively. d safe is safety lane change model.d n,back −v max , ∆x <0, v max −θ(−∆x )α is the distance between the vehicle and the vehicle in the adjacent lane after correction by the value function, 1+min{d n,otℎer +1,v max }−min *V n +1，v max + is Limit Lane distance. The parameters α and θchange according to the psychological status of driver. If α>1, the greater α is, the more careful the driver is. If θ>1, the greater θis, the more careful the driver is. When α=1，θ=1,that ’s Lane changing model.（21） （22）In order to discuss the αandθ, we use Cellular automata simulation. In a two lane road with a length of7.5km, adopting the open boundary condition, each lane is composed of 1000cells with a length of7.5km, the maximum speed of vehicle v max=5. The random slowing down rate was 0.2.8Security analysis based on multivariate statistical regression modeAimed at the prevention of the accident, we use multiple linear regression to establish a function between the number of traffic accidents and the following four factors: toll square gradient, service level, Toll plaza entrance section of the longitudinal slope, the Pavement performance of Toll station .Figure 8-1Cause analysis of accident8.1Study on the rate of change of Toll PlazaFan in and fan out area of toll plaza are designed to make the gradual vehicles more natural smoothly in and out of the toll plaza. In order to drive vehicle easily , there has a requirement on its gentle gradient change. Otherwise the driver could produce driving deviation, which may cause improper operation and endangers safety.The relationship is as follow:（23）l=b,LAccording to the experience, the vehicles with straight into another lane deviation than at around 0.9m s⁄, drivers usually have no move feeling and uncomfortable feeling.Figure 8-1 The relationship between Accident number and Toll plaza ramp rateFigure 8-1 shows the relation curve between highway toll plaza ramp rate and traffic accident, the figure demonstrates that as the toll plaza ramp rate increases, the traffic accidents will increase, whereas the security of the toll plaza will decrease.Through the data regression analysis, we get the related models between toll plaza ramp rate and the number of traffic accidentsY =1.423e .0064xIn this equation, Y is the forecasted numbers of traffic accident corresponding to the toll plaza ramp rate , x is the toll plaza ramp rate of toll plaza.The correlation coefficient in the model R 2=0.8621, it shows that description model of correlation is higher, From the model ,we can learn that the occurrence of traffic accident frequency is proportional to the toll plaza ramp rate. Gradient length is insufficient, so it can't meet to slow down and change lanes entering the toll plaza vehicle safety requirements, resulting in the occurrence of traffic accidents .8.2 Study on the longitudinal slope of entrance section ofToll PlazaHighway toll entrance section of the longitudinal slope design without fully considering the characteristics of vehicles entering the toll plaza, a long downhill or turn downhill and so on bad road alignment, those will affect the normal operation of the pilot and make the vehicles entering the toll plaza slowdown not sufficient, longitudinal safe driving distance not enough and driving direction can't adjust to the charge lane ,which will causetraffic accidents. This will lead to serious losses. （24）Figure 8-0-4 entrance section of the longitudinal slope and accident numberThrough regression analysis, we get the relevant model between the toll plaza entrance section of longitudinal wave and traffic accidentsY =2.6254e 0.638xIn this equation, Y is the forecasted numbers of traffic accident corresponding to the toll plaza ramp rate , x is the longitudinal wave of t oll plaza’s entry section .The correlation coefficient in the model R 2=0.9219,it shows the correlation of this model is relatively high. But we can learn that toll station ‘s traffic accident and its entrance section of longitudinal wave have a positive correlation from figure model representation ,.The greater the slope, the lower charge war security.8.3 Research on service level of toll stationBased on the previous research of service performance of toll station, we take V C as the measure of service level and Cite previous results. 8.4 Study on pavement performance of toll stationAccording to the vehicle dynamics, the vehicle's braking distance can be expressed as follows:d =u 257.9(f:I) In this equation, d is automotive braking distance , u is the speed at the beginning of the automobile brake, f is the tire and road surface friction coefficient, Iis road longitudinal slope（25）9 Safety performance evaluation model of toll stationBased on the above analysis, the evaluation model of descriptive can be written as the equation form, using multiple linear regression model .Y is the number of traffic accidents in toll stations every year , x 1=1l ,x 2=V C ,x 3=i,则Y =β0+β1x 1+β2x 2+β3x 3N is sample size , Y i (i =1,2,…,N ) represent the Y value of sample i , x i 1,x i 2,…x i n (i =1,2…，N) represent the value of each variable insample I, respectively.令Y =[Y 1Y 2⋮Y n], X =[11⋮1x 11x 21⋮x n 1⋯⋯⋮⋯x 1n x 2n ⋮x n n ] β=[β0β1⋮βn ] Y =Xβ,making maximum likelihood estimate of each variable coefficient β1，β2，…βn , it can get a normal equations:X T Xβ=X T YSo you can get the following regression equationY =−4.4012−9.947511l +10.098V C +11.25i 10 Cost analysis model of toll stationWe selected the American New Jersey a toll plaza to make cost analysisFirstly, according to relevant data, we learn that New Jersey’s average price is （26） （27）（28）（29）（30）$3500 per mu,And the toll plaza which we analyzed occupies about 5 mu, therefore, the land price of the toll plaza is about $17500;Second, the road construction costs include labor and material cost, and the local construction industry ’s average monthly salary is $3000, we use it to calculate labor, this occupies the largest in the road construction costs; As for material cost, we calculate by the current prices in the United States, is about $40 per cubic meter, then according to the size of the toll plaza, it will cost about $45000.In conclusion, the cost of toll plaza spend mainly on the labor cost of highway construction, the material cost also accordingly account for part of it.11Analysis of the influence of lane geometry parameters on its capacity11.1Determination of lane changing rateAccording to the analysis of vehicle trajectory and running state of vehicle , vehicle trajectory in the middle of the gradual path is similar to vehicle lane changing trajectory, and considering the factors when the driver turns, we select the easement curve trajectory model to design the gradual change section of toll plaza. And in the middle of the two convex type curve , we join a long for L straight section , it is shown in the figure belowFigure 11-0-5Toll plaza improvementsAccording to characteristics of convex curve geometric elements, we can use the following formula to calculate the first period of convex curve of easement curve tangent length T1:T1=(R1+p1)tanα1+q1（31）2In this equation, R 1 is the radius of the first section of convex curve points , ρ1 is Within shift, q 1 is tangent increment, α1 is curve angle, and α1=2β1, β1 is easement curve angleSuppose the first and second convex curve gradient width are ∆W 1 and ∆W 2 respectively, the width of one side with the gradient is ∆W .Depending on the figure with the easement curve in orbit, there are: ∆W 1=T 1∙sin α1∆W 2=T 2∙sin α2∆W =∆W 1+∆W 2+Lsinα1∆W =0(R 1+p 1)(1−cos L S1R 1 )+q 11∙sin L S1R 1 +0(R 2+p 2)(1−cos L S2R 2)+q 21∙sin Ls2R 2 +Lsinα1 L S1 and L S2 are the length of easement curve of two convex curve respectivelyL is radial tangent of two convex curve, so α1=α2,then it Can be introduced as follows:L S1R 1 =L S2R 2 Associate (38) and (39),we can get the length of easement curve of two - Section convex curve L S1 and L S2, then the transition section longitudinal distance L y can use the following formula to calculate:L y =[(R 1+p 1)tan L S12R 1 +q 1+(R 2+p 2)tan L S22R 2 +q 2](1+cos L S1R 1 )+Lcosα1 Suppose the ramp rate of transition period is K ,then we can adopt the following equation:K =∆WL y From this equation , we can learn that the driving radius and the straight line segment L have a great influence on the length and the gradient of the gradient. The greater the radius, the longer the straight line, the longer the length of the gradient, the smaller the rate of change（32） （33） （34） （35） （36）（37）（38）11.2 I nfluence of geometric parameters on the flow of thecar laneAssuming C 0 and C 1=dC dl represent respectively bend and itsgradient , l represents the length of the curve itself , we can get C (l )=C 0+C 1lso ，the bend of the direction Angle isφ(l )=φ0+∫C(τ)l 0dτ=φ0+C 0l +12C 1l 2 The bend of the longitudinal distance x(l) and transverse distance y(l) are{x (l )=x 0+∫cosφ(τ)dτl 0y (l )=y 0+∫sinφ(τ)dτl 0 Assuming sinφ≈φ,cosφ≈1,and when x 0(l )=0,x (l )=l , then the bend of transverse distance y(x) and direction angle φ(x) can be expressed{φ(x )=φ0+C 0x +12C 1x 2y (x )=y 0+φl +12C 0x 2+16C 1l 3 Using the ideas of analytical mechanics, assuming that the longitudinal velocity along the x axis for x ′, along the y axis transverse speed for y ′ , along the z axis of horizontal pendulum angular velocity as the bits of ψ′, then from The Lagrange's equations we can get{ d dt .ðE T ðẋ/−ψðE T ðẏ=F Q 1d dt .ðE T ðẏ/+ψðE T ðẋ=F Q 2d dt .ðE T ðψ/+ẋ ðE T ðẏ−y ðE T ðẋ=F Q 3 Defining the system kinetic energy E T =12m (ẋ+ẏ)+12I z ψ2In the formula, m,I z respectively represent Vehicle quality and Rotary inertia take the derivative of (46),we can get{ d dt .ðE T ðẋ/−ψðE T ðẏ=d dt(mẋ)−ψ (mẏ)d dt .ðE T ðẏ/+ψðE T ðẋ=d dt (mẏ)−ψ (mẋ)d dt .ðE T ðψ/+ẋ ðE T ðẏ−y ðE T ðẋ=d dt (I z ψ)−x (mẏ)−y (mẋ) （39）（40）（41）（42）（43）Delimiting generalized force: {F Q 1=∑F xF Q 2=∑F y F Q 3=∑M zIn summary we can get the Vehicle longitudinal coupling model.We mainly consider the lateral situation∑F y =F yr +F xf +F xf cosδ If the vehicle driving in the bend is only disturbed by small disturbance near the equilibrium state, the front wheel angle is small enough , so cosδ≈1,sinδ≈δ ∑F y =−(C f +C r )y ẋ−(aC f −bC f )ψẋ+(F xf +C f )δ We put the formula () and formula () into ()y =−d 2ẏẋ−.ẋ+kd 3ẋ/ψ−(F xf :C f m )δ In the formula d 2=C f :C r m ,d 3=aC f ;bC rI z ,k =I z mThen, the resultant force ∑M z along the vertical direction is∑M z =aF xf sinδ+aF xf cosδ−bF yrWhen sinφ≈φ,cosφ≈1,then∑F y =−(a 2C f +b 2C r )ψẋ−(aC f −bC f )ẏẋ+a(F xf +C f )δψ=−d 4ψẋ−−d 3y ẋ+a I z (F xf :C f m )δ In the formula, d 4=(a 2C f :b 2C r )I z 11.3 E nergy consumption analysis based on cellularautomata modelConsidering the influence of different shapes on traffic performance is mainly reflected in the curve, we mainly study the influence of the curve on the whole problem. On the road segment, Lane set of sections containing only one plane curve, the curve is provided with the deceleration section of L , the road will be regarded as the length of the L 1D discrete lattice chain, each lattice point at each moment or is empty or occupied for a car.m 、p and v max represent the quality of the vehicle, the （44） （45）（46）（47） （48） （49） （50）（51）stochastic delay probability and maximum speed ,respectively, g is the local acceleration of gravity, r and u represent the static friction coefficient of curvature radius and static coefficient of friction between wheel and road, respectively. The vertical direction of the vehicle is subjected to a pair of balance forces, and the influence of tangential friction on the vehicle is mainly reflected in the change of the speed, Therefore , the centripetal force required for the safety of the vehicle is provided by the normal static friction force,v safe is maximum speed of safetyturning, then mv safe2r =μmg,⁄v safe =√μgr .In each step of t →t +1 , all vehicles are in accordance with the following rules of the evolution of the speed and location of the synchronization update :Determine the vehicle delay probability p ：When the vehicle is in the buffer section , if v >v safe,take the probability of delay p =p 1 (larger), in other cases, take p =p 2 (smaller),Acceleration process: v n (t)→min (v n (t )+1,v max );deterministic deceleration process: v n (t)→min (v n (t ),gap n (t))Stochastic deceleration process with probability p ：v n (t)→max (v n (t )−1,0) deceleration process ：When the vehicle is in the corner of the road, and the speed v (t )>v safe , in order to turn the corner ，it must be slowed down :v n (t)→min (v n (t ),v safe )location update process: x n (t )→x n (t )+v n (t)Among them, v n (t) and x n (t ) are the speed and position of the first n vehicle at time t respectively , x n:1(t ) is the position of the first n +1 vehicle at time t . gap n (t )=x n:1(t )−x n (t )−1is the spacing between the first n car and the foregoing vehicle which is close to it.Definition of energy consumptionSuppose the mass of vehicle is m , when it slows down, its kinetic energy is reduced, we define the kinetic energy reduction for energy consumption, e(n,t) represents that energy consumption of the first n vehicles from time t to t+1 .e (n,t )={m,v 2(n,,t );v 2(n,,t:1)-2v (n,t )>v (n,t +1);0,v (n,t )≤v (n,t +1)The average energy consumption per vehicle per unit time:E d =1T 1N ∑∑e(n,t) N n<1t0:T;1t<t0 N is the total number of vehicles on the driveway, t 0 is relaxation time. For（52） （53）the energy consumption of the vehicle, if it is because the speed of t moment is greater than the Vehicle-to-vehicle distance v(n,t)>gap n(t), the vehicle decelerates, thatis defined as the interaction energy, denoted by E di; If it is because of the random deceleration caused, defined as the random deceleration energy consumption, denotedby E dr;if it is because the car speed In the corner v(n,t)>v safe, there is deceleration for the sake of driving safely, defined as safe energy consumption, denoted by E ds.Then total energy consumption is:E d=E di+E dr+E ds（54）Numerical simulation and analysis of the resultsTo simplify the problem, assuming that the length of actual road is 7.5km, Divided into 1000lattices, equivalent to the actual length of each grid correspondsto 7.5m, Delay probability p1=0.8,p2=0.25,Quality unit is defined 1. Entering probability changes from 0~1.0.The state of each vehicle is represented by its own speed v, v∈,0,v max-We let v max=5cell he actual speed is135km/h.We take8×104time steps every run .Influence of curvature radius on energy consumptionThe arc length s, the friction coefficient μand the radius of curvature of r are carried out numerical simulation. parameters are as follows: s=30m,μ=0.5,r=10、50、100、200、300m.According to v max=5cell/s,the maximum speed of the vehicle v max=37.5m/s. Results show that when r=300m, the safetyspeed v safe=√μgr=38.73m/s,v safe>v max, the bottleneck of the curve disappears and the speed limit is lost. The change of the probability in_p of therandom energy consumption（E di、E dr、E ds、E d）is shown in the figure.。

Meritorious Winner 641个队（9%），一等奖
Honorable Mention 2266个队（31%），二等奖 Successful Participant 4685个队（57%）。另有 Unsuccessful Participant 22个队（1%）。
8
主要内容2
美国大学生数学建模竞赛 中国大学生数学建模竞赛
13
主要内容3
美国大学生数学建模竞赛 中国大学生数学建模竞赛
“华东杯”大学生数学建模竞赛
14
“华东杯”大学生数学建模竞赛
华东杯大学生数学建模邀请赛（又名“华东杯”数模竞 赛）是一项由复旦大学数学科学学院发起，华东地区数学建 模联盟组织开展的竞赛。本项赛事开展十六年以来，在规模 和影响上都有了很大的提高，已经成为面向华东地区乃至全 国数十所重点大学的校际通讯赛，在全国高校中享有较高声 誉。比赛吸引了复旦大学、清华大学、上海交通大学、浙江 大学、南京大学、中国人民大学、中山大学、同济大学、华 东师范大学、西南交通大学等来自全国各地院校的同学参加。 华东杯大学生数学建模邀请赛网址： /hdmcm
“华东杯”大学生数学建模竞赛
9
中国大学生数学建模竞赛
1989年我国大学生（北京大学、清华大学、北 京理工大学共4个队）首次参加美国大学生数学建 模竞赛，经过两三年的参与，师生们都认为这项竞 赛有利于学生的全面发展，也是推动数学建模教学 在高校迅速发展的好形式。教育部领导及时发现并 扶植、培育了这一新生事物，决定从1994年起由 教育部高教司和中国工业与应用数学学会共同主办 全国大学生数学建模竞赛，每年一届。目前该项赛 事已成为全国性大学生科技竞赛活动。
学建模竞赛（ ICM ， The Interdisciplinary Contest in