全美数学建模大赛A论文-环岛城市交通

For office use onlyT1________________ T2________________ T3________________ T4________________Team Control Number7018Problem ChosencFor office use onlyF1________________F2________________F3________________F4________________ SummaryThe article is aimed to research the potential impact of the marine garbage debris on marine ecosystem and human beings，and how we can deal with the substantial problems caused by the aggregation of marine wastes.In task one，we give a definition of the potential long-term and short-term impact of marine plastic garbage. Regard the toxin concentration effect caused by marine garbage as long-term impact and to track and monitor it. We etablish the composite indicator model on density of plastic toxin，and the content of toxin absorbed by plastic fragment in the ocean to express the impact of marine garbage on ecosystem. Take Japan sea as example to examine our model.In ask two, we designe an algorithm, using the density value of marine plastic of each year in discrete measure point given by reference，and we plot plastic density of the whole area in varies locations. Based on the changes in marine plastic density in different years， we determine generally that the center of the plastic vortex is East—West140°W—150°W, South—North30°N—40°N. According to our algorithm, we can monitor a sea area reasonably only by regular observation of part of the specified measuring pointIn task three，we classify the plastic into three types，which is surface layer plastic，deep layer plastic and interlayer between the two. Then we analysis the the degradation mechanism of plastic in each layer. Finally，we get the reason why those plastic fragments come to a similar size.In task four， we classify the source of the marine plastic into three types，the land accounting for 80%，fishing gears accounting for 10%，boating accounting for 10%，and estimate the optimization model according to the duel-target principle of emissions reduction and management. Finally, we arrive at a more reasonable optimization strategy.In task five，we first analyze the mechanism of the formation of the Pacific ocean trash vortex， and thus conclude that the marine garbage swirl will also emerge in south Pacific，south Atlantic and the India ocean. According to the Concentration of diffusion theory, we establish the differential prediction model of the future marine garbage density，and predict the density of the garbage in south Atlantic ocean. Then we get the stable density in eight measuring point .In task six, we get the results by the data of the annual national consumption ofpolypropylene plastic packaging and the data fitting method, and predict the environmental benefit generated by the prohibition of polypropylene take-away food packaging in the next decade. By means of this model and our prediction，each nation will reduce releasing 1.31 million tons of plastic garbage in next decade.Finally, we submit a report to expediction leader，summarize our work and make some feasible suggestions to the policy- makers.Task 1:Definition:●Potential short-term effects of the plastic: the hazardeffects will be shown in the short term.●Potential long-term effects of the plastic: thepotential effects, of which hazards are great, willappear after a long time.The short- and long-term effects of the plastic on the ocean environment:In our definition, the short-term and long-term effects of the plastic on the ocean environment are as follows.Short-term effects:1）The plastic is eaten by marine animals or birds.2） Animals are wrapped by plastics, such as fishing nets, which hurt or even kill them.3）Deaden the way of the passing vessels.Long-term effects:1）Enrichment of toxins through the food chain: the waste plastic in the ocean has no natural degradation in theshort-term, which will first be broken down into tinyfragments through the role of light, waves,micro-organisms, while the molecular structure has notchanged. These "plastic sands", easy to be eaten byplankton, fish and other, are Seemingly very similar tomarine life’s food,causing the enrichment and delivery of toxins.2）Accelerate the greenhouse effect: after a long-term accumulation and pollution of plastics, the waterbecame turbid, which will seriously affect the marineplants (such as phytoplankton and algae) inphotosynthesis. A large number of plankton’s deathswould also lower the ability of the ocean to absorbcarbon dioxide, intensifying the greenhouse effect tosome extent.To monitor the impact of plastic rubbish on the marine ecosystem:According to the relevant literature, we know that plastic resin pellets accumulate toxic chemicals , such as PCBs、DDE , and nonylphenols , and may serve as a transport medium and soure of toxins to marine organisms that ingest them[]2. As it is difficult for the plastic garbage in the ocean to complete degradation in the short term, the plastic resin pellets in the water will increase over time and thus absorb more toxins, resulting in the enrichment of toxins and causing serious impact on the marine ecosystem.Therefore, we track the monitoring of the concentration of PCBs, DDE, and nonylphenols containing in the plastic resin pellets in the sea water, as an indicator to compare the extent of pollution in different regions of the sea, thus reflecting the impact of plastic rubbish on ecosystem.To establish pollution index evaluation model: For purposes of comparison, we unify the concentration indexes of PCBs, DDE, and nonylphenols in a comprehensive index.Preparations:1）Data Standardization2）Determination of the index weightBecause Japan has done researches on the contents of PCBs,DDE, and nonylphenols in the plastic resin pellets, we illustrate the survey conducted in Japanese waters by the University of Tokyo between 1997 and 1998.To standardize the concentration indexes of PCBs, DDE,and nonylphenols. We assume Kasai Sesside Park, KeihinCanal, Kugenuma Beach, Shioda Beach in the survey arethe first, second, third, fourth region; PCBs, DDE, andnonylphenols are the first, second, third indicators.Then to establish the standardized model:j j jij ij V V V V V min max min --= （1,2,3,4;1,2,3i j ==）wherej V max is the maximum of the measurement of j indicator in the four regions.j V min is the minimum of the measurement of j indicatorstandardized value of j indicator in i region.According to the literature [2], Japanese observationaldata is shown in Table 1.Table 1. PCBs, DDE, and, nonylphenols Contents in Marine PolypropyleneTable 1 Using the established standardized model to standardize, we have Table 2.In Table 2，the three indicators of Shioda Beach area are all 0, because the contents of PCBs, DDE, and nonylphenols in Polypropylene Plastic Resin Pellets in this area are the least, while 0 only relatively represents the smallest. Similarly, 1 indicates that in some area the value of a indicator is the largest.To determine the index weight of PCBs, DDE, and nonylphenolsWe use Analytic Hierarchy Process (AHP) to determine the weight of the three indicators in the general pollution indicator. AHP is an effective method which transforms semi-qualitative and semi-quantitative problems into quantitative calculation. It uses ideas of analysis and synthesis in decision-making, ideally suited for multi-index comprehensive evaluation.Hierarchy are shown in figure 1.Fig.1 Hierarchy of index factorsThen we determine the weight of each concentrationindicator in the generall pollution indicator, and the process are described as follows:To analyze the role of each concentration indicator, we haveestablished a matrix P to study the relative proportion.⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=111323123211312P P P P P P P Where mn P represents the relative importance of theconcentration indicators m B and n B . Usually we use 1，2，…，9 and their reciprocals to represent different importance. The greater the number is, the more important it is. Similarly, the relative importance of m B and n B is mn P /1（3,2,1,=n m ）.Suppose the maximum eigenvalue of P is m ax λ, then theconsistency index is1max --=n nCI λThe average consistency index is RI , then the consistencyratio isRICI CR = For the matrix P of 3≥n , if 1.0<CR the consistency isthougt to be better, of which eigenvector can be used as the weight vector.We get the comparison matrix accoding to the harmful levelsof PCBs, DDE, and nonylphenols and the requirments ofEPA on the maximum concentration of the three toxins inseawater as follows:⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=165416131431P We get the maximum eigenvalue of P by MATLAB calculation0012.3max =λand the corresponding eigenvector of it is()2393.02975.09243.0，，=W1.0042.012.1047.0<===RI CI CR Therefore,we determine the degree of inconsistency formatrix P within the permissible range. With the eigenvectors of p as weights vector, we get thefinal weight vector by normalization ()1638.02036.06326.0'，，=W . Defining the overall target of pollution for the No i oceanis i Q , among other things the standardized value of threeindicators for the No i ocean is ()321,,i i i i V V V V = and the weightvector is 'W ,Then we form the model for the overall target of marine pollution assessment, （3,2,1=i ）By the model above, we obtained the Value of the totalpollution index for four regions in Japanese ocean in Table 3T B W Q '=In Table3, the value of the total pollution index is the hightest that means the concentration of toxins in Polypropylene Plastic Resin Pellets is the hightest, whereas the value of the total pollution index in Shioda Beach is the lowest(we point up 0 is only a relative value that’s not in the name of free of plastics pollution)Getting through the assessment method above, we can monitor the concentration of PCBs, DDE and nonylphenols in the plastic debris for the sake of reflecting the influence to ocean ecosystem.The highter the the concentration of toxins,the bigger influence of the marine organism which lead to the inrichment of food chain is more and more dramatic.Above all, the variation of toxins’ concentration simultaneously reflects the distribution and time-varying of marine litter. We can predict the future development of marine litter by regularly monitoring the content of these substances, to provide data for the sea expedition of the detection of marine litter and reference for government departments to make the policies for ocean governance.Task 2:In the North Pacific, the clockwise flow formed a never-ending maelstrom which rotates the plastic garbage. Over the years, the subtropical eddy current in North Pacific gathered together the garbage from the coast or the fleet, entrapped them in the whirlpool, and brought them to the center under the action of the centripetal force, forming an area of 3.43 million square kilometers (more than one-third of Europe) .As time goes by, the garbage in the whirlpool has the trend of increasing year by year in terms of breadth, density, and distribution. In order to clearly describe the variability of the increases over time and space, according to “Count Densities of Plastic Debris from Ocean Surface Samples North Pacific Gyre 1999—2008”, we analyze the data, exclude them with a great dispersion, and retain them with concentrated distribution, while the longitude values of the garbage locations in sampled regions of years serve as the x-coordinate value of a three-dimensional coordinates, latitude values as the y-coordinate value, the Plastic Count per cubic Meter of water of the position as the z-coordinate value. Further, we establish an irregular grid in the yx plane according to obtained data, and draw a grid line through all the data points. Using the inverse distance squared method with a factor, which can not only estimate the Plastic Count per cubic Meter of water of any position, but also calculate the trends of the Plastic Counts per cubic Meter of water between two original data points, we can obtain the unknown grid points approximately. When the data of all the irregular grid points are known (or approximately known, or obtained from the original data), we can draw the three-dimensional image with the Matlab software, which can fully reflect the variability of the increases in the garbage density over time and space.Preparations:First, to determine the coordinates of each year’s sampled garbage.The distribution range of garbage is about the East - West 120W-170W, South - North 18N-41N shown in the “Count Densities of Plastic Debris from Ocean Surface Samples North Pacific Gyre 1999--2008”, we divide a square in the picture into 100 grids in Figure (1) as follows:According to the position of the grid where the measuring point’s center is, we can identify the latitude and longitude for each point, which respectively serve as the x- and y- coordinate value of the three-dimensional coordinates.To determine the Plastic Count per cubic Meter of water. As the “Plastic Count per cubic Meter of water” provided by “Count Densities of P lastic Debris from Ocean Surface Samples North Pacific Gyre 1999--2008”are 5 density interval, to identify the exact values of the garbage density of one year’s different measuring points, we assume that the density is a random variable which obeys uniform distribution in each interval.Uniform distribution can be described as below:()⎪⎩⎪⎨⎧-=01a b x f ()others b a x ,∈We use the uniform function in Matlab to generatecontinuous uniformly distributed random numbers in each interval, which approximately serve as the exact values of the garbage density andz-coordinate values of the three-dimensional coordinates of the year’s measuring points.Assumptions(1)The data we get is accurate and reasonable.(2)Plastic Count per cubic Meter of waterIn the oceanarea isa continuous change.(3)Density of the plastic in the gyre is a variable by region.Density of the plastic in the gyre and its surrounding area is interdependent , However, this dependence decreases with increasing distance . For our discussion issue, Each data point influences the point of each unknown around and the point of each unknown around is influenced by a given data point. The nearer a given data point from the unknown point, the larger the role.Establishing the modelFor the method described by the previous,we serve the distributions of garbage density in the “Count Pensities of Plastic Debris from Ocean Surface Samples North Pacific Gyre 1999--2008”as coordinates ()z y,, As Table 1:x,Through analysis and comparison, We excluded a number of data which has very large dispersion and retained the data that is under the more concentrated the distribution which, can be seen on Table 2.In this way, this is conducive for us to get more accurate density distribution map.Then we have a segmentation that is according to the arrangement of the composition of X direction and Y direction from small to large by using x co-ordinate value and y co-ordinate value of known data points n, in order to form a non-equidistant Segmentation which has n nodes. For the Segmentation we get above,we only know the density of the plastic known n nodes, therefore, we must find other density of the plastic garbage of n nodes.We only do the sampling survey of garbage density of the north pacificvortex,so only understand logically each known data point has a certain extent effect on the unknown node and the close-known points of density of the plastic garbage has high-impact than distant known point.In this respect,we use the weighted average format, that means using the adverse which with distance squared to express more important effects in close known points. There're two known points Q1 and Q2 in a line ,that is to say we have already known the plastic litter density in Q1 and Q2, then speculate the plastic litter density's affects between Q1、Q2 and the point G which in the connection of Q1 and Q2. It can be shown by a weighted average algorithm22212221111121GQ GQ GQ Z GQ Z Z Q Q G +*+*=in this formula GQ expresses the distance between the pointG and Q.We know that only use a weighted average close to the unknown point can not reflect the trend of the known points, we assume that any two given point of plastic garbage between the changes in the density of plastic impact the plastic garbage density of the unknown point and reflecting the density of plastic garbage changes in linear trend. So in the weighted average formula what is in order to presume an unknown point of plastic garbage density, we introduce the trend items. And because the greater impact at close range point, and thus the density of plastic wastes trends close points stronger. For the one-dimensional case, the calculation formula G Z in the previous example modify in the following format:2212122212212122211111112121Q Q GQ GQ GQ Q Q GQ Z GQ Z GQ Z Z Q Q Q Q G ++++*+*+*=Among them, 21Q Q known as the separation distance of the known point, 21Q Q Z is the density of plastic garbage which is the plastic waste density of 1Q and 2Q for the linear trend of point G . For the two-dimensional area, point G is not on the line 21Q Q , so we make a vertical from the point G and cross the line connect the point 1Q and 2Q , and get point P , the impact of point P to 1Q and 2Q just like one-dimensional, and the one-dimensional closer of G to P , the distant of G to P become farther, the smaller of the impact, so the weighting factor should also reflect the GP in inversely proportional to a certain way, then we adopt following format:221212222122121222211111112121Q Q GQ GP GQ GQ Q Q GQ GP Z GQ Z GQ Z Z P Q Q Q Q G ++++++*+*+*=Taken together, we speculated following roles:(1) Each known point data are influence the density of plastic garbage of each unknown point in the inversely proportional to the square of the distance;(2) the change of density of plastic garbage between any two known points data, for each unknown point are affected, and the influence to each particular point of their plastic garbage diffuse the straight line along the two known particular point; (3) the change of the density of plastic garbage between any two known data points impact a specific unknown points of the density of plastic litter depends on the three distances: a. the vertical distance to a straight line which is a specific point link to a known point;b. the distance between the latest known point to a specific unknown point;c. the separation distance between two known data points.If we mark 1Q ，2Q ，…，N Q as the location of known data points,G as an unknown node, ijG P is the intersection of the connection of i Q ，j Q and the vertical line from G to i Q ，j Q()G Q Q Z j i ,,is the density trend of i Q ，j Q in the of plasticgarbage points and prescribe ()G Q Q Z j i ,,is the testing point i Q ’ s density of plastic garbage ,so there are calculation formula:()()∑∑∑∑==-==++++*=Ni N ij ji i ijGji i ijG N i Nj j i G Q Q GQ GPQ Q GQ GP G Q Q Z Z 11222222111,,Here we plug each year’s observational data in schedule 1 into our model, and draw the three-dimensional images of the spatial distribution of the marine garbage ’s density with Matlab in Figure (2) as follows:199920002002200520062007－2008(1)It’s observed and analyzed that, from 1999 to 2008, the density of plastic garbage is increasing year by year and significantly in the region of East – West 140W-150W, south - north 30N-40N. Therefore, we can make sure that this region is probably the center of the marine litter whirlpool. Gathering process should be such that the dispersed garbage floating in the ocean move with the ocean currents and gradually close to the whirlpool region. At the beginning, the area close to the vortex will have obviously increasable about plastic litter density, because of this centripetal they keeping move to the center of the vortex ,then with the time accumulates ,the garbage density in the center of the vortex become much bigger and bigger , at last it becomes the Pacific rubbish island we have seen today.It can be seen that through our algorithm, as long as the reference to be able to detect the density in an area which has a number of discrete measuring points,Through tracking these density changes ,we Will be able to value out all the waters of the density measurement through our models to determine,This will reduce the workload of the marine expedition team monitoring marine pollution significantly, and also saving costs .Task 3:The degradation mechanism of marine plasticsWe know that light, mechanical force, heat, oxygen, water, microbes, chemicals, etc. can result in the degradation of plastics . In mechanism ,Factors result in the degradation can be summarized as optical ，biological，and chemical。

SummaryWith the rapidly developing of traffic, freeway gradually becomes the mainstream way of short-distance travel. In order to make the means of transportation become more perfect, we need to improve in as many aspects as possible. To measure the performance of a freeway, we must consider the following two factors: traffic flow and safety. These are the main aspects that we must take into consideration to weigh whether a freeway is good or bad.In order to better simulate the actual situation, we established a simulationmodel .We adopted the core ideas of the Cellular Automata Model, on whose basis, we established a new model suitable to the simulation of the performance on freeway. The key point of our model is regarding time and space to be discrete which is actually continuous. Every vehicle must be in certain discrete position. In this problem, we divide the road into many same-size rectangular grids, the vehicle must move in a fixed place. he number of grids stands for the distance, the number of the grids that a vehicle move per unit time stands for it‘s speed. According to different rules, different small models are respectively established to study which rule is better. In a word the model we designed has combined the advantages of the Cellular Automata Model and the most important aspects of the actual situation on the highway.To study the performance more accurately, We have studied under the following three conditions:1. under very light traffic load;2. under a medium traffic load (normal traffic conditions)(main part);3. under a very heavy traffic load.In each case, we have analyzed the performance on freeway and discussed the traffic flow both in theory and by simulation. We have also calculated how the drivers on freeway guarantee their safety quantitatively. After that, we examined tradeoffs between traffic flow and safety, and analyzed the how each case limit the speed and overtaking ratio. Through analysis, we have got relatively reasonable conclusions. Differently, in case1, we gave an actual example to test our model. In case 2, we respectively analyzed the following and passing phenomenon in detail.Safety on freeway is so important that we have studied how much the traffic flow and speed influence it, we have calculated the two safety correlation coefficients of the traffic flow and speed and conclude that speed influence safety most.We have made comprehensive evaluation of ―the rule that requires drivers to drivein the right-most lane unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane‖ , and designed a new rule that―two lane used equally‖ to promote greater traffic flow while guaranteeing safe. The new rule has been tested by simulation.In countries where driving vehicles on the left is the norm, we have analyzed their performance on freeway,we found that my solution cannot be carried over with a simple change of orientation, additional requirements that the position of cab be changed should be needed.If vehicle transportation on the same roadway was fully under the control of an intelligent system, the most obvious change is the change of overtaking ratio (becomes almost 100%), this change will decrease traffic flow in our earlier analysis.ContentsAssumption and it‘s Rationality (5)1. Model (5)1.1 Basic model (5)1.2 Feasibility and rationality of the model (6)1.3 How we set the parameters in the model (6)1.4 Simulation of different situation that we use in the article (6)1.4.1 Rules of the single-lane Cellular Automata model (6)1.4.2 The lane changing model (7)1.4.2.1 The lane changing rules (7)1.4.2.2 Explanations of the lane changingrules (7)1.4.3 Lane Changing Model verification (8)2. Different traffic density (8)2.1 Under very light traffic load (9)2.1.1 Traffic flow calculation and simulation (9)2.1.2 Safety guarantee (10)2.1.3Speed limit (11)2.1.4 Overtaking ratio limit (11)2.1.5An actual example (11)2.2 Medium traffic load (Normal traffic conditions) (12)2.2.1 Three factors influencing on traffic flow andsimulation (12)2.2.2 Safety guarantee (16)2.2.2.1 Following phenomenon (16)2.2.2.2 Overtaking phenomenon (17)2.2.3Speed limit (18)2.2.4 Overtaking ratio limit (18)2.3 Very heavy traffic load (18)2.3.1 Safety factors analysis (18)2.3.2Influence on traffic flow and simulation (19)2.3.3Speed limit(very low speed) (19)2.3.4 Overtaking ratio limit (19)2.4. Safety correlation coefficient (19)3. A better rule (20)3.1 Description (20)3.2 Simulation (21)4. For countries driving on the left (21)5. Intelligent controlled transportation system (22)Futher analysis of our model (22)Conclusion (23)Reference (24)Assumption and it’s RationalityAll the length is dispersive. Our model describes the movement of each individual vehicle according to the study for their interaction by taking vehicles as dispersive particles. Cellular Automata model divides a section of road into many cells of 2 meters in length.The time interval is one second. As length is dispersive, the time is dispersive. We make the minimum time interval is one second. One second is short enough to describe the motion of the car.The length of the car is the same. In some freeway the big truck is prohibited. The number of small cars dominates. We just study the situation that small car driving on the freeway. The length of the car is 4 meters or so. We take it as a average 2 cell length.The number of the cars on a selected section of the road is a constant. We only study a section of the road. We designed it as a closed loop which means one car gets out and one car enters. So the number of the cars on a selected section of the road is a constant. In this way, the density of the cars on the road is a constant.We ignore the factor of weather and season. Different weather may lead to different traffic. The situation is complex that we have to ignore these factors.The steering wheel is on the right side of the car. It is a common that n countries where driving vehicles on the left is the norm the steering wheel is on the right side of the car. It is also a fact in US and China.Passing is not allowed to single road. At the same time a cell can be occupied by only one car. So the car cannot pass another car in front on the same road. Analysis of the problem1. Model1.1 Basic modelThe key point of our model is regarding time and space as discrete which is actually continuous. Every vehicle must be in certain discrete position. In this problem, we divide the road into many of the same size rectangular grids, the vehicle must move in a fixed place.The number of grids stands for the distance, the number of the grids that a vehicle move per unit time stands for it‘s speed.1.2 Feasibility and rationality of the modelWhen we analyze the problem, the distance we consider is long enough, and time is also long enough, dividing time and space into many small parts will not influence the results of analysis and simulation so much. On the contrary, the way we make time and space discrete will simplify the analysis and calculation process to a great extent, it can also make simulation much more easy.1.3 How we set the parameters in the modelConsidering the various aspects of factors, the Basic parameter definiteness is as follows:In this model, the length of each cell is 2 meters, per 2 successive cells containone vehicle and these 2 successive cells are in the same state at moment t, i.e. thespeed of vehicle contained. Maximum speed of vehicle is 120km/h（33m/s）. Minimum speed of vehicle is 80km/h（22m/s）.Thus in this model, maximum speed (v m) is 16 cell length/second, minimum speed(v min) is 11 cell length/second. Speed value range is v min～v m and renewal time interval is 1 second.1.4 Simulation of different situation that we use in the article1.4.1 Rules of the single-lane Cellular Automata modelVariable symbols used in this Model are defined as follows.x n(t):the position of the vehicle at moment t;v n(t):the speed of the vehicle at moment t;a n(t):the acceleration of the vehicle at moment t~t+1;g n(t):the number offree sites ahead of the vehicle, i.e.g n(t)＝x n-1(t)－x n(t)－2.The states of all vehicles on road conduct synchronous renewal according to the following rules.Acceleration Rule: if v n(t) ≤ g n(t), the vehicle will accelerate.If g n(t) - v n(t) < 2, then a n(t) = g n(t) - v n(t).If g n(t) - v n(t) ≥ 2, then a n(t) = 2.If v n(t) = v m, then a n(t) = 0.Deceleration Rule:If v n(t) >g n(t), the vehicle will decelerate.If g n(t) - v n(t) > -2, then a n(t) = g n(t) - v n(t).If g n(t) - v n(t) ≤ -2, then a n(t) = -2.Correction Rule:If the acceleration of the vehicle is a n(t) at moment t, on the assumption that the forward vehicle is decelerated at maximum deceleration, then at moment t+1.If v n(t+1) ≤ g n(t+1), then the acceleration of the vehicle is a n(t).If v n(t+1) >g n(t+1), then the acceleration of the vehicle is a n(t)-1, and recalculate the v n(t+1) and g n(t+1), until v n(t+1) ≤ g n(t+1).Thus, the actual acceleration of the vehicle is a corrected value.1.4.2 The lane changing modelLane changing is the emphasis and difficulty of multi-lane road traffic flow simulation. A lane change decision process is assumed to have the following three steps: production of lane changing desire, feasibility analysis on lane changing activity and implementation of lane changing activity (Zou,2002).Based on the single-lane NS model, K. Nagel has put forward the multi-lane traffic simulation model, in which, the vehicles moving in each lane shall conform to the NS rule and satisfy the Lane-changing rules (Nagel,1998/ Wagner,1997) when changing lanes. This article put forward a kind of lane-changing model that is suitable for vehicle movement in order on the urban roads under the unobstructed condition, which is shown to match the real vehicle activities well through computer. Simulation.1.4.2.1 The lane changing rulesVariable symbols used in this model are defined as follows.g n(t) = x n-1(t) - x n(t) - 2 (1) Here:g n(t)--the number of free sites ahead of the vehicle on the present lane at moment t g l(t)--the number of free sites between the vehicle and the forwardvehicle on target lane at moment tg b(t)--the number of free sites between the vehicle and the backward vehicle on target lane at moment tv l(t) --the speed of the forward vehicle on target lane at moment tv b(t)--the speed of the backward vehicle on target lane at moment ts b(t) --the emergency braking distance of the backward vehicle on target lane at moment tThe lane changing model is as follows:(1) ifg n(t) <v m, then the vehicle will produce lane changing desire(2) ifg l(t) ≥ g n(t) and v l (t) > v n-1 (t) and s b(t) ≤ s b(t), then the vehicle will change lane at v n(t) at probability pchangeHere, s b(t) = v b + max(v b - 2,0) + max(v b- 4,0) . (2)1.4.2.2 Explanations of the lane changing rulesIn this model, g n(t)<v m means due to the reason that the speed of forward vehicle isslower, that this vehicle will produce the desire of changing lane in order to reach faster speed and obtaining more free driving space.After producing the desire of changing lane, a vehicle will determine the feasibility of changing to adjacent lane according to observation. In general, a vehicle may chan- ge its lane only when the spaces between it and forward vehicle and it and backward vehicle are large enough. On condition of meeting g l(t)≥g n(t) and v l(t) > v n-1 (t), a vehicle can ensure that it will not collide with forward vehicle on target lane after changing its lane. On condition of meeting s b(t)≤s b(t), a vehicle will not collide with backward vehicle on target lane because the emergency braking distance of backward vehicle on target lane is less than the space between them. Only when meeting these conditions, a vehicle will implement lane changing activity at a certain probability. 1.4.3 Lane Changing Model verificationWe select 500-meter sections of two innermost lanes on the 4th Ring Road in Beijing as observation objectives to survey the lane changing condition at different time and under different flow in the condition of free flow. Observation period is 2 hours. Diamond shape points in Figure 1 are the survey number of lane changing under different volume. By linear regression fit, we can find that the relationship between number of lane changing and volume is linear.In accordance with the aforesaid lane-changing Cellular Automata model, we make a computer simulation for the lane-changing condition under the condition of free flow. During the simulation, we set up 500 cells, among which, 250 cells on the preparatory section (500m) and the other 250 cells on simulation section (500m), and the simulation time is 3900 seconds. The simulation within 0～300 seconds is the stage to clear up the bad effect, after a movement of 300 seconds, the road is full of vehicles. The simulation begins from the 301st second and simulation data is recorded after the first 250 cells, the flow diagram of lane-changing CellularAutomata model simulation is as follows.Simulations were conducted according to the above-mentioned process under different flows (i.e. 2500veh/h, 2600veh/h, 2700veh/h, 2800veh/h, 2900veh/h, 3000 veh/h), each flow is simulated for five times to acquire the average values, and thus, the lane-changing times under different flows are obtained. Comparing those simulated results (while p b=0.5 and p c=0.8)with the observed values, they are matching with each other by a large while p b and pc value are correctly selected so as to verify the validity of this Lane Changing Model.2. Different traffic densityThere‘s different performance under different traffic load so we must analyze in three parts:2.1 Under very light traffic loadWhen in light traffic, a vehicle is almost not constrained by other vehicles (free running). Drivers will run at a speed as much as possible to get the more benefits of driving such as shortening the travel time. It may raise traffic flow in some degree, however, this psychological state will cause certain threat to the safety. So the traffic flow and safety assessment in light traffic is necessary.2.1.1 Traffic flow calculation and simulationThough under low traffic load vehicles can run at a very high speed, the very low vehicle density plays a negative role. What‘s worse, the low vehicle density influence more on traffic flow in this case. In other words, the traffic flow will be very low.We assume that any vehicle can pass each other freely. The average interval of the vehicles is two thousand meters. The speed of vehicles varies from 80km/h to 120km/h. For the sake of simplicity, we choose only five kinds of speed: 80km/h, 90km/h, 100km/h, 110km/h and 120km/h. We assume that the quantity of each kind of speed of the vehicles is an equal.Compare this rule to the condition that all the vehicles run in one road without any pass.①Passing18090100110120/5052++++-=⨯=traffic flow hour (3) ②.No Passing ( the speed of almost all the cars is limited to under 80 km/h) 80/402traffic flow hour -== (4) This the result we get through calculation.Let‗s see the result of simulation:Fig1.under very low traffic loadThrough a certain tool, we can get the traffic flow (the number of vehicles through a cross-section we set in an hour).we have simulated 10 times and the data we got is as follows:42,44,49,38,45,46,44,43,47,51,45 (per hour)The average:40+42+38+44+40+41+42+45+44+43/=41.910traffic flow h -= (5) Comparing the theoretical calculation and simulation results, we can come to a similar conclusion with two methods, which has also supported our model.2.1.2 Safety guaranteeUnder very low traffic load, the main factor that influence safety is speed. Though there‘re other factors that may also influence, they are negligible relative to speed.The distance from the drivers found obstacles to the vehicle to a full stop is the sum of the reaction distance and braking distance. Shown in figure 2.Fig2. brake when finding an obstacleReaction distanceis the distance from the point where the driver finds an obstacle to the point where he starts to brake:1=t 3.6V S (6)Braking distance is the distance during the whole braking process:22=254(f+i)V S (7) The stopping sight distance:2=t+3.6254(f+i)V V S (8) Here:V--the speed of the vehicle (km/h);t--reaction time of the driver(s);f--coefficient of road adhesion (for dry pavement f=0.6);i--the tilt degree of the road (for level road i=0).L--the distance when the driver finds the obstacle between the obstacle and the vehicle.Suppose the safe distance is d, when +d ＞L S , t he vehicle will be in danger; when +d L S ≤, the vehicle is safe.2.1.3 Speed limitWhen the traffic load is light, vehicles can run as fast as possible under the biggest speed limit, however it will increase risk of accident; if the speed of some vehicles is too low, we can‘t make the best of the freeway thus reducing flow. So, under the premise of ensuring safety, we can run at a relatively high speed to increase traffic flow as possible as we can. A too high speed may lead to an accident.Speed is the main factor that influence the traffic flow.2.1.4Overtaking ratio limitSince the traffic load is very low, the possibility of overtaking phenomenon is very low, and in extreme cases the overtaking ratio can even be seen as zero.That is, in this case, overtaking is a very minor factor that influence traffic flow.2.1.5 An actual exampleWe have found an actual example in this case:2011, one day in July, Shanghai-Nanjing Freeway in Jiangsu province.Considering the weather and road condition, some experts major in it confirm that the coefficient of road adhesion f is 0.40. And according to the Shanghai-Nanjing Freeway designing information, the tilt degree of the road i is 0. The visibility that day is 55 meters. The safe distance is 5 meters.Substituting the data into equation ：22.5d +53.6254(f+i)V S V +=+， (9) If the result we calculate is more than 55 meters, the vehicle can‘t brake in time, which will cause a collision between the vehicle and the obstacle.So under such condition, the speed of each vehicle must be limited.For example, a vehicle ran at V=80km/h that day on Shanghai-Nanjing Freeway,22.580d 80+5123.553.6254(0.40+0)S m +=⨯+≈ (10) This result is much higher than the visibility 55 meters, so V=80km/h is a very dangerous speed.We can also calculate the highest speed that is allowed under the terrible condition:Let:22.5d+5553.6254(f+i)VS V m+=+≤, (11)We get: V≤43.52km/h (12) We can see that in this example, drivers must control the speed under 43.52km/h in order to guarantee their safety.2.2 Medium traffic load (Normal traffic conditions)Medium traffic density is the most common case, that is to say, this is the most consistent with the actual situation under normal circumstances. Therefore, we personally think that studying this case makes the most common sense. When the traffic density is not so big or so small, due to the rule requiring drivers to drive in the right-most lane unless they overtake from the left lane, the motion of vehicles is not untrammeled，each one is in interference and constraints produced by others. The performance of vehicles on freeway is mainly following and overtaking, through practical experience.2.2.1 Three factors influencing on traffic flow and simulationThe main factors that influence the traffic flow are overtaking ratio, traffic density and speed of vehicles, the three factors are not completely independent, there‘s certain mutual restraint and influence between them.“overtaking ratio--- traffic flow” relationWe choose the overtaking ratio as the main verification index when we study the process of overtaking. Through a survey that has been made and a relative simulation, the traffic flow changes with the overtaking ratio. The survey method is as figure3,the survey conclusion is as the table 1.Fig 3.Sketch map of section observatin method for field surveyTab 1. Survey of traffic flow and overtaking ratioTo get more accurate result, we have made a simulation. To make sure how the traffic flow changes with the overtaking ratio, we set a series of overtaking ratios. Through the simulation, we get the ‖ traffic flow—overtaking changing curve.Fig 4. Traffic flow—overtaking changing curveComparing the results of the survey and the simulation, the rationality of the model can be made sure. According to the curve, the changing process is divided into two sections: the first section shows that in two-lane freeway, the overtaking ratio increases with the traffic flow raising, to the biggest; the second section shows that with the traffic flow raising, the overtaking ratio decreases, when the traffic flow increases to 2900pcu/h, the overtaking ratio is almost zero.“traffic density-- traffic flow” relationAccording to the equation:Q=KV (13)Here:Q---the traffic flow (pcu/h);K---traffic density (pcu/km);V---the average speed (km/h)If there‘s no special situation such as rear-ending, when V is a constant ,Q ∝K, the image is as figure 5.Fig5. Q-K relationHowever, our simulation result is as figure 6.and 7Fig 6 S imulation result of ―traffic density -- traffic flow‖ relationFig 7 . ―Traffic density-- traffic flow‖ relation curveDifference explanation :Increased density cannot be unlimited, Q = KV is the ideal case, the actual case will be affected by external factors, our simulation result is more realistic.Analysis :When the traffic density is less than the optimum density of traffic flow,traffic flow is in th e f ree driving state,the average speed of cars is high. Traffic flow does not reach the m aximum value.The increasing of density leads to the increasing of trafficflow;when th e traffic density is equal or close to the optimum density of traffic flow, traffic team fo llowing phenomenon appears, the speed will be limited. Different kinds of car approa- ching a speed constant speed, traffic volume will reach the maximum value; when the traffic density is greater than the optimum density of traffic flow, traffic flow is in the congestion state, because of traffic density increases gradually, vehicle speed and traff ic volume decrease at the same time and traffic jam happens or even parking phenome non.From the figure, we can get the following information:①When K=0,Q=0,the curve pass O of the coordinate system; ②0=dK dQ ,m j K K K ==21 ③From the point c ，if K become larger ,Q becomes smaller ，when K= K j ，V=0 Q=0④Drawing radius vector from the coordinate origin to any point on the curve, the slope of the radius vector stands for the average speed of the point.⑤ K ≤ Km: not crowded; K>Km: crowded.“speed -- traffic flow” relationAccording to the equation:Q=KVIf there‘s no special situation such as rear -ending, when K is a constant ,Q ∝V, the image is as figure 8.Fig 8 Q-A relationOur simulation also confirms the linear relationship.Further discussionThe equation Q=KV can be shown in an more unified way (figure 9)Fig9 .3-D image of Q=KVWe have known that )1(j f K K V V -=, so )1(jj V V K K -=, (14) So we can get a more specific form :)(2fj V V V K KV Q -==, (15) figure 9 has shown the equation.Fig 10.Q-V-K relation2.2.2 Safety guarantee2.2.2.1 Following phenomenonAccording to the accident statistics annals, rear-ending is the main part of the traffic accident, so we must guarantee the security when a vehicle follows another. We can easily come to a conclusion that the speed is the main factor influencing safety under the state of vehicle following the front one. When the front vehicle suddenly brake, whether the following vehicle can stop in time to avoid collision, and maintain at a safe distance determines the safety of the two vehicles. This process is shown infigure 11.Fig11.brake when the front vehicle brake suddenlyAccording to AASHTO parking stadia model, the distance that the front vehicle A run from starting braking to stopping completely is:2254(f+i)A A V S (16)After reaction time, vehicle B also start to brake, the distance that the front vehicle B run from starting braking to stopping completely is:2t 3.6254(f+i)B B B V V S =+(17)Here: S A the speed of the front vehicle A (km/h);S B --the speed of the latter vehicle B (km/h);t--the reaction time of driver (s);f--coefficient of road adhesion (for dry pavement f=0.6);i--the tilt degree of the road (for level road i=0).Suppose two vehicles are L away from each other when the front one brake suddenly, set safety distance d,When ＜A B S L S d ++, or 22＜t +d 254(f+i) 3.6254(f+i)A BB V V V L ++, vehicle B can‘t brakein time, A and B can‘t hold a safe distance, accident may happen. Otherwise they are safe.2.2.2.2 Overtaking phenomenonWhen a freeway is in medium density, which is the most common case, overtaking often happens, in order to get rid of the limit of the slower vehicle in front of it. If an overtaking is successfully completed, the biggest driving satisfaction will be achieved. On freeway, overtaking will increase the traffic flow more or less, which is the main difference between single lane and two lanes. However, overtaking is a relatively dangerous behavior, we must make sure that we can safely finish a overtaking. This process is shown in figure 12.Fig 12. Overtaking phenomenon processVehicle P wants to overtake because there‘s a vehicle C from which P will be a dangerous distance away.We can put the overtaking process down into two lane changing process, which is the key to the analysis of overtaking.In the first lane changing process, the following inequalities must be satisfied:L1≤d;L2≤d; (18)L3≤d;In the second lane changing process, with the same reason, the following inequalities must be satisfied:L‖1≤d;L‖2≤d;L‖3≤d; (19)L‖4≤d;The L‖1, L‖2 , L‖3and L‖4 can be get by the following equations:L‖1=L1+V P t-V A t;L‖2= L2+V B t-V P t;L‖3=V P t-V C t-L3; (20)L‖4= L4+V D t-V P t.Here:L1 /L2/ L3/L4—the distance between A/B/C/D and P;d--safe distance;V A/V B/V C/V D/V P--the speed of vehicle A/B/C/D/P;t--total overtaking time.Now we can use these inequalities and equations to judge whether an overtaking is safe or not in theory.2.2.3Speed limitIn this case, the vehicles must run at a moderate speed, if an vehicle runs too fast, the risk of rear-ending will increase; if an vehicle runs too slow, it will increase the number of overtaking phenomenon per unit time per unit length thus security cannot be guaranteed.2.2.4 Overtaking ratio limitBecause of the vehicles around, the overtaking ratio can‘t be too low; the overtaking conditio n satisfied doesn‘t mean the happening of a successful overtaking, we must be aware that there‘s selective overtaking, that is, drivers may not overtake even if the safe condition has been ensured.2.3 Very heavy traffic loadWhen the freeway is under so heavy load that there‘s few overtaking behavior, the main factor that may limit the traffic flow is the overall movement speed. The performance on the freeway is mainly following, and the intervals are relatively very small.2.3.1 Safety factors analysis。

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. Table.5.1 measured results for the unenforced speed limit scenariodem q case#1 #2 #3 #4 #5 TTS:mean(std ) TPN 4700no shock 494.7452.1435.9414.8428.3445.21(6.9%) 5:4wave 3 5 8 8 0 14700nocontrolled520.42517.48536.13475.98539.58517.92(4.9%)6:364700 controlled 513.45488.43521.35479.75-486.5500.75(4.0%)6:244700 no shockwave493.9472.6492.78521.1489.43493.96(3.5%)6:034700 uncontrolled635.1584.92643.72571.85588.63604.84(5.3%)7:244700 controlled 575.3654.12589.77572.15586.46597.84(6.4%)7:19●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 ofthe 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, the 85V of some researchers for the typical countries from Table 6.1[ 21]: Table 6.1 Operating speed prediction modeAuthorCountry Model Ottesen andKrammes2000America LC DC L DC V C ⨯---=01.0012.057.144.10285Andueza2000Venezuel a ].[308.9486.7)/894()/2795(25.9885curve horizontal L DC Ra R V T ++--= ].[tan 819.27)/3032(69.10085gent L R V T +-= Jessen2001 America ][00239.0614.0279.080.86185LSD ADT G V V P --+=][00212.0432.010.7285NLSD ADT V V P -+=Donnell2001 America 22)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 DC V 124.0164.6685-= DC E V 4.046.3366.5585--= 2855.035.1119.0745.65DC E DC V ---= Fitzpatrick America KV 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 traffi csimulations 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。

美赛数学建模A题翻译版论文The document was finally revised on 2021数学建模竞赛(MCM / ICM)汇总表基于细胞的高速公路交通模型自动机和蒙特卡罗方法总结基于元胞自动机和蒙特卡罗方法,我们建立一个模型来讨论“靠右行”规则的影响。

首先,我们打破汽车的运动过程和建立相应的子模型car-generation的流入模型,对于匀速行驶车辆，我们建立一个跟随模型,和超车模型。

然后我们设计规则来模拟车辆的运动模型。

我们进一步讨论我们的模型规则适应靠右的情况和,不受限制的情况, 和交通情况由智能控制系统的情况。

我们也设计一个道路的危险指数评价公式。

我们模拟双车道高速公路上交通(每个方向两个车道,一共四条车道),高速公路双向三车道（总共6车道)。

通过计算机和分析数据。

我们记录的平均速度,超车取代率、道路密度和危险指数和通过与不受规则限制的比较评估靠右行的性能。

我们利用不同的速度限制分析模型的敏感性和看到不同的限速的影响。

左手交通也进行了讨论。

根据我们的分析,我们提出一个新规则结合两个现有的规则(靠右的规则和无限制的规则)的智能系统来实现更好的的性能。

1介绍术语假设2模型设计的元胞自动机流入模型跟随模型超车模型超车概率超车条件危险指数两套规则CA模型靠右行无限制行驶规则3补充分析模型加速和减速概率分布的设计设计来避免碰撞4模型实现与计算机5数据分析和模型验证平均速度快车的平均速度密度超车几率危险指数6在不同速度限制下敏感性评价模型7驾驶在左边8交通智能系统智能系统的新规则模型的适应度智能系统结果9结论10优点和缺点优势弱点引用附录。

1 Introduction今天,大约65%的世界人口生活在右手交通的国家和35%在左手交通的国家交通流量。

[worldstandards。

欧盟,2013] 右手交通的国家,比如美国和中国,法规要求驾驶在靠路的右边行走。

多车道高速公路在这些国家经常使用一个规则,要求司机在最右边开车除非他们超过另一辆车,在这种情况下,他们移动到左边的车道、通过，返回到原来的车道。

环岛交通优化设计数学建模Designing a Traffic Circle1 Restatement of The ProblemMany cities and communities have traffic circles—from large ones with many lanes in the circle (such as at the Arc de Triomphe in Paris and the Victory Monument in Bangkok) to small ones with one or two lanes in the circle. Some of these traffic circles position a stop sign or a yield sign on every incoming road that gives priority to traffic already in the circle; some position a yield sign in the circle at each incoming road to give priority to incoming traffic; and some position a traffic light on each incoming road (with no right turn allowed on a red light). Other designs may also be possible.The goal of this problem is to use a model to determine how best to control traffic flow in, around, and out of a circle. State clearly the objective(s) you use in your model for making the optimal choice as well as the factors that affect this choice. Include a Technical Summary of not more than two double-spaced pages that explains to a Traffic Engineer how to use your model to help choose the appropriate flow-control method for any specific traffic circle. That is, summarize the conditions under which each type of traffic-control method should be used. When traffic lights are recommended, explain a method for determining how many seconds each light should remain green (which may vary according to the time of day and other factors). Illustrate how your model works with specific examples.2 Analysis of The Problem交通环岛是为了减少冲突点而设置的交通设施,车辆按同一方向行驶,将冲突点转变为交叉点,以减少交通事故的发生，我们这也俗称"转盘"。

车道被占用对城市道路通行能力的影响摘要随着城市化进程加快，城市车辆数的增加，致使道路的占用现象日益严重，同时也导致了更多交通事故的发生。

而交通事故发生过程中，路边停车、占道施工、交通流密增大等因素直接导致车道被占用，进而影响了城市道路的通行能力。

本文在视频提供的背景下通过数据采集，利用数据插值拟合、差异对比、车流波动理论等对这一影响进行了分析，具体如下：针对问题一，首先根据视频1中交通事故前后道路通行情况的变化过程运用物理观察测量类比法、数学控制变量法提取描述变量（如事故横断面处的车流量、车流速度以及车流密度）的数据，从而通过研究各变量的变化，来分析其对通行能力的影响。

而视频1中有一些时间断层，我们可根据现有的数据先用统计回归对各变量数据插值后再进行拟合，拟合过程中利用残差计算值的大小来选择较好的模型来反应各变量与事故持续时间的关系，进而更好地说明事故发生至撤离期间，事故所处横断面实际通行能力的变化过程。

针对问题二：沿用问题一中的方法，对视频2中影响通行能力的各个变量进行数据采集，同样使用matlab对时间断层处进行插值拟合处理，再将所得到的的变化图像与题一中各变量的变化趋势进行对比分析，其中考虑到两视频的时间段与两视频的事故时长不同，从而采用多种对比方式（如以事故发生前、中、后三时段比较差值、以事故相同持续时间进行对比、以整个事故时间段按比例分配时间进行对比）来更好地说明这一差异。

由于小区口的位置不同、时间段是否处于车流高峰期以及1、2、3道车流比例不同等因素的影响，采用不同的数据采集方式使采集的变量数据的实用性更强，从而最后得到视频1中的道路被占用影响程度高于视频2中的影响程度，再者从差异图像的变化波动中得到验证，使其合理性更强。

针对问题三：运用问题1、2中三个变量与持续时间的关系作为纽带，再根据附件5中的信号相位确定出车流量的测量周期为一分钟，测量出上游车流量随时间的变化情况，而事故横断面实际通行能力与持续时间的关系已在1、2问中由拟合得到，所以再根据波动理论预测道路异常下车辆长度模型的结论，结合采集数据得到的函数关系建立数学模型，最后得出事故发生后，车辆排队长度与事故横断面实际通行能力、事故持续时间以及路段上游车流量这三者之间的关系式。

RELATIONSHIP BETWEEN CONGESTION AND TRAFFIC ACCIDENTS ON EXPRESSWAYS AN INVESTIGATION WITH BAYESIAN BELIEF NETWORKSBy Charitha Dias**, Marc Miska***, Masao Kuwahara****, and Hiroshi Warita*****1. IntroductionAccidents and congestion are two frustrating events, which can be observed very frequently on roads. Accidents, especially on expressways, can trigger heavy traffic congestions imposing huge external costs and reducing the level of service. Therefore it is obvious that accidents clearly have an impact on congestion. But the opposite, i.e. the effect of congestion on occurrence of accidents, is less studied and still questionable 11). One can argue that congestion can reduce the high speeds on expressways and as a result of that the accident rate is reduced. But in a congested road section vehicles are closely packed and as a result of that rear-end collisions, back-up collisions as well as side collisions can occur. Therefore it is important to analyze the impact on the accidents by congestion so that the policy makers can implement relevant measures to reduce the external costs of both accidents and congestion.This paper investigates the effects of traffic congestion on the occurrence of accidents on 8 radial routes (inbound direction) of Metropolitan Expressway (MEX). Data were obtained from the International Traffic Database (ITDb) 6). Two softwares, namely WinMine Toolkit 2) and MSBNx 5), which use the concept of Bayesian Belief Networks (BBN), were used to model the interrelationships among occurrence of accidents and other variables such as congestion index (CI), traffic density and volume.2. Relationship between congestion and accidentsVery limited attempts have been made, in the past by several authors, to describe the relationship between accidents and congestion. Among those, Wang et al.11) claimed that traffic congestion, controlling other factors such as flow, curvature, gradient, section length, no. of lanes etc., has little or no impact on frequency of accidents (fatal or non-fatal), using data for M25 highway. But the CI values in their data were relatively low, i.e. less than 0.5, for most of the cases. Therefore, it is questionable that those data really represented congested situations.Noland and Quddus8) used a series of negative binomial models to analyze the effect of congestion on road safety. Their results were not conclusive, suggesting that there is little effect of congestion on road safety. They suspected that this might be due to the weakness of proxies they used to represent congestion, plus might be due to the method they implemented to model relationships. While above mentioned studies claimed that there is no any significant relationship between accidents and congestion, Golob and Recker 4), using nonlinear multivariate statistical analysis, concluded that rear-end collisions are more likely to occur under heavily congested stop-and-go traffic. Though this is an indication that congestion has an effect on accidents, the* Keywords: traffic accidents, congestion, Bayesian belief networks** Non-member of JSCE, M. Sc., Chodai Co., Ltd.(2-1-3 Higashi-Tabata, Kita-Ku, Tokyo, Japan 114-0013, Tel: +81-3-3894-3236, Fax: +81-3-3894-3265) *** Member of JSCE, Lecturer, Institute of Industrial Science, University of Tokyo(4-6-1 Komaba, Meguro-ku, Tokyo, Japan 153-8505, Tel: +81-3-5452-6419, Fax: +81-3-5452-6420)**** Member of JSCE, Professor, Institute of Industrial Science, University of Tokyo(4-6-1 Komaba, Meguro-ku, Tokyo, Japan 153-8505, Tel: +81-3-5452-6419, Fax: +81-3-5452-6420)***** Member of JSCE, Planning and Environment Department, Metropolitan Expressway Co., Ltd.(1-4-1 Kasumigaseki, Chiyoda-ku, Tokyo, Japan 100-8930, Tel: +81-3-3539-9389, Fax: +81-3-3502-2412)link between accidents and congestion has not elaborated clearly.Though some other authors have attempted to explore the relationship between accidents and traffic volume or flow 1)3), these studies may not describe the relationship between accidents and congestion, because according to speed-flow characteristics not only flow but also speeds are also needed to determine whether the prevailing traffic condition is congested or un-congested.These limited previous studies suggest us the need for more studies to better understand the impact of congestion on accidents. In this study BBNs, which can model and graphically interpret the relationships in any system, were used to model the interrelationships among CI, volume, density and occurrence of accidents.3. Methodology(1) Data descriptionFive-minutes aggregated volume, average speed, occupancy and incident data on inbound direction of 8 radial routes (Route numbers 1, 2, 3, 4, 5, 6, 7 and 9) of the MEX, collected over one week were used. One-week data (from 5th June 2006 to 11th June 2006) of ITDb on MEX is free for public and that free data was used for this analysis. Format of raw data is shown in Figure 2.(2) Data arrangementa) Pre-accident period.First the other incidents such as car breakdowns, road works etc. were removed and the 15 minutes time period before an accident was defined as pre-accident period (Figure 2). Here, 15 minutes was selected just to represent the average traffic conditions on the road section before an accident. b) Congestion Index (CI)Congestion index expresses the congestion level of a given road section relative to the free-flow conditions. It is non-negative and dimensionless value. Average speed data was converted in to congestion data, i.e. congestion indexes (CI), with slightly modified version of Taylor’s 9) method, as follows.{tionroad the for speed flow Free tionroad the for speed Average Where ifand if CI VV VV V VV V V V FFFFFF FFFFFF sec sec ;;0;/)(−−>>≤−=Figure 1: Metropolitan expressway (MEX)networkc) V olume classes, CI classes and density classes V olumes, CI’s and occupancies were categorized in to classes as shown in Table 1. This was done because categorized data were needed to learn BBNs.Table 1: Categorized volumes, CIs and densitiesFigure 2: Available data(3) Bayesian belief Networks (BBN)BBNs are probabilistic graphical models that represent a set of variables and their conditional independencies via a directed acyclic graph 12). BBN is an effective technique to understand the relationships among variables because BBNs can model the interrelationships among variables with their conditional probabilities in any kind of a system and represent them graphically.Two applications namely WinMine Toolkit2) and MSBNx5), which use the BBN concept, were used to identify conditional independencies among variables and to perform inference, respectively. WinMine toolkit is set of tools, designed for Windows environment, that allow constructing statistical models from categorized data. WinMine has many advantages compared with other traditional methods such as bar graphs, contingency tables and odd ratios to mine for information in data because it can provide a better picture of the factor interrelationships among variables 7). MSBNx is a component-based application, which can be used to create, assess and evaluate Bayesian networks 5). It is an excellent tool for inference or updating probabilities. Categorized volume, CI, density and event for each route were fed in to WinMine toolkit separately in order to obtain the dependency network, which is very similar to Bayesian network. For inference purposes the conditional probabilities, determined with WinMine, were fed in to MSBNx. Figure 3 depicts dependency network along with the conditional probability table (CPT) for the node “Event”, constructed with WinMine, and Figure 4 depicts the BBN with un-conditional probability tables for all nodes, constructed with MSBNx, for the inbound direction of Route 4 of MEX.At a glance some important information can be drawn from these figures. Figure 3 describes the dependencies among the variables in data fed in to WinMine. Figure 4 shows how the inbound direction of Route 8 functions. 15% of the time, within the considered one week time period, it is congested or heavily congested, 76% of the time medium volumes and 81% of the times low densities could be observed. And there is around 1% of chance of an accident.Figure 3: Dependency network constructed with WinMineFigure 4: BBN constructed with MSBNxUn-conditional probabilities, which are shown in Figure 4, are probabilities before any evidence is observed and those are called prior probabilities. When evidence is observed, for example when it is known that the CI reflects heavily congested situation, probabilities for all other nodes can be updated and those updated probabilities are called posterior probabilities. And this process of updating probabilities is called inference. Inference was performed for BBNs for each considered routes with MSBNx and updated probabilities were noted. Results are described in Section 4.4. ResultsProbabilities of occurring a pre-accident period were plotted against congestion levels, as in Figure 5, and probability of occurring a pre-accident period was plotted against density levels, as in Figure 6. Figure 5clearly shows that the chance of an accident is increasedwith the congestion level.High density reflects high congestion levels. When occurrence of accidents is increased with the increase of density levels, as shown in Figure 6, it reflects that probability of accident occurrence is increased with congestion levels. Therefore both Figure 5 and Figure 6 describe that the accident occurrence is increased with congestion levels.Table 2 compares the congestion levels and density levels when a pre-accident condition is evidenced and non-pre-accident condition is evidenced.When a pre-accident situation is evidenced, the probability that the road section is in congested conditions is in the range of [60%, 87%]. And compared to that, when none (a non-pre-accident condition or any other incident) is observed the probability that the road section is congested is pretty low, i.e. in the range of [8%, 20%]. This reflects that when an accident occurred most of the time road section was congested.These results probably describe the drivers’ behavior at congested situations. On congested roads, where stop-and-go conditions are prevailed, frustrated drivers try to accelerate resulting rear-end collisions. And some drivers may try to change their lanes resulting side collisions plus back-up collisions. However, it should be kept in mind that fatalities are less in congested road sections compare to un-congested sections where operating speeds are high 10).Figure 5: Probability of observing a pre-accidentcondition given the congestion level5. Summary(1) ConclusionsFigure 6: Probability of observing a pre-accidentcondition given the density levelFlow, speed, occupancy and event data on inbound direction of 8 radial routes of MEX, collected over one week period, were used to explore the impact of congestion on occurrence of accidents. BBNs were used to model the relationships among pre-accident conditions and other variables. It was found that when a road section is getting congested, i.e. when the CI is increased and density is increased, the chance for an accident could be increased. Analysis of accident types will more clearly provide the answer for why probability of accident occurrence increases with congestion level.(2) Further researchThese results may not totally describe the mechanism of occurrence of accidents and congestion on MEX. Broad analysis is needed, which considers all factors that may cause accidents and congestion such as weather, road geometry, driver characteristics etc., to get a betterTable 2: Conditional probabilities of CI and density ifpre-accident condition is observedpicture of pre-accident conditions.Although the probability of occurring a pre-accident situation is increased with the increase of congestion, accidents occur under congested situations are not fatal compared to accidents occur under high-speed situations. Here in this analysis, severity of accidents and types of accidents were not considered due to lack of data. Therefore, it is interesting to extend the analysis to consider the severity levels as well as types of accidents, too.6. AcknowledgementAll traffic measurement data for this study was provided by the International Traffic Database (ITDb). Data available to the public can be accessed through .References1) Ceder, A.: Relationships between road accidents and hourly traffic flow. II. Probabilistic approach, Accident Analysis and Prevention, 14 (1), pp.35–44, 1982.2) Chickering, D.: The WinMine Toolkit. Redmond, WA., Microsoft technical report no. MSR-TR- 2002-103, 2002.3) Dickerson, A., Peirson, J., Vickerman, R.: Road accidents and traffic flows: An econometric investigation, Economica, London School of Economics and Political Science, V ol. 67(265), pp. 101-21, 2000.4) Golob, T. F. and Recker, W. W.: Relationships Among Urban Freeway Accidents, Traffic Flow, Weather and Lighting Conditions, Institute of Transportation Studies, University of California, Berkeley, 2001.5) Kadie, C. M., Hovel, D., and Horvitz, H.: MSBNx: A Component-Centric Toolkit for Modeling and Inference with Bayesian Networks, Microsoft Research Technical Report MSR-TR-2001-67, 2001.6) Miska, M., et al.: The International Traffic Database Project, 14th World congress on intelligent transport systems, CD-ROM, 2007.7) Milburn, N. J. et al: Mining for information in accident data, Final report, Federal aviation administration, Civil Aerospace medical institute, Oklahoma city, 2006.8) Noland, R.B., Quddus, M.A.: Congestion and safety: a spatial analysis of London, Transportation Research Part A: Policy and Practice 39 (7-9), pp. 737-754, 2005.9) Taylor, M.A.P., Woolley, J.E., Zito, R.: Integration of the global positioning system and geographical information systems for traffic congestion studies. Transportation Research Part C: Emerging Technologies 8 (1-6), pp.257-285. 2000.10) Taylor, M. C.: The speeds of vehicles which are involved in fatal accidents, Traffic Engineering and Control 42(2), 2001.11) Wang, C., Quddus, M. A., Ison, S. G.: Impact of traffic congestion on road accidents: A spatial analysis of theM25motorway in England, Accident Analysis and Prevention, 2009.12) Wikipedia contributors: Bayesian network, Wikipedia, The Free Encyclopedia, /w/index.php?title=Bayesian_network&oldid=293220919 (accessed May 30, 2009).。

2.优秀论文一具体要求：1月28日上午汇报1）论文主要内容、具体模型和求解算法（针对摘要和全文进行概括）；In the part1, we will design a schedule with fixed trip dates and types and also routes. In the part2, we design a schedule with fixed trip dates and types but unrestrained routes.In the part3, we design a schedule with fixed trip dates but unrestrained types and routes.In part 1, passengers have to travel along the rigid route set by river agency, so the problem should be to come up with the schedule to arrange for the maximum number of trips without occurrence of two different trips occupying the same campsite on the same day.In part 2, passengers have the freedom to choose which campsites to stop at, therefore the mathematical description of their actions inevitably involve randomness and probability, and we actually use a probability model. The next campsite passengers choose at a current given campsite is subject to a certain distribution, and we describe events of two trips occupying the same campsite y probability. Note in probability model it is no longer appropriate to say that two trips do not meet at a campsite with certainty; instead, we regard events as impossible if their probabilities are below an adequately small number. Then we try to find the optimal schedule.In part 3, passengers have the freedom to choose both the type and route of the trip; therefore a probability model is also necessary. We continue to adopt the probability description as in part 2 and then try to find the optimal schedule.In part 1, we find the schedule of trips with fixed dates, types (propulsion and duration) and routes (which campsites the trip stops at), and to achieve this we use a rather novel method. The key idea is to divide campsites into different “orbits”that only allows some certain trip types to travel in, therefore the problem turns into several separate small problem to allocate fewer trip types, and the discussion of orbits allowing one, two, three trip types lead to general result which can deal with any value of Y. Particularly, we let Y=150, a rather realistic number of campsites, to demonstrate a concrete schedule and the carrying capacity of the river is 2340 trips.In part 2, we find the schedule of trips with fixed dates, types but unrestrained routes. To better describe the behavior of tourists, we need to use a stochastic model（随机模型）. We assume a classical probability model and also use the upper limit value of small probability to define an event as not happening. Then we use Greedy algorithm to choose the trips added and recursive algorithm together with Jordan Formula to calculate the probability of two trips simultaneously occupying the same campsites. The carrying capacity of the river by this method is 500 trips. This method can easily find theoptimal schedule with X given trips, no matter these X trips are with fixed routes or not. In part 3, we find the optimal schedule of trips with fixed dates and unrestrained types and routes. This is based on the probability model developed in part 2 and we assign the choice of trip types of the tourists with a uniform distribution to describe their freedom to choose and obtain the results similar to part 2. The carrying capacity of the river by this method is 493 trips. Also this method can easily find the optimal schedule with X given trips, no matter these X trips are with fixed routes or not.2）论文结构概述（列出提纲，分析优缺点，自己安排的结构）；1 Introduction2 Definitions3 Specific formulation of problem4 Assumptions5 Part 1 Best schedule of trips with fixed dates, types and also routes.5.1 Method5.1.1 Motivation and justification5.1.2 Key ideas5.2 Development of the model5.2.1Every campsite set for every single trip type5.2.2 Every campsite set for every multiple trip types5.2.3One campsite set for all trip types6 Part 2 Best schedule of trips with fixed dates and types, but unrestrained routes.6.1 Method6.1.1 Motivation and justification6.1.2 Key ideas6.2 Development of the model6.2.1 Calculation of p(T,x,t)6.2.2 Best schedule using Greedy algorithm6.2.3 Application to situation where X trips are given7 Part 3 Best schedule of trips with fixed dates, but unrestrained types and routes.7.1 Method7.1.1 Motivation and justification7.1.2 Key ideas7.2 Development of the model8 Testing of the model----Sensitivity analysis8.1Stability with varying trip types chosen in 68.2The sensitivity analysis of the assumption 4④8.3 The sensitivity analysis of the assumption 4⑥9 Evaluation of the model9.1 Strengths and weaknesses9.1.1 Strengths9.1.2 Weakness9.2 Further discussion10 Conclusions11 References12 Letter to the river managers3）论文中出现的好词好句（做好记录）；用于问题的转化We regard the carrying capacity of the river as the maximum total number of trips available each year, hence turning the task of the river managers into looking for the best schedule itself.表明我们在文中所做的工作We have examined many policies for different river…..问题的分解We mainly divide the problem into three parts and come up with three different….对我们工作的要求：Given the above considerations, we want to find the optimal。

The Mathmatic Model of Traffic RulesAbstractIn this paper, we study what effect the rule of driving automobiles on the right have on highway capacity by using Traffic Flow Theory. With the Symmetric Two-lane Cellular Automata (STCA) Model established, we put forward a flexible lane-changing rule, which can provide good theoretical basis for the Department of Transportation to develop traffic rules.We take the traffic flow of New York highway in a period for an example to set up Traffic Flow Theory and analysis the relationship between its main characteristics including density,speed and vehicle flow rate. Then, we use MATLAB software to make speed-flow scatter plot to describe the performance of this rule in light and heavy traffic. In order to promote better traffic flow we propose a flexible lane-changing rule and prove that it is very effective by establishing STCA Model. Besides, it also applies to the country where driving automobiles on the left is the rule. When vehicle transportation under the control of an intelligent system,we build a path-following algorithm under the MATLAB simulation and the numerical simulation have been carried out to verify the control performance. We conclude that intelligent control can improve traffic flow and safety.Keywords: Traffic Flow Theory, STCA Model, SimulationContents1 Introduction (3)1.1 Problem description (3)1.2 Background (3)2 Model Analysis (4)3 Assumptions (5)4 Model parameters (5)5 Method Description (5)5.1 Question 1 (5)5.1.1 Traffic flow theory (5)5.1.2 Traffic flow parameters of the three basic relationships (6)5.2 Question 2 (11)5.2.1 STCA Model (11)5.2.2 Improvement of lane changing rules (14)5.2.3 Improvement of other factors (16)5.3 Question 3 (16)5.3.1 Analysis of left- rules (16)5.4 Question 4 (17)5.4.1 Intelligent vehicle lane changing trajectory (18)5.4.2 Intelligent control model (18)6 Strengths and weakness (20)7 References (20)8 Appendix (21)1 Introduction1.1 Problem descriptionIn countries where driving automobiles on the right is the rule which require drivers to drive in the right-most lane at multi-lane freeways unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane. Overtaking is defined as a kind of traffic behavior when two vehicles driving in the same lane, the later in order to pursue higher speeds and greater driving space will move to the left lane then pass the former.Whatever in urban roads, rural roads or on the highway, overtaking is a universal phenomenon.On the highway, if the vehicle in front in the same lane driving slower on the rear of the vehicle in order to achieve the desired speed, the front left side of the car overtaking through the fast lane, then back to the original travel lane.In the complex process of overtaking, the driver in addition to the need for lateral control of the vehicle, but also must ensure the safety of the vehicle longitudinal direction, while overtaking factors rapidity and security is also in the process must be considered.1 Build and analyze a mathematical model to analyze the performance of this rule in light and heavy traffic.You can weigh it between traffic flow and safety, as well as the role of the speed limit, or other factors.2 Whether the rule can effectively improve better traffic flow?If not, please suggest possible alternatives to promote greater traffic flow, safety, or other factors that you deem important.3 If your plan applicable to the state driving on the left? Considering whether or not your solution can be carried over with a simple change of orientation, or would additional requirements be needed.4 Considering that if vehicle transportation on the same roadway was fully under the control of an intelligent system–either part of the road network or imbedded in the design of all vehicles using the roadway–to what extent would this change the results of your earlier analysis?1.2 BackgroundFrom the mid-20th century, the transportation issue has become a hot topic of concern in society, and also attracted a large number of scientists to study it.In the course of several decades of development, a lot of traffic flow models emerged, ofwhich the most famous are Car following Model,Hydrodynamic Model,Cellular Automaton Model. Car following Model was first proposed by the Pipes In the early 1950s, which deal the traffic flow with dispersed particles to describe the object as a single vehicle, through the study of the role of the front and rear of the vehicles, to understand the characteristics of the traffic flow, but since the car models are microscopic model, it difficult for large-scale transportation system simulation. Lighthill, Whitham, and Richardsl proposed LWR model independently in 1955, using density, velocity and flow volume to depict the average macroscopic cooperative behavior of the vehicle. LWR model can describe the "traffic shock" phenomenon, promote the development of traffic flow theory, but the model is built on speed and density equilibrium conditions do not apply in a non- equilibrium state is used to describe the nature of the transport phenomena, such as "ghost style " congestion, traffic hysteresis and so on, CA Model was proposed in the 1980s can make up for deficiencies of these two models above, because the traffic system is essentially a discrete system, and has a lot of non-linear characteristics, CA Model can be simple rules to reflect the macro- micro transport phenomenon, describe the unique advantages about traffic phenomenon.2 Model AnalysisFor Question 1, we build traffic flow model, and analyze its three main features, namely the density, speed and traffic volume. Calculating the quantitative relationship between the three characteristics, and using MATLAB software to make images, then descriptions the performance the right line rule in different situations.For Question 2, we analysis the result of issue 1 and get the advantages and disadvantages of the right line rule. In order to improve better traffic flow, we propose an elastic lane changing rules and establish a STCA model to check weather it is feasible.For Question 3, we build STCA model again to test if the elastic lane changing rules can apply to the left lane country just by change the direction of the right rules. If not, we will increase additional requirement to make it applicable for the left lane country.For Question 4, we analysis the vehicle overtaking process, and establish a intelligent vehicle control overtaking model based on the deviation between the actual vehicle traveling and the ideal vehicle traveling. Besides we use MATLAB simulation to establish the intelligent vehicle control algorithms in the process of overtaking thetrajectory followed, and verify the control performance of the algorithm by simulation, and analyze if it has any effect on the elastic lane changing rules.3 Assumptions1 Assuming that traffic flow only relate to vehicle flow, density and speed related, ignoring other factors.2 Assuming that vehicles with constant speed.3 Assuming that considering the case of two- lane only.4 Assuming that the average length of the vehicle is 7.5m.4 Model parametersTable 1 model parameters5 Method Description5.1 Question 15.1.1 Traffic flow theoryAnalyzing performance and congestion when analyze the performance of the right rule in light and heavy traffic. According to the typical traffic flow model, to ensure the safety of the situation, with the three elements of traffic flow -vehicle flow, speed,density.Traffic refers to the unit during a given period of time, through the road to a site, a section or a total number of vehicle lanes called traffic or traffic volume. Traffic is a random number, different time, place, traffic has change. It reflects the characteristics of the traffic flow in terms of the number. Traffic can be fixed survey obtained by the following formula N Q T = (5.1.1) Interval velocity, also known as travel speed, and is the vehicle miles traveled through the ratio of the time needed for the road. Capacity interval average velocity is the speed of standard of men in the study. Using the type is 11N i i LV tN ==∑ (5.1.2)Traffic density refers to the unit length of the road, a transient in the driveway or one direction on the number of vehicles, commonly used to say. It reflects the degree of close to each other between vehicles in traffic flow. Sometimes also can use known all the length of the vehicle on road sections combined with the ratio of length, said the driveway space share said. N K L = (5.1.3)5.1.2 Traffic flow parameters of the three basic relationshipsContinuous traffic flow characteristics available traffic, speed and traffic density three parameters describe. The relationship between the three parameters can be expressed asQ VK = (5.1.4) This relationship can be considered as three-dimensional curved surface, as shown in the figure known as the traffic flow model. In order to study the relationship between expressway three parameters, to obtain a velocity and density, thus a flow and flow velocity is deduced again density relationship. As shown in figure 1 and figure 2Figure 1 traffic flow parameters of the three basic relationshipsFigure 2 Q - K, V - K, V - Q relationship graphDiscovered by diagram can find reflect the characteristics of the traffic flow characteristics of some variable:Q,is the peak of the Figure 1.1 Huge trafficmV, that is, flow reaches maximum speed.2 The critical speedmK, the traffic density reaches the maximum.3 The best densitymK,traffic density that all vehicles can't move.4 Blocking densityfV, traffic density tends to zero, the average speed of traffic can5 Navigate speedfbe unimpeded.Green shields proposed a density linear velocity model in 1934. (1)f f K V V K =- (5.1.5)By the velocity and density curve can be seen in the Figure 2, if 0K =, then f V V =, Namely under the condition of the traffic volume is small, the vehicle can prevail. If f K K =, then 0V =, that is, in the traffic density is large, the vehicle speed tends to zero.The flow of traffic flow - density relation is the basic relation of traffic flow, traffic density model is built on the Green shields, a density based on the linear model of speed, one of the earliest research is a traffic density. Its formula is as follows: (1)f f K Q KV K =- (5.1.6)A secondary function of the relationship represented by Figure 2 shows that a parabola. maximum flow in the figure is m V , From this, the flow rate and decreased as the density, and blocking the density m K . Traffic at this time is 0Q =. For m K smaller than the dot density means no congestion, and the density is larger than m K dot indicates congestion.Considering speed-Density model, we can find that: (1)f f V K K V =- (5.1.7)Bringing on type to basic formula:2()f f V Q K V V =- (5.1.8) When Q C ≤,f V =(5.1.9)When Q C ≥,f V =(5.1.10)The same formula is expressed as a parabolic curve as shown in Figure 3, the shape and flow-density curve similar. Usually increases with the flow rate decreases until it reaches the flow capacity is reached. Crowded portion of the curve, the flow rate andvelocity are reduced.Figure 3 The relationship curves of traffic flow and vehicle speedTo sum up, according to speed-density model, flow-density model, the speed-flow model can be seen that m Q ,m V ,m K are the important features of the heavy traffic.When m Q Q ≤,m K K > and m V V <, is belong to the crowded traffic. When m Q Q ≤, m K K ≤ and m V V ≥, is belong to light traffic.According to the model, we use a set of New York highway speed traffic data to verify the model:Table 2 New York highway speed flow relational tables196*j k veh h -=.The design of the highway traffic capacity of New York is that 160000*C veh h -=. Navigate speed 1103.5*f V km h -=.Figure 4 New York highway speed flow scatter plotTraffic simulation results show that in low density area with the increase of density, maximum flow, with further increase of the density, flow continues to decrease. After is greater than the critical density, the closer it gets to the maximum density, curve under the present trend of concave.In the study of traffic flow theory, the flow relative to the highway traffic capacity is not big, most of the running speed of the vehicle driving in a free state, the speed of the vehicle is completely determined by the characteristics of vehicle and the driver itself, the operation of the vehicle speed and traffic there is no correlation. When traffic is bigger, the following vehicles gradually into the state, is gradually increasinginteraction between vehicles, traffic speed down. Increases the probability of traffic accident.On the highway to the vehicle's minimum speed limit is to prevent the vehicle car speed too slow affect the overall traffic, reduce the utilization rate of road. Maximum speed limit on highway was carried out on the vehicle is to prevent the vehicle speed too fast, reduce the security of driving.5.2 Question 2In actual traffic, due to personality differences in the driver's lane changing behavior they have taken very different.If they need to change lanes, conservative drivers tend to larger safe distance as the sole criterion lane change, this will delay the time changing lanes, waste the opportunity of changing lanes, but also not conducive to the elimination of traffic congestion, leading to a serious waste of road resources. Reckless driver then use the experience to determine the feasibility of changing channels, and may force and channel to produce a great security risk, the same is not desirable.However, the reckless driver will use the experience to determine the feasibility of changing channels, and may forcibly drove to the adjacent lane, which will produce a great security risk, which is equally undesirable.Right driving rules, the rules for overtaking vehicle set is unique, which reflects the conservative character of the driver's lane-changing behavior.It can not reflect the actual traffic diversity.Therefore, we improved the right road rules, proposed a new lane changing rules. In this article called adaptable lane changing rules for the different personalities driver, set a different lane changing rules and carried out on a computer simulation study .5.2.1 STCA ModelCellular automata model was first introduced in the transport sector by the Cremer and Ludwig in 1986, 90 years has been the rapid development. In the cellular automaton traffic flow model, the road is divided into equidistant grid, each grid represents a cellular.Each time through a unit according to the rules given state of the system is updated.Cellular automata model easier to computer operation, reflecting the complex nonlinear behavior of traffic flow, and other aspects of physical characteristics. Particularly suitable for parallel computing, and can be flexible to modify its rules to consider a variety of real traffic conditions, such as roadblocks, highway access ramp, randomized pilot overreaction caused by slowing the impactbefore the car brake lights and so on. First, we use two cells were made by the 1000 cells discrete cellular chain to represent two-lane, each cell represents the actual length of 7.5m, simulate actual road length of 75km, Vehicles are randomly distributed in the 1000 cells, K is the density of traffic on the road(Cellular vehicles account number and proportion of total cellular), by the provisions of the "PRC Road Traffic Safety Law," as per the definition of the maximum speed climbing by 3 grid, Express maximum speed per second by 5 grid, R is the proportion of the total number of vehicles the local train. Boundary conditions use periodic boundary conditions.In this model, time, space and speed are integer discretization. The road is divided into discrete lattice, each cell either empty or occupied by a car, The vehicle speed can take 0,1,2 , ..., max V where max V is the maximum speed. After a unit of time, each vehicle according to the following rules parallel update:1 Acceleration ：max min(1,)n n v v v =+，In reality corresponds to the desired maximum speed of the driver's driving characteristics.2 Deceleration ：(,)n n n v min v gap =，Since the lane can not overtake, the driver in order to avoid a collision with the vehicle in front and take measures to slow down .3 Random slow:(1,0)n n v max v =-, By a variety of uncertainties ( such as poor road conditions, the driver of a different mentality, etc. ) caused by the deceleration of the vehicle.4 Sports:n n n x x v =+, According to the adjusted speed driving vehicles.Here , n x , n v denote the position and velocity of the vehiclesn ,11n n n gap x x +=--; said the car between n and the front vehicle empty cell number.According to these four rules of numerical simulation to reflect the reality of some of the transport phenomena (such as stop walking phenomenon) model:max ..1,(1,),,,n n n n other n n back safe n n C d min v v d d d d C C else -<+>>⎧⎪=⎨⎪⎩ (5.2.1) n d , .n other d ,,n back d :n pitch of the vehicle and the vehicle ahead, the distance between the adjacent lane in front of the vehicle, and the distance between the rear of the vehicle in an adjacent lane; safe d x is defined security model change channelspacing.The STCA Model max safe d v =;Where n C is the n - car driveway ,1,0n C =;max (1,)n n d min v v <+;The type said n stop car in the driveway; .n other n d d >The type says the blockedvehicles can achieve faster in another lane; .n back safe d d >, The type says if changinglanes, safe lane changing distance accords with a condition, or in another lane, rear of the vehicle with a certain distance.When you change lanes, the driver of the vehicle was unable to quickly distinguish between adjacent express or climbing. Therefore, no matter from a security perspective, or from the reality (local train a smaller ratio) on the highway, should assume that the adjacent vehicles for express. Based on the above assumptions, this paper discusses a situation often occurs in real traffic flow, Assuming that '0b b t →=，.Figure 5 Lane changing circumstancesDigital cellular expressed occupied vehicle in the Figure.5. Digital is the speed of the vehicle. At t time, lane I vehicle b by c block. At this time, B can change in order to obtain high speed; However, .5b back d =, it can't meet the lane changing rules of model. .b back safe d d >; In the case of the does not conform to STCA model, If b is still to change that, we will discover that at time 1t + No conflict between vehicles a and b.In the specific performance, the space is very large, and more. do not have risk.We known from the analysis of the above, Outside the STCA lane changing rules Illegal encroachments and there was no danger. This reflects the STCA lane changingrules require too high, Especially in road safety spacing is set to max safe d v =It is not reasonable. It can't meet the demand of high speed vehicle lane changing, caused the road resource waste.In order to improve this situation, it is reasonable in the graph in a way, the author put forward in this flexible lane-changing rules.5.2.2 Improvement of lane changing rulesFirst we analysis in the concept of risk degree, When the vehicle in the lane changing has certain risk. Risk mainly comes from the lane changing vehicles with adjacent lanes behind the risk of conflict, It mainly depends on the size of the lane changing and moving a unit of time, the vehicle and the rear of the vehicle spacing d δ. In order to ensure the safety, In order to ensure the safety, The buffer distance is 1d δ≥between the two cars. And lane changing rules is derived. In order to more intuitive, we give a lane change microscopic scenarios.Figure 6 Microscopic lane-changingB in the diagram, vehicle lane changing in t time, and drive a unit of time..max max (1,)(1,)b back b a d min v v min v v d δ++=++ (5.2.2) Command 1d δ≥, Combined with the type can be obtained:.max max 1(1,)(1,)b back a b d min v v min v v ≥++-+ (5.2.3) In this way, we can get improvement of lane changing rulesmax ...1,min(1,),,1(1,)(1,),n n n n other n n back back other max n max n C d v v d d d min v v min v v C else-<+>>++-+⎧⎨⎩ (5.2.4)On the road, the driver is often difficult to accurately judge the rear of the vehicle speed, reckless drivers with experience the STCA - Ⅰ model. In order to further enhance the security of lane changing, we assume that the adjacent track the rear of the vehicle to full speed ahead..max 1,(1,),,1(1,),n n n max n other n n back max n n C d min v v d d d v min v v C else -<+>>+-+⎧⎨⎩ (5.2.5)When the density is small, the road resources is abundant, the performance of the traffic is free, express even thwarted by the local train, the vehicle will also be able to get great security spacing of a lane change. Therefore, this is no way to highlight STCA - Ⅰ advantage of the model. But along with the increase of the density, the vehicle into a high-density area blocked traffic lane changing further increases in the demand. So this case, STCA model cannot meet the requirements of the lane changing, and follow the improvement of lane changing rules of two model can make up the vehicle smooth realization in a way. Than STCA model, STCA model - Ⅰ showed great advantages in low density area, it can make up the vehicle more flexible to change lanes, improve the efficiency of using the road resource. In the process of simulation, we found that there are many vehicles lane changing demand, that is to say, many vehicles up to high speed, .n back d does not meet the lane changing and gave up the lane changing. In the model of lane changing rate is gradually reduce with the increase of the density. Although STCA model can guarantee security, but too conservative fixed in channel spacing waste precious road resources. STCA model - Ⅰ received a great deal of utilization of resources, on the road and make the traffic flow parameters such as speed, flow rate has been greatly improved, but due to the technical conditions cannot be achieved, it is difficult to guarantee sufficient security. Success rate model of lane changing along with the increase of the density is gradually less.5.2.3 Improvement of other factorsHighway alignment design should give full consideration to the driver's physiological and psychological characteristics.Lines should be given priority to with straight line, and its merits, reasonable collocation.In easy to cause traffic accident a long straight flat road, managers should be intentionally made several section of rough road, to remind the driver; Still should according to the requirement of the psychology, improve the highway traffic environment.Establishing highway information management system, such as the sound of traffic and other media, information management system to the driver and the highway to provide all kinds of traffic information on the net, especially the vehicles pilot rolling remind of accident site location, topography, precautions for safe driving, etc.We should strengthen to the driver on the highway traffic safety knowledge education, traffic regulations and professional ethics education, continuously improve the comprehensive quality of drivers, to prevent and reduce the highway traffic accident is very important. There is strict car driving license examination system.5.3 Question 35.3.1 Analysis of left- rulesIntelligent transportation system (also known as" intelligent transportation system ", English abbreviation for ITS) is developed rapidly in the mid - 1980 - a new discipline, ITS research in the 21st century a new type of transportation mode, is a frontier of the current transport large areas, is the transportation professional basic course in the new century.The development of intelligent transportation system, the earliest can be traced back to a series of traffic diversion system and eighties of the 20th century the development and application of new technology. The United States in 1991 through the "ground transportation efficiency method" (ISTEA), commonly known as "iced tea", from the United States of IVHS research into macroscopic operation phase. In 1994, the United States will IVHS renamed ITS. Later, later, Europe, Japan and so on also have joined the ranks. After 30 years of development, the United States, Europe and Japan to become the world's three major bases of ITS research.Drivers of all kinds of information, timely warning to the driver and to help the driver get rid of the potential dangers. Traffic in a heavy traffic location can only order, in order to reduce collision with the traffic accident. In schools, residential areas, suchas location, can push the car's speed automatic control button, will the speed control in the permitted range.Management to solve the increasingly serious traffic problems, effectively save energy and reduce environment pollution.On city roads in recent 30 years, the world each developed country, the serious traffic problem in America, for example, the national automobile traffic has doubled, the total mileage of driving every year more than 3.2 trillion km, many cities in the peak time average speed only 13 km/h, delays the losses resulting from the estimated that as much as $120 billion a year, the number of people killed each year more than 40000 people.According to the forecast of scientists and engineers, after ITS application, can effectively improve the efficiency of the transportation, can reduce traffic congestion 20%-80%, oil consumption can be reduced by 30%, exhaust emissions by 26%.5.4 Question 4Intelligent transportation system (also referred to as "intelligent transportation system", English abbreviation for ITS) is quickly developed in the mid - 1980 - a new discipline, It studies a new mode of transport in the 21st century, is a frontier of the current transport large areas is transportation professional basic course in the new century.The development of intelligent transportation system, the earliest can be traced back to a series of traffic diversion system and eighties of the 20th century the development and application of new technology. The United States in 1991 through the "ground transportation efficiency method" (ISTEA), commonly known as "iced tea", In 1994, the United States will IVHS renamed ITS. Europe, Japan and so on also have joined the ranks. After 30 years of development, the United States, Europe and Japan to become the world's three major bases of ITS research.In the process of vehicle, the car's driving environment of various sensors can be automatically tell drivers of all kinds of information, timely warning to the driver and to help the driver get rid of the potential dangers. Traffic in a heavy traffic location can only order, in order to reduce collision with the traffic accident. In schools, residential areas, such as location, can push the car's speed automatic control button, will the speed control in the permitted range.For nearly 30 years, the world each developed country urban road traffic problem is increasingly serious. In America, for example, the national automobile traffic has。

环岛交通的优化设计Optimal Design for Traffic CircleAbstract欧仁艾纳尔（Ez-gene Herlerd ）受到19世纪艺术形式的影响首创了“环岛式交通枢纽”的道路交叉口的概念。

时至今日，由此产生的环岛式交通在世界各地广泛存在。

一些城市主干道上现有的环形交叉口由于通行能力不足，经常出现拥挤、混乱及堵塞的现象，往往是各向车辆争相进交叉口，却很难顺畅驶出。

面对这种状况，我们以六车道入口环岛为例建立了三个模型：1、通过对六车道环岛模型的分析，考虑不加任何控制设施建立模型，并推导出环岛的交通能力表达式（考虑到交织段长度影响和车辆分布不均匀的影响及非机动车干扰）：22()3600132()(11/6)(11/6)(11/6)230A A Z i Q Q Q A l Q Q p p t p l βββ''''-∆•=•=•=•-∆•••---+ 以某一环岛为例，代入上式求出此种情况下的通行能力。

2、建立指示牌控制通行能力的计算与信号灯控制通行能力计算的模型，并以上面提到的环岛为例计算出两种模式下通行能力，同时与上面模型比较，从而对交通工程师提出指导性建议。

3、信号灯控制模型, 根据交通状况的实际需求,以延误最小、停车最少和通行能力最大作为目标函数,利用可随交通需求实时变化的加权系数把这3个目标统一为单目标函数, 建立交叉口信号配时非线性优化模型如下:224(25/)1/321[(1.0)]min (,)2(2)0.65()2(1.0)2(1)0.9(1.0/)/(1.0)2(/3600)(/)2i x c i i i i i i i i i i c x c y c Z x c Y y y q y q c x c y c Y x c s +=-=-⋅+-+--⋅⋅---⋅⋅⋅∑ 在引入算例的情况下，将算例所提供的数据代入优化得到的模型，采用基于精英蚂蚁寻优策略进行求解。

2024数学建模美赛a题全文共四篇示例，供读者参考第一篇示例：2024年数学建模美赛A题的题目是一个挑战性的问题，需要参赛选手在短时间内进行思考和分析，然后给出一个合理的解决方案。

这个题目涉及到了数学建模、数据分析和计算机编程等多个领域，需要选手具备较强的逻辑思维能力和解决问题的能力。

题目要求参赛选手利用给定的数据集，对某个特定问题进行建模和分析，然后给出解决方案。

选手需要根据现有的数据集进行数据清洗和预处理，然后利用统计学和数学建模的方法对数据进行分析和建模，最终提供一个可行的解决方案。

在解题过程中，选手需要运用各种数学工具和编程语言来处理数据和进行计算，例如Python、R语言等。

选手还需要结合实际问题的背景知识和专业知识，对数据进行合理的解释和分析。

在解题过程中，选手需要注意数据的质量和可靠性，同时还需要对模型的准确性和稳定性进行评估。

最终，选手需要给出一个详细的报告，说明解决问题的方法和步骤，以及给出相关的结论和建议。

参加数学建模比赛可以锻炼选手的团队合作能力和解决问题的能力，同时也能够提高选手的数学建模和数据分析能力。

希望参赛选手在比赛中能够充分发挥自己的潜力，充分展现出自己的优势和才华，最终取得优异的成绩。

【字数不足，正在努力补充中……】第二篇示例：2024数学建模美赛a题分析数学建模是一门涵盖数学、计算机科学和工程等多学科知识的综合性学科，应用广泛，涉及领域广泛。

每年举办的数学建模比赛更是为广大热爱数学和挑战智力的学生提供了一个展示自己才华的舞台。

今天我们就来分析一下2024年数学建模美赛的a题。

让我们来看一下2024年数学建模美赛a题的具体问题描述：根据指定信息，设计出最佳的实体投资组合。

实体投资组合包括个人、公司、政府、银行等单位所投资的资金和资产，投资的目的是为了获得更高的回报率。

在实际投资中，投资者需要根据市场行情、经济形势等因素来选择不同的投资产品，以实现最大化的利润。

我们需要通过收集数据来分析市场行情和经济形势，以确定合适的投资产品。

数学建模竞赛题目公交线路最优选择摘要：奥运期间，为了让公众的出行更加通畅、便利，本文从实际情况出发，将问题转化为图论模型，提出了出行线路选择的模型与算法，满足了不同的市场需求。

我们对三个问题都分别建立了以时间、转乘次数、费用最小为目标的优化模型，具体结果如下：问题一：出发站↓终点站S3359↓S1828S1557↓S0481S0971↓S0485S0008↓S0073S0148↓S0485S0087↓S3676最短耗时（min）64 106 106 67 106 46 最少转乘次数（次） 1 2 1 1 2 2 最少费用（元） 3 3 3 2 3 2问题二：起始站点和目的站点总行程最短时间（分钟）换乘次数最佳路线S3359→S182884．5 3 L15→S3068→D8→D38→S3262→L041S1557→S0481117．0 2 L84→S1919→D20→D24→S537→L516S0971→S048596．0 2 L94→S567→D1→D21→S464→L104S0008→S007353．5 3 L200→S2534→D15→D25→S525→L103S0148→S048587．5 1 D21→S464→L104S0087→S367633．00 D27→D36问题三：考虑现实中当两个站点的距离比较近的时候，乘客可以通过步行换站点，基于这种情况我们建立了模型。

关键字：Dijkstra算法，有向图一、问题重述乘公交，看奥运我国人民翘首企盼的第29届奥运会明年8月将在北京举行，届时有大量观众到现场观看奥运比赛，其中大部分人将会乘坐公共交通工具（简称公交，包括公汽、地铁等）出行。

这些年来，城市的公交系统有了很大发展，北京市的公交线路已达800条以上，使得公众的出行更加通畅、便利，但同时也面临多条线路的选择问题。

针对市场需求，某公司准备研制开发一个解决公交线路选择问题的自主查询计算机系统。

为了设计这样一个系统，其核心是线路选择的模型与算法，应该从实际情况出发考虑，满足查询者的各种不同需求。

连环罪犯居住地及作案时间地点的预测摘要本文主要通过“圆周假设理论”的改进行地理轮廓预测，根据Rossmo公式预测出了罪犯居住地的可能范围。

对时间和地点运用灰度预测方法预测了下次案发时间地点。

对于发展一种辅助警察调查方法，并运用这种方法生成地理轮廓，讨论引入了“圆周假设理论”。

在“圆周假设理论”的基础上，对该理论进行不同角度的改进，最后总结出三个确定地理轮廓的方案：改进圆周假设理论，中心图解法，最匹配圆改进方法，对Peter Sutcliffe的案例进行检验得到三个可能居住地坐标为：(0.9062,0.4051),(0.8872,0.3390),(0.8930,0.3460)都接近实际居住坐标(0.88,0.45)。

然后运用Rossmo公式求的概率分布矩阵并生成二维伪彩色图和灰度图，以此预测出最可能的居住范围，预测范围准确并且很小，可以很有效的缩小警察的排查范围。

通过对已有案例的时间和地点分析预测下一次案例的发生时间和地点。

通过GM(1,1)模型对案发的时间间隔以及案发地与居住点的距离进行预测，以Peter Sutcliffe 的案例进行检验，最后一次作案实际时间间隔为46，预测的时间间隔为63，误差17天，准确性为63%。

预测最后5次案发地与居住点的距离，与实际情况比较后，发现准确度为60%左右。

已经可以很有效的缩小警察的搜索预警范围。

关键词犯罪地理分析 Rossmo模型 GM（1,1）一、问题重述在Peter Sutcliffe13起谋杀案中，一种用来缩小搜索罪犯所在范围的方法是找到这些罪犯的点的“重心”。

从那时开始更多更复杂的的技术被发展起来通过系列犯罪的地点用来确认罪犯的“地理轮廓”。

为一个地方警署发展一种辅助他们调查连环犯罪的方法。

这种方法至少用两种不同的方案生成“地理轮廓”运用一种方法结合其他方法的结果生成一个对警察有用的预测。

根据以前的作案时间和地点对下一次可能的作案时间地点进行预测。

目录1．绪论………………………………………………………………………………1.1研究的背景和意义…………………………………………………………1.2国内外研究现状……………………………………………………………1.3研究思路及方法……………………………………………………………2.城市公共交通存在的问题……………………………………………………… 2.1车流密度太大………………………………………………………………2.2公共交通面临私人交通的竞争……………………………………………2.3道路交通规划建设不大合理………………………………………………3城市交通工具选择的数学模型…………………………………………………3.1模型…………………………………………………………………………3.2模型的意义…………………………………………………………………3.3实验与分析…………………………………………………………………4.城市交通道路建设选择的数学模型……………………………………………4.1模型…………………………………………………………………………4.2意义…………………………………………………………………………4.3实验与分析…………………………………………………………………5.提出缓解交通拥堵对策研………………………………………………………5.1改变交通消费观念…………………………………………………………5.2大力发展城市快速交通……………………………………………………5.3结论…………………………………………………………………………参考文献 (17)致谢 (18)1 绪论1.1研究背景和意义城市化水平不断提高和机动车数量的快速增长，给世界各城市的交通带来了越来越大的压力。

在我国，伴随着城市快速扩张和机动车快速增长，交通量快速增加，城市交通问题不断出现。

据公安部交管局日前发布的数据显示，目前中国机动车保有量已达2.13. 亿辆，其中汽车 9200 多万辆。

2013高教社杯全国大学生数学建模竞赛承诺书我们仔细阅读了《全国大学生数学建模竞赛章程》和《全国大学生数学建模竞赛参赛规则》（以下简称为“竞赛章程和参赛规则”，可从全国大学生数学建模竞赛网站下载）。

我们完全明白，在竞赛开始后参赛队员不能以任何方式（包括电话、电子邮件、网上咨询等）与队外的任何人（包括指导教师）研究、讨论与赛题有关的问题。

我们知道，抄袭别人的成果是违反竞赛章程和参赛规则的，如果引用别人的成果或其他公开的资料（包括网上查到的资料），必须按照规定的参考文献的表述方式在正文引用处和参考文献中明确列出。

我们郑重承诺，严格遵守竞赛章程和参赛规则，以保证竞赛的公正、公平性。

如有违反竞赛章程和参赛规则的行为，我们将受到严肃处理。

我们授权全国大学生数学建模竞赛组委会，可将我们的论文以任何形式进行公开展示（包括进行网上公示，在书籍、期刊和其他媒体进行正式或非正式发表等）。

我们参赛选择的题号是（从A/B/C/D中选择一项填写）： A 我们的参赛报名号为（如果赛区设置报名号的话）：所属学校（请填写完整的全名）：参赛队员 (打印并签名) ：1.2.3.指导教师或指导教师组负责人 (打印并签名)：（论文纸质版与电子版中的以上信息必须一致，只是电子版中无需签名。

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如填写错误，论文可能被取消评奖资格。

）日期： 2013 年 9 月16日赛区评阅编号（由赛区组委会评阅前进行编号）：2013高教社杯全国大学生数学建模竞赛编号专用页赛区评阅编号（由赛区组委会评阅前进行编号）：全国统一编号（由赛区组委会送交全国前编号）：全国评阅编号（由全国组委会评阅前进行编号）：车道被占用对城市道路通行能力的影响摘 要本文针对车道被占用对城市道路通行能力的影响建立了相应的数学模型。

针对问题一，根据视频1，统计交通事故发生至撤离期间在相同时间段内通过横断面的车辆数，并换算成标准车当量数，得到第二、三车道被占用时的各单位时间内的实际通行能力值。