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1、PAGE For office use onlyT1_T2_T3_T4_Team Control Number66666Problem ChosenAFor office use onlyF1_F2_F3_F4_2014 Mathematical Contest in Modeling (MCM) Summary SheetThe analysis of transportation system based on traffic rules SummaryTraffic flow and safety conditions of freeways are closely related to

2、 freeways driving rules. In this paper, we shall focus on many aspects of impact caused by freeways driving rules. In order to analyze the Trade-offs of road security and traffic flow, we come up with the concept of safe following distance between two running cars. Through the analysis of the factor

3、s that can influence the safe following distance, we build a mathematical m-odel. And obtain a conclusion that only following the most right-rule, there cannot reach a balance between the safety and traffic flow when in light and heavy traffic. When considering the role of under- or over-posted spee

4、d limits, we establish the CA model. Meanwhile use cellular automata to simulate and draw temporal evolution pattern under different speed limits. We come up with the conclusion that road safety and traffic flow is easier to achieve a balance when road speed limit at 60 120km / h.At the same time, a

5、ccording to the CA model, we get a relational graph about traffic density and traffic flow by use of Matlab. We get the following conclusions, when in light traffic, the increase of the traffic density can cause traffic to go up; when the traffic flow reaches the maximum, the traffic density can cau

6、se the traffic flow to go down; so we can see that the given rules cannot increase the traffic flow when the freeways is in heavy traffic. Basedontheaboveconclusions,inordertoincreasethedrivingefficiency, weputforwardthefresh rule of driving on different lanes, accordingtothelimitationofspeedondiffe

7、rent lanes,thelengthofthecars, theproportionsofcarsindifferentsizes,andso on. Combined with safe following distance, by drawing comparison and analysis, we believe that the new rules could improve the efficiency of traffic traveling. And the new rule can be carried over with a simple change of orien

8、tation.In the discussion of the traffic rules and the design of lane for the driving in the future, we introduce cloud computing and big data to make an intelligent control. Firstly based on cars on the certain lane to build the private cloud of it that collects information of cars and the surroundi

9、ng of it, then every private clouds are converged to the public cloud of the lane, finally some algorithms of the big data mining can be adopted to analyze and process on computing platform and feedback the order to each car. Through the above, we can get an intelligent control system of the traffic

10、; moreover the design of lane for driving also is obtained easily. Attheendofthispaper,wetry to makeapopularizationaboutCA model and Cloud computing applications.Keywords：Safe Following Distance, CAmodel,cellularautomatamodel, the rule of parting lane about type of cars, cloudcomputing, bigdataminin

11、g, intelligenttransportationsystems. Team # 27752 Page PAGE 19 of NUMPAGES 19PAGE Contents TOC o 1-3 h z u HYPERLINK l _Toc379863341 I. Introduction PAGEREF _Toc379863341 h 3 HYPERLINK l _Toc379863342 1.1 Background Knowledge PAGEREF _Toc379863342 h 3 HYPERLINK l _Toc379863343 1.2 An issue to be sol

12、ved PAGEREF _Toc379863343 h 3 HYPERLINK l _Toc379863344 II. The Description of the Problem PAGEREF _Toc379863344 h 4 HYPERLINK l _Toc379863345 2.1 Problem statement PAGEREF _Toc379863345 h 4 HYPERLINK l _Toc379863346 2.2 Analysis of Specific Issues PAGEREF _Toc379863346 h 4 HYPERLINK l _Toc379863347

13、 III. Basic assumption PAGEREF _Toc379863347 h 4 HYPERLINK l _Toc379863348 IV. Glossary & Symbols PAGEREF _Toc379863348 h 5 HYPERLINK l _Toc379863349 Glossary PAGEREF _Toc379863349 h 5 HYPERLINK l _Toc379863350 Symbols PAGEREF _Toc379863350 h 5 HYPERLINK l _Toc379863351 V. Models PAGEREF _Toc3798633

14、51 h 6 HYPERLINK l _Toc379863352 5.1 Analysis and Solving of Question One PAGEREF _Toc379863352 h 6 HYPERLINK l _Toc379863353 5.2 Analysis and Solving of Question Two PAGEREF _Toc379863353 h 11 HYPERLINK l _Toc379863354 5.3 Analysis and Solving of Question Three PAGEREF _Toc379863354 h 13 HYPERLINK

15、l _Toc379863355 5.4 Analysis and Solving of Question Three PAGEREF _Toc379863355 h 14 HYPERLINK l _Toc379863356 VI. Error analysis and sensitivity analysis PAGEREF _Toc379863356 h 17 HYPERLINK l _Toc379863357 6.1 Error analysis PAGEREF _Toc379863357 h 17 HYPERLINK l _Toc379863358 6.2 Sensitivity ana

16、lysis PAGEREF _Toc379863358 h 18 HYPERLINK l _Toc379863359 VII. Evaluation and Promotion of Model PAGEREF _Toc379863359 h 18 HYPERLINK l _Toc379863360 7.1 Advantages PAGEREF _Toc379863360 h 18 HYPERLINK l _Toc379863361 7.2 Disadvantages PAGEREF _Toc379863361 h 18 HYPERLINK l _Toc379863362 7.3 Promot

17、ion PAGEREF _Toc379863362 h 19 HYPERLINK l _Toc379863363 . References PAGEREF _Toc379863363 h 19I. Introduction1.1 Background Knowledge1. Driving habits of each countryIn most countries, cars travel in right car lane, only some island countries are left-travelling. Right-car-travelling considers the

18、 security of driving. It is said that when we hold the steering wheel with both hands, most people will subconsciously turn the steering wheel to the right in case of emergency. The behavior of driving on the right side does not impinge upon the opposite lane reverse, which means less danger. Among

19、the worlds six billions of population, the right line of the right is about 4 billion, left the line leftist is about 2 billion. Right, contains typical multi-continental countries such as the United States, China, Russia, Germany, France, and Brazil; Leftist mostly includes typical island countries

20、 and peninsula, subcontinent countries: the United Kingdom, Japan, India, Pakistan, Indonesia, Thailand, Australia and New Zealand. Right line or left line is not fixed at the beginning, but the result of a long-term evolution. In ancient times, both Chinese and foreign, roads are fairly localized n

21、orms, but as the road extending, intercourse expending, local habits regionalization, regionalization habit becomes a national norm.2. Intelligent Transportation SystemIntelligent Transportation System combines people, vehicles and roads closely. We use information technology, data communications tr

22、ansmission technology, intelligent control technology, sensor technology and computer processing technology effectively throughout the transportation system. So we can establish an informative, intelligent, socialized new transport integrated management system. It is the best way to solve the intern

23、ationally recognized city and highway congestion, improve traffic safety, improve operational efficiency, improve environmental quality, etc. To be sure, ITS will become the mode and direction of development in the 21st century modern of transportation system ground. Is an important symbol that tran

24、sportation enters the information age?1.2 An issue to be solved1. 2.1 Problem one requires to build and analyze a mathematical model to analyze the performance of this rule in light and heavy traffic. And we should examine tradeoffs between traffic flow and safety, the role of under- or over-posted

25、speed limits1.2.2. In problem 2, we should consult whether this rule is effective in promoting better traffic flow. If not, we should suggest and analyze alternatives (to include possibly no rule of this kind at all) that might promote greater traffic flow, safety, and/or other factors that you deem

26、 important.1.2.3. In countries where driving automobiles on the left is the norm, we need to argue whether or not our new rules can be carried over with a simple change of orientation, or would additional requirements be needed. 1.2.4. Intelligent traffic management and control systems including dyn

27、amic data traffic flow data， intelligent transportation subsystems and static road environment data, etc.II. The Description of the Problem2.1 Problem statementOverall context can be shown in the program flow chat like fig 1.Fig1 program flow chat2.2 Analysis of Specific IssuesWe use safe distance b

28、etween the two vehicles and safe distance between the two vehicles to show security. And use Cellular Automata to consult traffic flow in each time, and each section under different speed limits.By analyzing the relationship between traffic density and traffic flow, this rule is effective in promoti

29、ng better traffic flow. Combined with the previous Safe Following Distance Model, we consider two factors that are different lane speed limit and different car body length，finally develop a more appropriate rules.We identify the difference between driving on the left and right road considering the b

30、alance between flow of traffic and safety - following distance, and the problems of different lane speed limit in order to prove our rules.Question four introduces the intelligent transportation systems that is popular in todays era, and requires us to analyze and improve the mode we established pre

31、viously. We propose the concept of big data, private cloud and public cloud, combine these with the transportation system, and make the information passed and feed backed。By considering the priority, condition and safety distance and other factors, the system assigned signals and commands assigned t

32、o the vehicle, and ultimately the highway driving become safe and effective.III. Basic assumptionThe road section which occurs overtaking traveling is straight and flat, the overtaking vehicle is in good condition, which satisfies the overtaking demand.In the car- distance model, in order to facilit

33、ate the calculation, we assume that every car is the same.Considering the vehicle needs to open the lane changing lights ahead when it performs transcending. Therefore, setting the overtaking car completes the surpassing in the original lane with no vehicle traveling front and rear in the near passi

34、ng lane, ranging from the open lane changing lamps to complete changing lanes and transform the road course. And the rear -following cars maintain adequate safety distance with the overtaking car.The other vehicles are driving normally on the overtaking road. The overtaking car returns to the origin

35、al lane after the completion.Vehicles are ideal vehicles. The traveling road is also ideal and flat road. In the process of moving, there is no vehicle roll, yaw and other sports, and the direction of vehicle driving is always forward, remaining unchanged. Vehicles on the road were only divided into

36、 large trucks and cars.When changing lanes, we ignore the acceleration and deceleration behavior in the process. If the vehicles meet the requirement of changing road conditions, it should change set to the next position in the adjacent lane directly. If the speed of vehicle is 0, the lane change is

37、 not allowed.IV. Glossary & SymbolsGlossaryLoad degree: V / C is maximum traffic service divided by basic capacity under ideal conditions,. The basic capacity is the maximum amount of traffic on the four-hour service level half.Traffic flow: flow of the traffic stream is defined as the numbers of ve

38、hicles per unit of time. In practice, it usually counts as hour. Flow can be calculated as the inverse of the interval of time between continuous vehiclesSymbolsNumberSymbolsSignificance1the traveling speed of the in front car2the traveling speed of the in behind car3maximum braking deceleration of

39、the in front car4maximum braking deceleration of the behind car5the safe distance between two vehicles after the car stopped 6the growth time of deceleration7the reaction time and the brake initial time8the distance of preventing angle touch9the distance of preventing scratching10the total density o

40、f traffic on two lane11the rate of large trunkV. Models5.1 Analysis and Solving of Question One5.1.1 ProblemProblem one requires to build a mathematical model to analyze the performance of this rule in light and heavy traffic. And we should examine tradeoffs between traffic flow and safety, the role

41、 of under- posted or over-posted speed limits (that is, speed limits that are too low or too high), and/or other factors that may not be explicitly called out in this problem statement. We use safe distance between the two vehicles and safe distance between the two vehicles to show security. And use

42、 Cellular Automata to consult traffic reports in each time, and each section under different speed limits. 5.1.2 Definition of Risk1. The balance of traffic flow and security balanceIn order to ensure the safety of the highway, vehicle spacing of two cars and Lateral distance of car on the far right

43、 lane and the adjacent lane should be attended. Rule requires drivers to drive in 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. In other word, two lanes are to be used. Calculate the safe dista

44、nce between the two vehicles and security - following distance. Located in front of the car is a car, the back of the car is the car 2. The Figure 2 is about diversions, overtaking and regress. Fig2. Three phase of overtaking processWe want to discuss three cases, those are the speed of car 1 is hig

45、her than car 2, the speed of car 1 is same with car 2 and the speed of car 1 is lower than car 2.Model Safe Following Distance Modelthe speed of car 1 is lower than car 2The speed of car 1 and car 2 is set to and. The distance that car 1 and car 2 traveled is and .Maximum braking deceleration of two

46、 cars isand. Increasing time of deceleration is. is reaction time of driver and brake. The car 1 is stopped and the safe distance between car 2 is. If the vehicle speed is greater than the speed of the vehicle in front, Because the car1 is made uniform deceleration in the case of the prepared. Car 1

47、 hasnt reaction time. Braking distance1 is (1)After the car 1 the brake deceleration, car 2 has reaction time . Then car 2 Begins to decelerate. The total distance traveled of car 2 is (2)Safe following distance of two cars is . (3)The speed of car 1 is same with car 2Safe following distance of two

48、cars is . (4)The speed of car 1 is higher than car 2When the speed of car 1 is lower than car 2, follow is safer. But when car 2s deceleration is equal to the speed of the car 1, car 2 must take deceleration operation in order to ensure the safety of follow. The time that car1s speed slows (5)During

49、 this time the car 1run on the original speed. The distance that car 1 traveled is (6)When car 2s deceleration is equal to the speed of the car 1, car 2 must take deceleration operation. Distance traveled by this process . (7)Because the car1 is made uniform deceleration in the case of the prepared,

50、 braking distance is same with the former. Two car-following safety distances is (8)Now we consider the case about overtaking like figure 3 in order to facilitate the calculation.Fig3 .the distance of preventing angle touch Assuming the length of the vehicle is, overtaking angle is .We can see it in

51、 fig 4.Fig4. Overtaking FigureWhen car 2 performs beyond, safe following distance between car 1 and car 2 in the same lane is (9)Similarly, when car 2 performs beyond, safe following distance between car 1 and car 2 in different road is. (10)Drivers reaction time and brake coordinated universal time

52、, its general value is . Increasing time of deceleration is, its general value is. Maximum braking deceleration of two cars isand, its general value is. The length of the vehicle is, we set it is 6m, and we set is. Assuming a vehicle traveling with uniform speed in the original lane (Speed limit is

53、60 km/h). The speed is 50km/h. The car in adjacent lane traveling with uniform speed in the original lane (Speed limit is 80 km/h). The speed is 70km/h. The following table can be calculated.Tab 1 Safe Following Distance under different speed limitsConditionVehicleSpeed limit(60km/h)Speed limit(80km

54、/h)car 150506060car 255607080ds(m)16.7721.1624.1634.86dd(m)16.8121.2024.2034.90car 150607080car 250607080ds(m)12.3014.9017.0619.30dd(m)12.3414.9417.1019.34car 150507070car 240455060ds(m)8.8811.615.5213.78dd(m)8.9211.655.5613.82Thus it can be seen in table, in the section of the road, when the speed

55、of car 1 is lower than car 2, ,，is least. In another word, safe following distance 2 between two cars is least. If guarantee road safety, hat is not a collision. In this state roads have more traffic.ConclusionWhen the traffic load is relatively low, drivers to drive in the right-most lane unless th

56、ey are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane. In this case, the distance between the two vehicles on the same lane is generally greater than. The distance between the two vehicles on the adjacent lane is generally greater

57、than. At this point, all vehicles on the road is in a safe state. Under conditions of low traffic load is relatively small.Under heavy traffic, when the risk does not occur on Dual carriageway, the speed of car 1 is higher than car 2 and beyond Safe Following Distance, traffic flowis the most. When

58、the traffic is heavier and heavier, the balance will be broken. The distance between the two vehicles will be less than the safe following distance. The risk of accidents will be larger. To no security risk, Vehicle distance must meet the Safe Following Distance Model conditions. So inevitably reduc

59、e traffic flow. Under this rule, traffic is bound to be limited because of security reasons.2. The relationship of time and space under traffic conditions and speed limit. Model CA model We consider the characteristics of two-lane highway continuous traffic flow, each lane were divided into L consec

60、utive Cellular, cellularis empty or occupied by the speed of vehicle is v(v=0,1,2, is the maximum allowed by the vehicle traveling) .Using x (i, t) denote the -th vehicle position anddenote the-th velocity at time, is the number of cellular in the space -th between the vehicle and in front of the ve