2013数学建模国赛,美赛形式论文.doc

the Impact of the Lane Occupied on Urban Road Capacity Problem AMember:For office use onlyT1_T2_T3_T4_Team Control Number201401Problem ChosenBFor office use onlyF1_F2_F3_F4_SummaryLane occupancy will change the capacity of the road, and have an impact on urban traffic order. In this paper, we evaluate and predict the impact of lane occupied for urban transport capacity, based on the video given by title we do a lot of data mining, define the difference of the actual capacity and stability degree of difference, established what based on the difference of je eves cross-sectional differences in the capacity of different models. The establishment of a multiple regression analysis model and cellular automata mode help us to describes the queue length of contact with other indicators, finally test the model and apply it to the problem of four, to estimate the approximate time when the vehicle queue length reach of the upstream intersection. For question one, combining the essence of the actual maximum capacity, considering the traffic of accident cross section in video one majority at dynamic stability of maximum traffic, regard maximum traffic per unit time traffic state in cross-section of the accident as its actual maximum capacity. Through the video data collection and analysis, the variation of the actual maximum capacity and the main factors can be got. For question two, use the same manner to process video twos data, test for normality using spss software, define the difference of the actual capacity and stability degree of difference, established what based on the difference of jeeves cross-sectional differences in the capacity of different models. The result is that the impact of the actual capacity occupied by2,3-lane 64.58% larger than that occupied by 1,2 driveway.For question three, based on the six vehicle accidents queue length, the upstream traffic, accidents duration, maximum capacity index statistics in video, analyse the queue lengths relationship with the other three indicators, preliminary derive queue length contact with the other three indicators, and introduce the contribution factor to deal with the issue that different sources of vehicles have different influence on the queue length. Meanwhile, based on the cellular automata theory, we established a more realistic cellular automata model for road accidents. Then run the cellular automaton model simulation times, next compare the simulation results with the results from the actual video to verify the accuracy of the model and scientific.For question four, firstly , use the traffic statistics data in video one to build a model, then based on the model to predict 1500pcu / h traffic in the space (different lanes) and time allocation of this problem, on the basis of cellular automata model of issue three, we can get a true reflection of the situation of the four issues on cellular automata model, after several times runs of the model, we can get a reasonable amount of time through estimates.Team201401 Page 22 of 22ContentI.Abstract2II.Introduction2III. Problem restatement2IV.Analysis3V. The basic assumption4VI. Symbols4VII. Model design and solution5Model and solutions of Question 15Definitions and understandings of actual traffic capacity5Data collection and statistics6Factors affecting the actual capacity7Model and solutions of Question 28Video 2 data processing8Establishment of model 9The solution of the model12Model and solutions of Question 313Sign regulations13Determining the start and end positions in the video of the accident13Counting the changes of four indicators of every accident14Gradually establish links between indicators based on statistical data15Model and solutions of Question 420VIII. Evaluation and improvement of the model21Advantages and disadvantages of a model in problem one21Advantages and disadvantages of a model in problem two21Advantages and disadvantages of a model in problem three and four22IX. References22I.AbstractLane occupancy will change the capacity of the road, and have an impact on urban traffic order. In this paper, we evaluate and predict the impact of lane occupied for urban transport capacity, based on the video given by title that we do a lot of data mining, define the difference of the actual capacity and stability degree of difference, established what based on the difference of jeeves cross-sectional differences in the capacity of different models and est for normality using spss software. The establishment of a multiple regression analysis model and cellular automata mode help us to describes the queue length of contact with other indicators, and introduce the contribution factor to deal with the issue that different sources of vehicles have different influence on the queue length .Then we run the cellular automaton model simulation times, next compare the simulation results with the results from the actual video to verify the accuracy of the model and scientific. And on the basis of cellular automata model of issue three, we can get a true reflection of the situation of the four issues on cellular automata model, after several times runs of the model, we can get a reasonable amount of time through estimates.Keyword: actual traffic capacity statistics, the degree of difference contribution coefficient, cellular automata, model simulation and verificationII.IntroductionTraffic has important strategic significance for the development of the national economy, and it has been a key state construction content. With the rapid growth in the number of various modes of transport, traffic congestion worsening, all these will not only lead to a series of serious social and environmental problems, and restricting economic development, so the traffic problems caused by the widespread attention government agencies, research institutions and academia, as well as city residents.As the city roads with traffic density, continuity, and other characteristics, one lane is occupied, it may reduce the capacity of all sections of lanes, even a short time, it may cause the vehicle queuing in traffic congestion. If not handled properly, there may even be a regional congestion. The right lane is occupied estimate the impact of urban road capacity, traffic management departments will properly guide the vehicle, approval lane construction, design of road drainage scheme, set up roadside parking spaces and a set of non-bay bus station to provide theory.III. Problem restatementIn order to better estimate the degree of influence on the lane occupied by urban road capacity, in turn asked the following question.(1)According to Video 1 (Annex 1),to describe the video traffic accidents during the evacuation of the accident in which the capacity of the cross section of the actual process of change.(2)According to the conclusions based on Question 1, combined with video 2 (Annex 2), differences analysis shows the impact of sharing the same cross-section of the different lanes of traffic accidents on The actual capacity of the cross-sectional.(3)Construct a mathematical model, analyze the relationship between the vehicles affected by road traffic accidents queue length and the actual cross-section capacity accidents, accidents duration, road traffic upstream.(4)If the video 1 (Annex 1) in which the cross-section from the upstream intersection accidents becomes 140 meters, and sections downstream demand unchanged, meanwhile sections upstream traffic is 1500pcu / h, the initial accident occurred when the vehicle queue length is zero, and the accidents continuous and not evacuate. Please estimate that from the beginning of the accident, how long the vehicle will arrive at the upstream intersection queue length.IV.AnalysisQuestion oneQuestion asked to describe a video from traffic accidents during the evacuation to the accident in which the cross-section of the actual capacity of the change process. First, we need to be clear, what is the actual capacity? In a clear concept for the future use, video saturation cross section when the vehicle traffic count to reflect the actual capacity.Question twoSubject of the request to combine two video analysis shows that the differences in the same lane occupied by the cross-sectional cross-sectional accident actual capacity impacts. Because video 1 and 2 accident occurred in the same road, at the same cross-section of the different lanes, therefore, the size of the cross section can reflect the traffic capacity of the cross-section of the same cross-section of different accidents affect actual capacity percentage differences when comparing two lanes of traffic accidents. Using the same approach as the question one, for the second video information processing, calculate the size of the corresponding capacity, and for comparison.Question threeQuestion three asked to build a mathematical model, analyze the relationship between the vehicles affected by road traffic accidents queue length and the actual cross-section capacity accidents, accidents duration, road traffic upstream. In the Video 1, a total of six times a vehicle can be extracted queue accident, we can analyze the six times of the accident data to derive the initial queue length relationship with the other three indicators. For a more accurate description of the model, we can use cellular automata theory to model. Modeling clear vehicle classes, changes in traffic flow, traffic distribution in different lanes, vehicle speed, road downstream demand and other factors, establishing a more accurate model and then validate the model.Question fourQuestion four given a hypothetical accident conditions, at the same time, given the traffic, asked to predict how long a vehicle to achieve the expected queue length. According to the analysis, problems only given the total upstream traffic, not carried out a detailed allocation for each traffic lane, so we need to refer to a traffic variation in question one to predict the title to get to the 1500pcu / h on the distribution of the different lanes (including the distribution of the type of vehicle).Based on the above, applying the models created in question three can we know how long when the queue length reaches 140m.V. The basic assumption(1)Accidents caused by traffic congestion will not affect traffic flow upstream of the junction;(2)This section does not consider the impact of the temporary parking of vehicles roadside traffic flow;(3)Just consider more than four-wheel vehicles, electric vehicles traffic;(4)Since the vehicle itself has a width, and the width of the lane restrictions, when stopping the vehicle does not exist between the mutually interpenetrating.VI. SymbolsTable 1SymbolMeaningUnitVideo ones actual traffic volumeVideo twos actual traffic volumeThe stability of the corresponding C1The stability of the corresponding C2The degree of differenceThe actual difference in the degree of capacityDifferences in the degree of stabilityVII. Model design and solutionModel and solutions of Question 1Definitions and understandings of actual traffic capacity Through access to relevant information, these related definition and formal of computation can be obtained:Traffic capacity means how many passing vehicle the road can afford. According to the nature of the road capacity and use requirements, its divided into three categories: basic capacity, design capacity and the actual capacity. (1)basic capacity The basic capacity refers to the road and traffic in the ideal case, each lane maximum traffic volume in unit time can pass through. The calculation formula is as follows: -The driving speed(km/h);-Travel time between two cars (s) -Two vehicles intervals(m);-The average length of the vehicle(m);-The braking distance of the vehicle(m);-The driving distance of the time that the driver react(m).(2)design capacity The design capacity base on basic capacity, taking into account the actual road and traffic conditions to determine the correction coefficient, using the correction coefficient multiplied by the basic capacity, to obtain the design capacity in actual road, traffic and certain conditions.The different factors affecting the correction coefficients include: 1)road conditions influencing traffic capacity in many ways ,and generally we only consider the main factorscorrection coefficient about lane width ;correction coefficient about lateral clearance ;correction coefficient about longitudinal grade;correction coefficient about inadequate ocular distance;correction coefficient about conditions among the way. 2)transportation condition which refers to the vehicle components especially in the mixed traffic conditions, the numerous vehicle type ,different size ,different road area occupied ,different Pavement performance ,different speed interfering mutually and seriously affecting the traffic capacity. Correction coefficient of it is noted as .(3)actual capacity The actual capacity is usually used as a basis for planning and design of roads. Just make sure the design capacity and then multiply it by the ratio of a given level of service to the service of the traffic volume and capacity is the actual capacity. Visibly, the actual capacity is the result of a basic capacity or design capacity corrected according to the specific situation, refers to the actual circumstances of a certain cross section of a certain section of the maximum hourly traffic volume, reflecting the real capacity of road. Watching the video, the data we need cant be accurate measured, so we cant make use of the above formula to model. However, most of the video period, the adjacent two cars is at a safe distance and pass successively and slowly through cross-section of incidents, which meet the concept of actual capacity, so we can take advantage of transection surface per hour traffic to reflect the actual capacity of the road.Data collection and statisticsVideo 1 is not continuous but intermittent, the date shown above is a video February 26, 2013, the time is 16:38:39-17:03:50, time segment of video1 is recorded shown as follows: Table 2: Record of video 1 time segment Event Segment Length Time of the video 16:38:3917:03:501511sIncident duration period 16:42:3317:00:091056Vehicle shortage state 16:42:3316:42:40 16:44:1616:44:3278sVideo jump period1 16:49:3816:05:0426s2 16:56:0516:57:54119S3 15:58:1816:59:0749s417:00:0717:00:2916s5 17:02:0917:03:0980s According to the accident occurrence time and end time, there are three Periods when no information is available, so its necessary to Processing the missing information, for simplicity, the average value pad the first part of missing information,After 16:56:00,its too much information we can not get to discard the data in these times. Combining Annex 4 and Annex 5,it can be seen by the upstream intersection control, the traffic across the upriver crossroad reached traffic accidents are divided into three sections: straight vehicles, right-turning vehicles, cell junctions vehicles. Which occupying most of the proportion of the vehicle is straight, and they are subject to the control of traffic lights, changing periodically in accordance with 30s cycle; right-turning vehicles occupy a small proportion of the parts and is out of the traffic light control; proportion from community intersection is smaller ,and has randomness. In addition, the traffic lights at each full minute and half a minute witch, therefore we take 30s as a time interval, from 16:43:00 to 16:56:00 count up the numbers of cars, Battery car and bus through the accident cross section. There 27 sets of data. Detailed statistical tables in Annex 1. According to the standard translation of Highway Engineering Standards (JTG B01-2003)1,to get equivalent factor of cars, electric cars, buses converted into a standard car 1,0.5,1.5.The maximum capacity is calculated as follows: Maximum capacity calculated in Annex 1, with Microsoft Excel mapping as follows:Graph 1Factors affecting the actual capacity (1) Before the traffic accident, the available lanes are three; during traffic accidents, road congestion occurs, blocking two lanes to one lane available; after dealing with traffic accidents, the available lanes reply three. Traffic and vehicle type assigned is different in various lanes, and the traffic constantly changes. (2) The bus due to the large size which road need more conditions and longer time have a greater impact on maximum capacity. (3)The level of traffic chaos has greatly affected the maximum cross-sectional capacity. With combination of the factors and image analyze that the actual capacity of the cross section shows the fluctuating unstable state, but the overall volatility in a straight line from top to bottom. At the second time point it declines because of the time the accident happens to just being the time when many car last green traffic light passing reach accident cross-section. Because the people had still their choice driveway, but when found in a car accident, will transfer car to the right-turn lane, so the right-turn lane at the start of a short time kee