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1、For office use only T1 _ T2 _ T3 _ T4 _ Team Control Number 69427 Problem Chosen B For office use only F1 _ F2 _ F3 _ F4 _ 2017 MCM/ICM Summary Sheet Optimal Optimal D Design of esign of T Toll oll P Plaza laza B Based onased on MMinimum inimum R Risk isk MMaximum aximum F Flowlow The design of high
2、way toll plaza is crucial to the traffic flow and tollbooths operation efficiency. We study the optimal design program of toll plaza from three aspects：accident rate, traffic flow and construction cost. At the same time, we give the design figures and merging pattern of toll plaza. The first stage,
3、we determine the number of tollbooths by assuming that the traffic condition is normal. The number of toll lanes is decided by traffic capacity, traffic flow and service level. We establish a function model of tollbooths through the above three indexes. When the number of lanes is 3, we know that th
4、e number of single- way toll lanes should be 7 by calculating the traffic data from the highway tollbooths of 417 highway in Florida. We find in the sensitivity analysis that the traffic flow is positively related to the number of toll lanes. The second stage, the optimal model of the merging patter
5、n based on minimum risk and maximum throughput is established. This model is on account of the analysis of the performance of the existing toll plaza to optimize its design program, and we regard the deceleration shunt and acceleration merging of the whole toll plaza as a directed and weighted netwo
6、rk flow. Similarly, by using the data of the highway tollbooths of 417 road in Florida, we obtain the program of merging pattern (Shown in Fig.5). The maximum traffic flow of this program can reach 1375 vehicles per hour, the accident rate can be reduced to 0.9%. The third stage, taking into account
7、 the vehicles variable motion in the toll plaza, we employ the driving distance between the front and rear vehicles and the braking distance of the rear vehicle to determine the size of the toll plaza, and establish a optimization model to minimize the construction cost. Likewise, using the data fro
8、m the highway tollbooths of 417 road in Florida, we obtain the smallest toll plaza (Shown in Fig.6) whose area about 4650.1875 square meters. Remarkably, we test the model in detail. The traffic flow and the accident rate are lower in light traffic flow. When the traffic flow is larger, the accident
9、 rate is increased by 0.05% compared with the slight traffic flow, that is, the size of traffic flow on the toll plaza design is not significant. After examining the impact of adding autonomous vehicles into mixed traffic, we add 500 autonomous vehicles into the traffic flow based on unit traffic fl
10、ow on Highway 95 in New Jersey. And the accident rate was reduced by 0.83%. In view of the proportion of the three tollbooths, the greater the proportion of automatic tollbooths, the smaller the entire toll area, the smaller the number of tollbooths, the stronger the capacity of the tollbooths. Fina
11、lly, we apply the model to study the optimal design of the highway toll plaza in New Jersey. We select the New Jersey Highway No.95 as the research object, and we get its shape about toll plaza and the figure of merge pattern (See Fig.12). The number of toll lanes is 10, and the proportions of the t
12、hree tollbooths is 5:3:2, the area of the toll plaza is 9614.56 2 m. Last but not least, writing a letter to the New Jersey Turnpike Authority about the design scheme Contents 1 Introduction . 1 1.1 Background . 1 1.2 Previous Research . 1 1.3 Our Work . 2 2 Analysis of Overall and Key Points 2 2.1
13、Overall Analysis 2 2.2 Key Points Analysis 3 2.2.1 Analysis of Tollbooth Number . 3 2.2.2 Performance Analysis of Toll Plaza 3 2.2.3 Cost Analysis of Toll Plaza Design 3 3 Assumptions and Justification . 3 4 Symbols and Definitions . 4 5 The Model . 4 5.1 Model I: The Determination of the Toll Lane
14、Number B 5 5.1.1 Modeling Ideas 5 5.1.2 Supplementary Assumptions and Justification 5 5.1.3 The Calculation of the Toll Lane Number B . 5 5.1.4 Model Calculation and Result Analysis 8 5.1.5 Sensitivity AnalysisParameter Sensitivity of DHV . 8 5.2 Model II: Optimal Merging Pattern Design Model Based
15、on Minimum Risk and Maximum Flow . 9 5.2.1 Modeling Ideas 9 5.2.2 Supplementary Assumptions and Justification 9 5.2.3 Minimum Risk and Maximum Flow Model 9 5.2.4 Model Calculation and Result Analysis 11 5.3 Model : An Optimization Model for the Minimum Cost of Toll Plaza 13 5.3.1 Modeling Ideas 13 5
16、.3.2 Supplementary Assumptions and Justification 13 5.3.3 The Design of the Minimum Cost Toll Plaza Based on the Optimization Model . 13 5.3.4 Model Calculation and Result Analysis 14 6 Testing the Model 15 6.1 Influence of Traffic Flow on Model 15 6.2 The Influence of Traffic Combination of Autonomous Vehicles on the Model . 16 6.3 The Influence of the Proportion of Th
