美赛B题O奖论文56731中英对照版.docx

1、美赛B题O奖论文56731中英对照版For office use onlyT1 T2 T3 T4 Team Control Number56731Problem ChosenB For office use onlyF1 F2 F3 F4 2021MCM/ICMSummary Sheet(Your teams summary should be included as the first page of your electronic submission.)Type a summary of your results on this page. Do not include the name

2、 of your school, advisor, or team members on this page.A New Type of Toll Plaza Based on Bionics-HoneycombSummaryIn this paper, we analyze the performance of commonly used toll plaza based on our proposed mathematical model. A new improved toll plaza is proposed to reduce the cost, decrease the prob

3、ability of collision at the merging point and increase the throughput.The distribution of our proposed tollbooths resembles the honeycomb. At the center of each regular hexagonal honeycomb, there are two tollbooths, which serve two separated vehicle streams. The vehicles in these two separated strea

4、ms are merged in advance before they continue their journey on the highway. Due to the specific pattern of the new toll plaza, the total area can be reduced significantly. Meanwhile, the average wasted time caused by queuing can be diminished, which means that the throughput will be raised. Addition

5、ally, by splitting the merging procedure into two stages, the possibility of accidents can also be decreased.The main contributions of this paper are as follows:(1)The new designed cellular architecture can greatly reduce the construction area compared with traditional linear distributed toll gates.

6、(2)We analyze the throughput of toll plazas by means of the queuing theory. To verify our theory, we simulate the behavior of the large number of vehicles passing the toll plaza with the help of PTV- VISSIM. Simulation results show that the ideal cellular distributed toll booths have better results

7、compared with traditional toll stations, especially when the traffic flow is heavy, the average travel time reduced by about 55% and the average delay time of each lane is reduced by about 70%.(3)We analyze the influence of the proportions of different types of tollbooths to our design. According to

8、 relevant documents, the impact of exact-change tollbooths is similar to manual tollbooths, so we only consider two kinds of tollbooths: human-staffed tollbooths and E-ZPass tollbooths. PTV-VISSIM simulation results show that full ETC tollbooth is 8 times faster than full MTC tollbooth.(4)We simulat

9、e the performance of the cellular toll plaza under different traffic throughput. Simulation results show that the average transit time remains at about 11 seconds under different throughputs from 0 to 2000 (Unit: veh / h). We can infer that this model is not sensitive to traffic flow variations and

10、has strong robustness which is suitable for practical construction.(5)To further reduce the possibility of accident, we improve the cellular tollbooth concept model: make the transition zone more smooth and arrange different kinds of tollbooths more equitable.(6)For self-driving vehicles, in the cen

11、ter of the toll plaza, we reserve special E-ZPass tollbooths, which match the characteristics of autonomous vehicles: safer and faster.Electronic toll collection and autonomous vehicles are the trends of modern transportation, our new designed model can improve the performance of toll plaza in the a

12、spects of cost, throughput and accident prevention.一种基于仿生蜂窝的新型收费广场概要在本文中，我们基于我们提出的数学模型分析了常用收费广场的表现。提出了一种新的改良的收费广场，以降低本钱，降低在合并点的碰撞概率，提高吞吐量。我们建议的收费站的分布类似于蜂窝。在每个正六边形蜂窝的中心，有两个收费站，为两个别离的车流提供效劳。这两条分开的河流中的车辆在高速公路上继续前行之前被合并。由于新收费广场的具体模式，总面积可以大大减少。同时，排队造成的平均浪费时间可以减少，这意味着吞吐量将会提高。另外，通过将合并过程分成两个阶段，也可以减少事故的可能性。本

13、文的主要奉献如下：1与传统的线性分布式收费站相比，新设计的蜂窝式架构可以大大减少建筑面积。2通过排队论分析收费广场的吞吐量。为了验证我们的理论，我们在PTV-VISSIM的帮助下模拟了通过收费广场的大量车辆的行为。仿真结果说明，理想的蜂窝分布式收费站比传统收费站效果更好，特别是在交通流量大的情况下，平均出行时间减少了约55，平均每个车道延误时间减少了约70 。3分析不同类型收费站的比例对我们设计的影响。根据有关文件，精确改造收费站的影响与手动收费站类似，所以我们只考虑两种收费站：人力收费站和E-ZPass收费站。 PTV-VISSIM仿真结果显示，完整的ETC收费站比完整的MTC收费站快8倍。

14、4模拟不同业务吞吐量下蜂窝收费广场的性能。仿真结果说明，在02000的不同吞吐量下，平均通过时间约为11秒单位：veh / h。我们可以推断出这个模型对交通流量变化不敏感，具有很强的鲁棒性，适用于实际建设。5为进一步降低事故发生的可能性，我们改良了蜂窝收费站的概念模型：使过渡区更加顺畅，并使不同种类的收费站更加平等。6对于自驾车辆，在收费广场中央，我们预留了符合自动驾驶汽车特点的特殊E-ZPass收费车：更平安，更快捷。电子收费系统和自动驾驶汽车是现代交通运输的趋势，新设计的模式可以提高收费广场在本钱，吞吐量和事故预防方面的性能。I.Introduction1.1Problem Backgro

15、undWith the number of vehicles increasing, expressway is confronted with great traffic pressure, especially at the toll plaza. The congestion problem at the toll station becomes more and more serious due to the outdated design. Related research found that 36% of the total travel time in China is del

16、ay time caused by tolling 1. In addition, as a vehicle-intensive place, toll plaza has become an accident-prone section because of the drivers improper operation 2.With the widespread use of Electronic Toll Collection (ETC) and E-ZPass, the efficiency of toll collection has been improved significant

17、ly and further the congestion at the toll plaza is released. However, due to the high speed of the vehicles passing through the toll plaza, the probability of collision in the merging zone is increased. Moreover, the construction of future toll plaza is very expensive. Considering above factors, it

18、is necessary to design new toll plaza to improve its throughput, reduce the cost of construction and decrease the possibility of collision in the merging zone.In this paper, we design a toll station model based on bionics-honeycomb as shown in Figure 1.1. The hexagonal tiling creates a partition wit

19、h equal-sized cells, while minimizing the total perimeter of the cells. Known in geometry as the honeycomb conjecture, this was given by Jan Broek and proved much later by Thomas Hales 3. Cellular Structure is widely used in many aspects of life. For example, the base stations of mobile communicatio

20、ns are distributed like the honeycomb. In our new designed toll plaza model, the tollbooths are located in the center of each regular hexagonal.1.2Notations DescriptionFigure 1.1 HoneycombTotal time cost: The average time interval for a vehicle from the beginning point of the detection area to the e

21、nding point of the detection area is the total time cost.Theoretical time cost: If there is only one vehicle in the system and that vehicle is not limited by the control signal, the time interval for that vehicle from the beginning point of the detection area to the ending point of the detection are

22、a is the theoretical time cost.Time delayed: The difference between the total time cost and the theoretical time cost is the Time delayed.L: the number of lanes in each direction of the highway. B: the total number of tollbooths in each direction.1.3Our WorkWith the popularization of ETC equipment a

23、nd autonomous vehicles, the MTC lanes will be totally replaced by the ETC lanes in the next 20 years, which will increase the road capacity and decrease the time cost by each car passing through the toll station.At present the traditional design of toll stations covers a large area, and the cost of

24、construction is high. With the raise of the vehicles speed, there will be congestions at the merging point, which may increase the possibility of accident. We designed a cellular toll booth model, designed its shape, size and merge. In order一，简介1.1问题背景随着车辆数量的增加，高速公路面临着巨大的交通压力，特别是在收费广场。由于设计陈旧，收费站的拥堵问

25、题越来越严重。相关研究发现，中国旅行总时间的36是由收费引起的延误时间1。此外，作为一个车辆密集的地方，由于司机的不当操作，收费广场已经成为一个事故多发的路段2。随着电子收费ETC和E-ZPass的广泛使用，收费效率显着提高，收费广场的拥堵得到进一步释放。然而，由于车辆通过收费广场的速度很快，合并区的碰撞概率增加了。而且，未来收费广场的建设非常昂贵。考虑到上述因素，有必要设计新的收费广场，以提高吞吐量，降低施工本钱，减少合并区碰撞的可能性。在本文中，我们设计了一个基于仿生蜂窝的收费站模型，如图1.1所示。六边形瓷砖创立一个大小相等的单元划分，同时最小化单元的总周长。在几何学上称为蜂窝猜测，这是

26、由扬布罗克JanBroek给出的，后来由托马斯海斯Thomas Hales3证明。细胞结构在生活的许多方面被广泛使用。例如，移动通信的基站像蜂窝一样分布。在我们新设计的收费广场模型中，收费站位于每个正六边形的中心。图1.11.2符号说明总时间本钱：车辆从检测区域起点到检测区域终点的平均时间间隔为总时间本钱。理论时间本钱：如果系统中只有一辆车，且车辆不受控制信号的限制，那么从检测区起点到检测区终点的车辆的时间间隔为理论时间 本钱。时间延迟：总时间本钱与理论时间本钱之间的差异是时间延迟。L：高速公路每个方向的车道数量。 B：各方向的收费站总数。1.3我们的工作随着ETC设备和自动驾驶车辆的普及，M

27、TC车道将在未来20年被ETC车道完全取代，增加每辆车通过收费站的道路容量，降低时间本钱。目前收费站的传统设计占地面积大，建设本钱高。 随着车速的提高，在交汇点会出现挤塞现象，这可能会增加事故发生的可能性。设计了一个蜂窝收费站模型，设计了它的形状，大小和合并。 为了使收费站更加适应实际应用，我们从区域，吞吐量，事故预防，混合车道和唯一的ETC车道，自驾车等方面升级。to make the cellular toll booth more adaptable to practical application, we escalated from the aspects of the area,

28、the throughput, the accident prevention, the hybrid lane and the only ETC lane, self-driving vehicle and so on. Through the analysis of the toll station area model, we quantified how much we could reduce the toll station area. We use the VISSIM to simulate whether the cellular toll station can gathe

29、r and distribute traffic in batches, and reduce the average travel time and average delay time of vehicle merging. We use the VISSIM to analyze the traffic capacity of the cellular toll station in the mixed (artificial charge, ETC, change) lane, pure ETC-type toll lane, both for heavy traffic flow a

30、nd light flow. We improved our design from 3 different aspects. We analyzed the influence of the traffic flow to the capacity of the toll station. We analyzed whether the toll station can meet the need of the autonomous vehicles.Figure 1.2 Design evolution diagramII.General AssumptionThe arrival of

31、vehicles obeys the Poisson distribution;In general, the traffic of ETC toll stations should be much heavier than the traffic of other types of toll station.All toll stations are ETC or E-ZPass unless otherwise specified.There is no ramp or other exits near the tollbooth. We do not consider the possi

32、bility of additional vehicle access, only consider the vehicles already on the main road.The service procedure of the toll stations and the merging procedure of the vehicles after the tollbooths are both queuing system. They follow the principle of first come first served.III.Design Scheme of Honeycomb-like Toll plazaIn traditional toll plazas, there are always more tollbooths than the incoming