2017美赛B题O奖论文56731中英对照版

.For office use onlyT1 T2 T3 T4 Team Control Number56731Problem ChosenBFor office use onlyF1 F2 F3 F4 2017MCM/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 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 probability 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 streams 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. Additionally, 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.(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 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 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 simulate 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 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 center 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 aspects 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。提出了一种新的改进的收费广场，以降低成本，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，为两个分离的车流提供服务。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。本文的主要贡献如下：（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。仿真结果表明，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。（4）模拟不同业务吞吐量下蜂窝收费广场的性能。仿真结果表明，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，我们改进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：更安全，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成本，吞吐量和事故预防方面的性能。;.I. Introduction1.1 Problem BackgroundWith 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 delay 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 significantly 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 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 with 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 communications are distributed like the honeycomb. In our new designed toll plaza model, the tollbooths are located in the center of each regular hexagonal.1.2 Notations DescriptionFigure 1.1 HoneycombTotal time cost: The average time interval for a vehicle from the beginning point of the detection area to the ending 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 area 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.1.3 Our WorkWith the popularization of ETC equipment and 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 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，降低施工成本，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。六边形瓷砖创建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想，这是由扬布罗克（JanBroek）给出的，后来由托马斯海斯（Thomas Hales）3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符号说明总时间成本：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成本。理论时间成本：如果系统中只有一辆车，且车辆不受控制信号的限制，则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 成本。时间延迟：总时间成本与理论时间成本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，MTC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，降低时间成本。目前收费站的传统设计占地面积大，建设成本高。 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, 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 gather 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 and 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 Assumptionl The arrival of vehicles obeys the Poisson distribution;l In general, the traffic of ETC toll stations should be much heavier than the traffic of other types of toll station.l All toll stations are ETC or E-ZPass unless otherwise specified.l There is no ramp or other exits near the tollbooth. We do not consider the possibility of additional vehicle access, only consider the vehicles already on the main road.l 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 lanes of traffic. A toll plaza consists of the fan-out area before the barrier toll, the toll barrier itself, and the fan-通过对收费站面积模型的分析，我们量化了收费站面积的减少程度。使用VISSIM模拟手机收费站是否能够批量收集和分配交通，减少车辆的平均旅行时间和平均延误时间。利用VISSIM对混合（人工费，ETC，变更）车道，纯ETC型收费车道中的细胞收费站的通行能力进行分析，对于交通流量大，光通量大的情况。我们从三个不同方面改进了我们的设计。分析了交通流量对收费站容量的影响。7.我们分析了收费站是否能够满足自动驾驶汽车的需求图1.2II。 一般假设l l车辆到达服从泊松分布;l l一般来说，ETC收费站的流量要比其他类型收费站的流量重得多。l l除非另有规定，所有收费站均为ETC或E-ZPass。l l收费站附近没有坡道或其他出口。 我们不考虑增加车辆通行的可能性，只考虑已经在主要道路上的车辆。l l收费站的服务程序和收费站后的车辆合并程序均为排队系统。 他们遵循先到先得的原则III。 蜂窝状收费广场设计方案。在传统的收费广场，总是有更多的收费站比进入的车道。 收费广场包括障碍通行前的扇形区域，收费障碍本身以及收费障碍后的扇形区域。 收费障碍通常沿着与高速公路交叉的方向垂直的高速公路建成。 所以收费广场的面积相当大。 为了减少收费广场的面积，进一步节省建设成本，我们设计了一个新的基于蜂窝结构的收费广场。 此外，通过将合并程序分为两个阶段，我们新设计的收费广场可以降低碰撞概率，与传统的新兴程序相比，大量车辆同时集中到高速公路。 我们设计的演变如图3.1所示，我们平滑过渡区避免急转弯，并在自动车辆的中间增加一些预留的收费站。in area after the toll barrier. The toll barriers are often constructed in a straight line placed across the highway, perpendicular to the direction of traffic flow. So the area of toll plaza is pretty large. To reduce the area of the toll plaza and further save the construction cost, we design a new toll plaza based on the structure of the honeycomb. In addition, by splitting the merging procedure into two stages, our new designed toll plaza can reduce the probability of collision, in contrast with the traditional emerging procedure, where large number of vehicles concentrate into the highway simultaneously. The evolution of our design is shown in Figure 3.1, where we smooth the transition zone to avoid sharp turn and add some reserved tollbooths in the middle for autonomous vehicles.Figure 3.1 Evolutionary processIV. Model Design4.1 Estimated Cost of the Toll PlazaThe cost of building a toll station mainly includes the construction cost of the road surface and the construction cost of the toll booth. We assess its area and try to minimize it. Toll booths total area S can be divided into the area of the transition zone and the area of toll gates.We assume that the number of the toll gates is nt,the number of the lanes of the highway is nl, the width of the lane is wl, the tangential offset width is wo, the design speed is v, the length of the transition zone is lt, the width of the toll gates is wt, the area of the traditional toll station are ST1 and SC1 ,respectively, the area of the transition zone are ST2 and SC2 , respectively.图3.1IV。 模型设计4.1收费广场的预计成本收费站建设成本主要包括路面建设成本和收费站建设成本。 我们评估它的面积，并尽量减少它。 收费站总面积S可分为过渡区面积和收费区面积。假设收费站的数量为nt，公路的车道数为nl，车道的宽度为wl，切向偏移宽度为wo，设计速度为v，过渡区的长度 是lt，收费站的宽度是wt，传统收费站的面积分别是ST1和SC1，过渡区的面积分别是ST2和SC2。Figure 4.1 Symbol explanation4.1.1 Comparison of the Area of the Charging ZoneThe area of the traditional toll station:1 = 2( + )The area of the cellular toll station:= ( ( + 2 ) + )12 The difference in the area of the charging zone:131 = 1 1 = 2 + 2 04.1.2 Comparison of the Area of the Transition ZoneThe area of the traditional toll station: = ( + ) 22 =160 = 60 ( + )22 = 2 ( + ) + ) =120(22 + 22 + 22 22)The area of the cellular toll station: = ( 2 ) 2 =26012 = 60 ( 2 )1 12=(+ ) =( 2) 22 22 2 1204The difference in the transition zone:2 = 2 2 =23 (120 422 + 22 + 22) 04.1.3 Comparison of the Total AreaFrom the equations above, we can learn that the cellular toll station can significantly save space compared with traditional toll station. The effect can be seen in Figure 4.2 intuitively.图44.1.1充电区面积比较传统收费站的面积：蜂窝收费站的区域两者的区别：4.1.2过渡区面积比较传统的收费站的面积蜂窝收费站的区域两者区别：4.1.3总面积的比较从上面的公式可以看出，蜂窝收费站可以大大节省空间与传统收费站相比。 这个效果可以直观地在图4.2中看到。Figure 4.2 Area comparison4.2 Analyzation of the Throughput of Toll PlazasIn our model, we consider the entire process of tolling as the operation of two serially connected queuing systems. First, the process of vehicles passing through the toll booths and queuing in front of the toll booths is treated as a queuing system, and the process of vehicles passing through the merging points at the exit of the toll station as the second queuing system. Next, we will start from a briefly introduction to the queuing theory.4.2.1 A Brief Introduction of the Queueing ModelQueueing theory is the mathematical study of waiting lines, or queues. In queueing theory, a model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide a service 4.Figure 4.3 Elements of a queueing model4.2.2 Queueing System at Toll CollectorsIn reality, when vehicles enter the toll station, the drivers will head to a toll gate according to certain principles, such as the distance to each toll gate, the number of vehicles waiting in the queue. But in our model, the arrival interval of vehicles at each toll gate follows exponential distribution. Meanwhile, the time cost by each vehicle in the toll gate also follows exponential distribution. In addition, it is clear that each toll gate can handle only one lane at each time, so that although toll booths have multiple toll booths, there is still only one set of toll collection facilities for each toll gate. Although in our model there are two toll gates at each toll island, this is not contrary to the aforementioned principles.In summary, we believe that each toll gate can be considered as an M/M/1 queuing system.4.2.3 Queueing System at Merging PointsBased on the Burkes theorem，If the arrival time and service time of a M/M/1 queuing model is a Poisson process with parameters , the departure process of the queuing model is also a Poisson process 5. The output of the toll booth is a Poisson process; therefore, the arrival intervals of the merging points are also Poisson processes.The existing road design guidelines stipulate that lane merging can only be started from图4.24.2收费广场吞吐量分析在我们的模型中，我们将整个收费过程视为两个串联连接的排队系统的操作。 首先，将通过收费站并在收费站前排队的车辆作为排队系统，将通过收费站出口汇合点的车辆作为第二排队系统。 接下来，我们将从排队论的简要介绍开始。4.2.1排队模型简介排队论是等待线或排队的数学研究。 在排队理论中，建立一个模型，以便预测队列长度和等待时间。 排队理论通常被认为是运筹学研究的一个分支，因为结果往往是在做出关于提供服务所需资源的商业决策时使用的4。图4.34.2.2收费员排队系统实际上，当车辆进入收费站时，司机会按照一定的原则前往收费站，如到各收费站的距离，排队等候的车辆数量。 但在我们的模型中，每个收费站的车辆到达间隔遵循指数分布。 同时，收费站内各车辆的时间成本也遵循指数分布。 另外，显然每个收费站每次只能处理一条车道，所以虽然收费站有多个收费站，但每个收费站仍然只有一套收费设施。 尽管在我们的模型中，在每个收费岛上都有两个收费站，但这并不违背上述原则。总之，我们认为每个收费站都可以被看作是一个M / M / 1的排队系统。-4.2.3合并点排队系统基于Burke定理，如果一个M / M / 1排队模型的到达时间和服务时间是一个参数为的泊松过程，排队模型的离开过程也是一个泊松过程5。 收费站的输出是一个泊松过程; 因此，合并点的到达间隔也是泊松过程。现有的道路设计指南规定，车道合并只能从车辆行驶方向的右侧开始，一次只能合并一个车道6。 根据这一规定，也为了简化模型，我们将车道分为两类。 类型I不通过任何合并点，但类型II确实。 类型I的数量等于L-1，因为存在一条车道，即使直接连接到高速公路，但它也需要与其右侧的所有车道合并，如图4.4中的4号车道。the right side of the vehicles driving direction and only one lane can be merged at a time 6. According to this provision, and also to simplify the model, we will divide the lanes into two types. Type I doesnt pass through any merging point, but type II does. The number of type I equals to L-1, because there exists one lane, even it directly connects to the highway, but it needs to merge with all lanes at its right side, such as lane 4 in the figure 4.4.For the type I lanes, the vehicles can directly drive pass through them, we consider the time cost equals to number of merging points multiplies the time cost passing e