主路m条车道的车流服从M3分布下支路混合车流的通行能力

本文以可接受间隙理论为基础,利用概率论方法,对以大车和小车两种代表车型组成的混合车流进行分析,建立了无信号交叉口支路混合车流穿越主路m条车道,每一车道的交通流车头时距服从不同强度的M3分布的通行能力模型,发了无信号交叉口单一车型、单一车道车流理想条件的通行能力理论。     

基于跟车思想的一维元胞自动机交通流模型

提出一个改进的一维元胞自动机模型来模拟周期性边界条件下高速公路上车流运动.基于跟车模型的思想,根据所研究车辆与其前方紧邻车辆之间的间距和相对速度来确定该车的运动,间接地反映了次近邻车辆的影响.通过引入安全间距来描述高速运动车辆接近前方缓行车辆时的减速行为,并利用随机减速概率来反映减速行为中的随机因素.由于安全间距的引入,当减速概率大于零时在较高密度下就出现完全的阻塞相.同时在本模型中采用的是有条件减速,因而可以较好描述交通实测中观察到的现象.在临界密度附近,车流运动处于亚稳态并呈现出滞后现象.由于本模型对于车辆微观运动的合理描述,可以直接用以研究在交通灯控制下城市道路交通中的各种现象.     

一种确定信号交叉口拥堵的概率统计预警模型

研究信号交叉口的运行效率及车辆服务水平对于城市交通建设与发展具有重要的意义。本文针对信号交叉口各入口方向上车流的运行特性,从概率统计的角度研究各入口方向上通过信号交叉口车流的统计模型,并在此基础上得到了一种用于定时信号交叉口拥堵的概率统计实时交通状况预警判断模型。     

高速公路收费广场的结构设计和管理优化

2017年美国大学生数学建模竞赛B题"Merge After Toll"讨论高速公路收费广场的形状和通行管理方式的优化问题。本文在参考了部分获奖论文基本方法的基础上,对这一问题作了进一步分析,讨论了汇车变道对收费区大小、车流量和安全性的影响,导出了优化收费广场的几个量化指标,并在此基础上分析了收费区设计长度的确定和车流的优化管理方案,给出了相应的仿真计算结果。     

Y型交叉口绿灯释放初期电动自行车对机动车的影响

Y型道路交叉口属异形交叉口,趋于行驶车流角度,从而使灵活多变的电动自行车对机动车的影响较为突出.为研究Y型交叉口绿灯周期电动自行车对机动车的影响程度,统计了307组绿灯期电动自行车流量分布,确定了绿灯期0-10s为电动自行车释放初期,建立了基于Logistic逐步回归的电动自行车对机动车影响模型,通过实例验证了模型的有效性.结果表明,释放初期电动自行车的流量、占道间隙停车行为、自进口机动车第1车道驶入出口第2车道及自进口非机动车道驶入出口机动车第1车道的入侵行为对机动车影响显著,其中占道间隙停车行为对机动车影响最大.研究成果可为提高异形交叉口混合交通流通行效率、交叉口渠化设计及交通组织管理提供理论参考.     

考虑时间延误的高速公路应急救援模型研究

针对高速公路突发事件应急救援车辆资源调度问题,建立了考虑应急车道占用时间延误的高速公路应急救援车辆资源调度模型.首先对高速公路突发事件造成的交通拥堵情况结合集散波理论进行了分析.然后对由于应急车道被占用而产生的路段时间延误类型进行了分类讨论.在此基础上构建了基于LRP的高速公路应急救援车辆资源调度模型.最后以某高速公路网为算例进行实验分析.结果表明,为使整体救援时间最短,在事故点造成拥堵产生应急车道占用情况下,应急救援车辆资源需要尽早派出;在应急救援车辆资源对事故点进行救援而造成拥堵产生应急车道占用情况下,应急救援车辆资源需要在救援的最迟时间范围内,以最晚的时间派出.     

多收费方式收费系统资源配置优化方法

随着ETC技术的发展,高速公路收费系统从单人工收费方式逐渐向多收费方式格局演变.同时高速公路收费系统的设计涉及到政府、道路管理者、道路使用者及道路非使用者之间利益的协调发展,因此研究在多收费方式情况下,满足不同利益层面需求的系统资源的优化配置问题具有重要意义.通过建立收费系统资源优化配置模型,在收费制式既定的情况下,利用遗传算法对收费站位置与数量进行寻优,并利用非集计方法对多收费方式情况下的车道配置进行均衡求解,可定量计算出最佳系统资源配置方案,包括确定收费制式、收费站位置与数量、收费方式、各收费站不同收费方式车道组合情况.最后我们进行算例研究,并对优化结果进行了分析比较,可为收费制式的选择及收费站的车道布设提供理论依据.     

高速公路收费广场的设计和车流管理优化模型——MCM2017 B题简评

<正>1赛题分析2017年美国大学生数学建模竞赛B题为"Merge better after toll",研究高速公路收费广场的结构和车流管理的问题。这是一个思路开放、做法多样的题目。虽然题目要求的是以经济、高效和安全为主要目标,设计收费广场的结构、布局以及收费方式和车流管理模式,但本质上是探讨收费广场车辆缴费     

高速公路交通事件影响范围的模糊预测

高速公路交通事件的影响范围预测主要包括两个方面:排队长度预测和延误预测.在对排队长度和延误进行实时预测时,需精确预测出事件发生期间的交通流量和通行能力、事件持续时间及车辆到达事件点的时间等参数,而事实上,用于确定这些参数的信息是非常复杂的,得到的这些参数值是模糊的,但是其变化范围是可以精确确定的.充分考虑上述参数的模糊特性,及事件发生期间的交通流量和通行能力的模糊关系,运用α截集表示了车辆到达离去曲线,建立了交通事件排队长度模糊预测模型和延误模糊预测模型.利用2001年6月16日发生在美国210-E高速公路的交通事件验证了该模型的可行性,并分析了事件发生期间交通流量和通行能力及事件持续时间的模糊度变化对排队长度和延误预测结果的影响.     

例谈几何概率在实际中的应用

高中数学新教材以较多的篇幅充实了概率、统计等内容 ,特别强调了离散型随机变量的概型及应用 ,但学生课外教辅用书 ,以及竞赛题中常有几何概型的题目 ,笔者认为这些内容对学有余力的学生是一有益补充 ,可开阔学生视野 ,丰富学生研究性学习 ,现举例说明一些几何概率的典型应用 .在长度为a的线段AB上 ,有一长度为h的线段CD ,现在AB上任取一点P ,假定P取在AB上任何地方都是等可能的 ,则P取在CD上概率为 ha .象这样 ,可以定义关于角或面积的概率 ,叫做几何概率 .图 1　例 1图例 1　甲乙两人相约10天之内在某地会面 ,约定先到的人等候另一…     

A Lane-Based Optimization Method for Minimizing Delay at Isolated Signal-Controlled Junctions

This paper presents a lane-based optimization method for minimizing delay at isolated signal-controlled junctions. The method integrates the design of lane markings and signal settings, and considers both traffic and pedestrian movements in a unified framework. While the capacity maximization and cycle length minimization problems are formulated as Binary-Mix-Integer-Linear-Programs (BMILPs) that are solvable by standard branch-and-bound routines, the problem of delay minimization is formulated as a Binary-Mix-Integer-Non-Linear Program (BMINLP). A cutting plane algorithm and a heuristic line search algorithm are proposed to solve this difficult BMINLP problem. The integer variables include the permitted movements on traffic lanes and successor functions to govern the order of signal displays, whereas the continuous variables include the assigned lane flows, common flow multiplier, cycle length, and starts and durations of green for traffic movements, lanes and pedestrian crossings. A set of constraints is set up to ensure the feasibility and safety of the resultant optimized lane markings and signal settings. A numerical example is given to demonstrate the effectiveness of the proposed methodology. The heuristic line search algorithm is more cost-effective in terms of both optimality of solution and computing time requirement. This revised version was published online in July 2006 with corrections to the Cover Date.     

Discrete time dynamic traffic assignment models and solution algorithm for managed lanes

“Managed” lanes of highways usually refer to lanes that are not open to all types of vehicles, such as “High Occupancy Vehicles” (HOV) lanes and “High Occupancy Toll” (HOT) lanes, etc. The HOV lanes of highways are reserved only for vehicles with a driver and one or more passengers. Whereas, HOT lanes allow all vehicles but require tolls from the vehicles with no passenger except the driver. In this paper, we present a discrete-time traffic assignment system optimum model to predict the optimal traffic flows on managed lanes at various times in the entire planning horizon. This model minimizes the overall delay (travel time) and belongs to the class of dynamic traffic assignment (DTA) problems. When applied to general networks, DTA problems can be large and difficult to solve, but the problem is manageable when it is applied to a network with managed lanes. In particular, the DTA model in this paper for managed lanes is reduced to a mixed integer program for which several efficient heuristic algorithms exist. This paper also discusses the special properties of the discrete-time DTA model, based upon which a heuristic algorithm is proposed. Numerical results show that this algorithm is efficient for many cases of the managed lane problems.     

高速公路交通事故灰色Verhulst预测模型

在分析我国高速公路交通事故历史数据的基础上,引入灰色Verhulst预测理论,建立了高速公路交通事故灰色Verhulst预测模型.通过对2000～2007年我国高速公路交通事故死亡人数进行实例分析,发现灰色Verhulst模型的预测精度高于GM(1,1)模型.结果表明,灰色Verhulst模型的预测结果较好的反映了高速公路交通事故的发展趋势,该模型用于高速公路交通事故预测是可行的.     

Modeling the asymmetry in traffic flow (a): Microscopic approach

The asymmetric characteristic of a vehicle’s ability in deceleration and acceleration, as well as its impact to micro- and macroscopic traffic flow has caused increased attention from both theoretical and practical sides. However, how to realistically model this property remains a challenge to researchers. This paper is one of the two studies on this topic, which is focused on the modeling at the microscopic level from the investigation of car-following behavior. The second part of the study [H. Liu, H. Xu, H. Gong, Modeling the asymmetry in traffic flow (b): macroscopic approach, Appl. Math. Model. (submitted for publication)] is focused on the modeling of this asymmetric property from the macroscopic scale. In this paper, we first present an asymmetric full velocity difference car-following approach, in which a higher order differential equation is developed to take into account the effect of asymmetric acceleration and deceleration in car-following. Then, efforts are dedicated to calibrate the sensitivity coefficients from field data to complete the theoretical approach. Using the data recorded from the main lane traffic and ramp traffic of a segment of the US101 freeway, the two sensitivity coefficients have been successfully calibrated from both congested and light traffic environments. The experimental study reveals that in the studied traffic flow, the intensity of positive velocity difference term is significantly higher than the negative velocity difference term, which agrees well with the results from studies on vehicle mechanics.     

Stick balancing with reflex delay in case of parametric forcing

The effect of parametric forcing on a PD control of an inverted pendulum is analyzed in the presence of feedback delay. The stability of the time-periodic and time-delayed system is determined numerically using the first-order semi-discretization method in the 5-dimensional parameter space of the pendulum’s length, the forcing frequency, the forcing amplitude, the proportional and the differential gains. It is shown that the critical length of the pendulum (that can just be balanced against the time-delay) can significantly be decreased by parametric forcing even if the maximum forcing acceleration is limited. The numerical analysis showed that the critical stick length about 30 cm corresponding to the unforced system with reflex delay 0.1 s can be decreased to 18 cm with keeping maximum acceleration below the gravitational acceleration.     

On characterization of the core of lane covering games via dual solutions

The lane covering game (LCG) is a cooperative game where players cooperate to reduce the cost of cycles that cover their required lanes on a network. We discuss the possibilities/impossibilities of a complete characterization of the core via dual solutions in LCGs played among a collection of shippers, each with a number of service requirements along some lanes, and show that such a complete characterization is possible if each shipper has at most one service requirement.     

Integrated modelling and numerical treatment of freeway flow

The effectiveness of macroscopic dynamic freeway flow models at both uninterrupted and interrupted flow conditions is tested. Model implementation is made by finite difference methods developed here for solving the system's governing equations. These schemes are more effective than existing numerical methods, particularly when generation terms are introduced. The modelling alternatives and numerical solution algorithms are compared by employing a data base generated through microscopic simulation. Despite the effectiveness of the proposed numerical treatments, substantial deviations from the data at interrupted flows are still noticeable. In order to improve performance when flow is interrupted, we develop a modelling methodology that takes into account the ramp-freeway interactions so that all freeway components are treated as a system. We show that the coupling effects of the merging traffic streams are significant. Finally, the incremental benefits of using the more sophisticated high-order continuum models are assessed.