Two velocity difference model for a car following theory

In the light of the optimal velocity model, a two velocity difference model for a car-following theory is put forward considering navigation in modern traffic. To our knowledge, the model is an improvement over the previous ones theoretically, because it considers more aspects in the car-following process than others. Then we investigate the property of the model using linear and nonlinear analyses. The Korteweg-de Vries equation (for short, the KdV equation) near the neutral stability line and the modified Korteweg-de Vries equation (for short, the mKdV equation) around the critical point are derived by applying the reductive perturbation method. The traffic jam could be thus described by the KdV soliton and the kink-anti-kink soliton for the KdV equation and mKdV equation, respectively. Numerical simulations are made to verify the model, and good results are obtained with the new model.     

An asymmetric full velocity difference car-following model

This paper presents a car-following model that considers the asymmetric characteristic of the velocity differences of the vehicles in a traffic stream. The problems of the prevalent general force (GF) model and the full velocity difference (FVD) model were solved. Furthermore, the optimal velocity (OV) model, the GF model, and the FVD model are proved to be the special cases of the proposed asymmetric full velocity difference (AFVD) model. The mathematical model is presented, followed by simulation analysis which demonstrates the properties of the AFVD model.     

A new car-following model: full velocity and acceleration difference model

By introducing acceleration difference terms into the full velocity difference models (FVDM) by Jiang et al. (1995), we present a full velocity and acceleration difference model (FVADM). The main improvement upon the previous models is that the FVADM can exactly describe the driver’s behavior under an urgent case, where no collision occurs and no unrealistic deceleration appears in this model, while vehicles determined by the previous car-following models collide after only few seconds. The model is investigated by numerical methods. The simulation results indicate that the acceleration difference has an important impact on the traffic dynamics, especially under urgent conditions. Besides the urgent situations, the model still remains similar properties to those of the FVDM. In the model, the phase transition of traffic flow is observed, and the hysteresis loop is obtained in the headway- velocity plane, also.     

Intermittent unstable structures induced by incessant constant disturbances in the full velocity difference car-following model

In this paper, we study traffic flow patterns induced by incessant constant disturbances in the full velocity difference car-following model. It is found that intermittent unstable structures may occur in the convectively unstable traffic flow under certain situations. A phenomenological explanation of the phenomenon is given: the incessant constant disturbances mainly function to maintain the stationary oscillating structure while the stationary oscillating structure is not always stable, the intermittent instability of it leads to the intermittent unstable structures. The similarity of the stationary oscillating structure to the transition layer in the local cluster effect is pointed out. The dependence of the phenomenon on the headway of the initially uniform traffic, the safety distance x_c, the sensitivity parameters κ and λ, and the noise term is also investigated.     

Solid angle car following model

Existing traffic flow models give little consideration on vehicle sizes. We introduce the solid angle into car-following theory, taking the driver's perception of the leading vehicle's size into account. The solid angle and its change rate are applied as inputs to the novel model. A nonlinear stability analysis is performed to analyze the asymmetry of the model and the size effect of the leading vehicle, and the modified Korteweg–de Vries equation is derived. The solid angle model can explain complex traffic characteristics and provide an important basis for modeling nonlinear traffic phenomena.     

Jam emergence on a circular track in a car-following model

A discrete car-following model (a linear version of the Optimal Velocity Model) is evaluated for vehicles moving on a circular track. The model imposes physical limits on acceleration and deceleration. Braking is treated using a version of Gipps’ safety condition and incorporates the reaction time of drivers. Simulations with two versions of the model, one with a unique velocity-headway relationship and another with a non-unique relationship, show spontaneous emergence of a jam in agreement with the experiment of Sugiyama et al. [Y. Sugiyama, M. Fukui, M. Kikuchi, K. Hasebe, A. Nakayama, K. Nishinari, S. Tadaki, S. Yukawa, New J. Phys. 10 (2008) 033001].     

The stability analysis of the full velocity and acceleration velocity model

The stability analysis is one of the important problems in the traffic flow theory, since the congestion phenomena can be regarded as the instability and the phase transition of a dynamical system. Theoretically, we analyze the stable conditions of the full velocity and acceleration difference model (FVADM), which is proposed by introducing the acceleration difference term based on the previous car-following models (the optimal velocity model and the full velocity difference model, OVM and FVDM). By numerical simulations, it is found that when the traffic flow is unstable, the traffic jam in the FVADM is weaker than that in the FVDM. Also it is observed that the spreading speed of the jam is slower in the FVADM than that in the FVDM and the fluctuations of vehicles in the FVADM are smaller than those in the FVDM. Therefore, the acceleration difference term has strong effects on traffic dynamics and plays an important role in stabilizing the traffic flow.     

An improved cellular automaton traffic model considering gap-dependent delay probability

In this paper, the delay probability of the original Nagel and Schreckenberg model is modified to simulate one-lane traffic flow. The delay probability of a vehicle depends on its corresponding gap. According to simulation results, it has been found that the structure of the fundamental diagram of the new model is sensitively dependent on the values of the delay probability. In comparison with the NS model, one notes that the fundamental diagram of the new model is more consistent with the results measured in the real traffic, and the velocity distributions of the new model are relatively reasonable.     

多速度差模型及稳定性分析

在全速度差(Full Velocity Difference, FVD)模型的基础上，提出了一个扩展模型——多速度差(Multiple Velocity Difference, MVD)模型. 在MVD模型中，尝试利用多辆前车信息以提高交通流的稳定性，除了考虑前车与本车的速度差外，进一步利用了多辆前车间的速度差信息. 通过线性稳定性分析，对两个模型进行比较，发现在MVD模型中，自由流稳定的敏感系数临界值变小，稳定区域有明显增加. 数值仿真结果表明，MVD模型能有效地抑制交通流堵塞. 关键词： 交通流 稳定性分析 速度差 节能     

Optimal velocity difference model for a car-following theory

In this Letter, we present a new optimal velocity difference model for a car-following theory based on the full velocity difference model. The linear stability condition of the new model is obtained by using the linear stability theory. The unrealistically high deceleration does not appear in OVDM. Numerical simulation of traffic dynamics shows that the new model can avoid the disadvantage of negative velocity occurred at small sensitivity coefficient λ in full velocity difference model by adjusting the coefficient of the optimal velocity difference, which shows that collision can disappear in the improved model.     

Influence of lateral discomfort on the stability of traffic flow based on visual angle car-following model

Due to the poor road markings and irregular driving behaviors, not every vehicle is positioned in the center of the lane. The deviation from the center can cause discomfort to drivers in the neighboring lane, which is referred to as lateral discomfort (or lateral friction). Such lateral discomfort can be incorporated into the driver stimulus–response framework by considering the visual angle and its changing rate from the psychological viewpoint. In this study, a two-lane visual angle based car-following model is proposed and its stability condition is obtained through linear stability theory. Further derivations indicate that the neutral stability line of the model is asymmetry and four factors including the vehicle width and length, the lateral separation and the sensitivity regarding the changing rate of visual angle have large impacts on the stability of traffic flow. Numerical simulations further verify these theoretical results, and demonstrate that the behaviors of diverging, merging and lane changing can break the original steady state and cause traffic fluctuations. However, these fluctuations may be alleviated to some extent by reducing the lateral discomfort.     

最优速度模型与元胞自动机模型的比较研究

用解析分析与数值仿真的手段研究了一种典型的车辆跟驰模型(OV模型)与元胞自动机模型(NS模型)之间的区别与联系.首先通过对模型规则的分析,证明了确定NS模型是OV模型的一种离散形式.随后针对两模型更复杂的具体形式,通过数值仿真的手段进行了模型的密度-流量关系与模型在开放边界下的动态特性的研究.实验结果表明,从现象来看,OV模型与NS模型具有非常近似的性质,但两种模型的机制不相同,并且各自具有不能相互替代的优势.为交通流模型的使用和改进提供了参考.     

交通流双车跟驰模型与数值仿真

基于全速度差(FVD)模型,考虑双前车信息的影响,提出了交通流双车跟驰模型.通过线性稳定性分析,得到了改进模型的稳定性条件. 与FVD模型对比研究表明,改进模型的稳定区域有明显增加.数值模拟结果表明,改进模型通过调节次近邻前车信息,可以避免FVD模型中因为反应系数较小时出现负速度的缺陷.同时也表明次近邻前车对交通流存在不可忽视的影响. 关键词： 交通流 双车跟驰模型 模拟     

Cellular automaton model within the fundamental-diagram approach reproducing some findings of the three-phase theory

We propose a simple cellular automaton for traffic flow within the fundamental diagram, which could reproduce aspects of the three-phase theory. This so-called average space gap model (ASGM) is based on the Nagel–Schreckenberg model with additional slow-to-start and anticipation rules. The anticipation rule takes into account the average space gap of multiple leading vehicles and conveys to the model its three-phase property. Due to the anticipation rule, ASGM can show the transition from free flow to synchronized flow. Due to the slow-to-start rule, ASGM can show the spontaneous wide moving jam emerges in the synchronized flow. Simulations are carried out for periodic and open boundary conditions. Under periodic boundary condition, the fundamental diagram, and the properties of synchronized flow are studied. Under open boundary condition, different congested patterns induced by an on-ramp are analyzed. We found that the ASGM produces the same spatiotemporal dynamics as many of the more complex three-phase models. Due to its simplicity and its close relation to conventional slow-to-start models, this model can shed light on the relation between ‘two-phase’ and three-phase models.     

基于跟车行为的双车道交通流元胞自动机模型：

结合跟车行为中车辆相对运动的影响和安全驾驶条件,引入换道规则,提出了基于跟车行为的双车道元胞自动机模型．模型可以描述系统在临界密度附近的亚稳态性质,其仿真结果与实测数据符合很好．在对车辆换道仿真数据采集处理的基础上,研究满足换道条件的车辆数和车辆密度间的关系,定义了换道函数描述标准驾驶行为下的车辆换道过程,求得函数的解析解并使用函数预测经换道达到稳定的车辆密度值,为量化和深入研究车辆的换道行为提供参考．     

Cellular automaton model in the fundamental diagram approach reproducing the synchronized outflow of wide moving jams

Velocity effect and critical velocity are incorporated into the average space gap cellular automaton model [J.F. Tian, et al., Phys. A 391 (2012) 3129], which was able to reproduce many spatiotemporal dynamics reported by the three-phase theory except the synchronized outflow of wide moving jams. The physics of traffic breakdown has been explained. Various congested patterns induced by the on-ramp are reproduced. It is shown that the occurrence of synchronized outflow, free outflow of wide moving jams is closely related with drivers time delay in acceleration at the downstream jam front and the critical velocity, respectively.     

Nonlinear analysis of an improved continuum model considering mean-field velocity difference

Based on the velocity gradient model, an extended continuum model with consideration of the mean-field velocity difference is proposed in this paper. By using the linear stability theory, the linear stability criterion of the new model is gained, which proved that mean-field velocity difference has significant influence on stability of traffic flow. The KdV–Burgers equation is derived by using non-linear analysis method and the evolution of density wave near the neutral stability line is explored. Numerical simulations are carried out how mean-field velocity difference affect the stability of traffic flow, and energy consumption is also studied for this new macro model. At the same time, complicated traffic phenomena such as local cluster effects, shock waves and rarefaction waves can be reproduced in the new model by numerical simulation. Numerical results are consistent with the theoretical analysis, which indicates that the mean-field velocity difference not only suppresses traffic jam, but also depresses energy consumption.     

低速十字路口交通流模型相图

研究由两个单车道构成低速十字路口交通流模型.模型中两车道上的车辆更新遵循无交通灯管制下的并行规则.依据构建相图的原则并采用局部占有概率方法,建立相图,给出相图中的各部分区域的流量表达式.两车道均采用周期边界条件和确定性FI模型进行数值模拟,模拟结果与理论分析精确一致.模型中两条车道的行车规则更接近实际道路交通,该结果为交通管理提供一定的指导作用.     

影响气球车行驶效率及相关因素研究

对以气球喷气为动力的小车运动状态进行研究,从气球内部的压强入手,综合考虑摩擦力,对气球车的效率进行定义和研究,探究了小车效率的影响因素,并结合实验进行了合理的理论修正,确定了最大效率的范围.     

自助跟随平衡车的电子控制器设计与实现

随着科技的不断发展,多种智能感应技术被广泛使用,为人们的生活、工作、学习带来便利。平衡车作为新生的代步工具,具有体积小巧、携带方便、操作简单、代步快捷等优点,正被越来越多的年轻人所接受。但是,传统自主跟随平衡车的电子控制器存在多传感器交互性差、传感器数值运算逻辑滞后、控制响应度差等问题,导致用户体验度降低,限制了自助跟随平衡车的研究与发展。针对问题根源,提出了自助跟随平衡车的电子控制器设计与实现方法。采用多维运算逻辑、动态传感电路、瞬态信号回传技术,对传统自主跟随平衡车的电子控制器存在的问题进行改进设计。通过仿真实验测试证明,提出的自助跟随平衡车的电子控制器设计与实现方法,具有多感应器数据交互运算准确、执行响应度高、指令运行稳定等优点。