Analyses of Lattice Traffic Flow Model on a Gradient Highway

The optimal current difference lattice hydrodynamic model is extended to investigate the traffic flow dynamics on a unidirectional single lane gradient highway. The effect of slope on uphill/downhill highway is examined through linear stability analysis and shown that the slope significantly affects the stability region on the phase diagram.Using nonlinear stability analysis, the Burgers, Korteweg-deVries(KdV) and modified Korteweg-deVries(mKdV) equations are derived in stable, metastable and unstable region, respectively. The effect of reaction coefficient is examined and concluded that it plays an important role in suppressing the traffic jams on a gradient highway. The theoretical findings have been verified through numerical simulation which confirm that the slope on a gradient highway significantly influence the traffic dynamics and traffic jam can be suppressed efficiently by considering the optimal current difference effect in the new lattice model.     

Analyses of Lattice Traffic Flow Model on a Gradient Highway

The optimal current difference lattice hydrodynamic model is extended to investigate the traffic flow dynamics on a unidirectional single lane gradient highway. The effect of slope on uphill/downhill highway is examined through linear stability analysis and shown that the slope significantly affects the stability region on the phase diagram. Using nonlinear stability analysis, the Burgers, Korteweg-deVries (KdV) and modified Korteweg-deVries (mKdV) equations are derived in stable, metastable and unstable region, respectively. The effect of reaction coefficient is examined and concluded that it plays an important role in suppressing the traffic jams on a gradient highway. The theoretical findings have been verified through numerical simulation which confirm that the slope on a gradient highway significantly influence the traffic dynamics and traffic jam can be suppressed efficiently by considering the optimal current difference effect in the new lattice model.     

混合状态下城市快速路交通流短时预测

建立交通流短时预测状态空间模型, 研究混合状态下城市快速路交通流短时预测. 结合城市快速路自由流状态、拥挤流状态和阻塞流状态下交通流参数的时间和空间分布特性, 基于交通流守恒方程和速度动态模型, 借鉴偏微分方程组求解时空离散的思想, 建立三种状态下交通流短时预测模型; 同时考虑进出口匝道、车道数变更以及道路坡度等因素的影响, 将交通流短时预测模型转化为交通流短时预测状态空间模型, 实现混合状态下交通流短时预测. 研究表明, 该方法能够实现混合状态下道路网内的交通流短时预测, 预测精度可达90.23%. 相同条件下, 经典自回归滑动平均模型的预测精度仅为81%. 关键词： 交通流短时预测 自由流状态 拥挤流状态 阻塞流状态     

Effect of gravitational force upon traffic flow with gradients

We study the effect of gravitational force upon traffic flow on a highway with sag, uphill, and downhill. We extend the optimal velocity model to take into account the gravitational force which acts on vehicles as an external force. We study the traffic states and jamming transitions induced by the slope of highway. We derive the fundamental diagrams (flow-density diagrams) for the traffic flow on the sag, the uphill, and downhill by using the extended optimal velocity model. We clarify where and when traffic jams occur on a highway with gradients. We show the relationship between densities before and after the jam. We derive the dependence of the fundamental diagram on the slope of gradients.     

Intelligent driving in traffic systems with partial lane discipline

It is a most common notion in traffic theory that driving in lanes and keeping lane changes to a minimum leads to smooth and laminar traffic flow, and hence to increased traffic capacity. On the other hand, there exist persistent vehicular traffic systems that are characterised by habitual disregarding of lane markings, and partial or complete loss of laminar traffic flow. Here, we explore the stability of such systems through a microscopic traffic flow model, where the degree of lane-discipline is taken as a variable, represented by the fraction of drivers that disregard lane markings completely. The results show that lane-free traffic may win over completely ordered traffic at high densities, and that partially ordered traffic leads to the poorest overall flow, while not considering the crash probability. Partial order in a lane-free system is similar to partial disorder in a lane-disciplined system in that both lead to decreased traffic capacity. This could explain the reason why standard enforcement methods, which rely on continuous increase of order, often fail to incur order to lane-free traffic systems. The results also provide an insight into the cooperative phenomena in open systems with self-driven particles.     

A new lattice hydrodynamic model accounting for the traffic interruption probability on a gradient highway

In this paper, a novel lattice hydrodynamic model is presented by accounting for the traffic interruption probability on a gradient highway. The stability condition can be obtained by the use of linear analysis. Linear analysis demonstrates that the traffic interruption probability and the slope will affect the stability region. Through nonlinear analysis, the mKdV equation is derived to describe the phase transition of traffic flow. Furthermore, the numerical simulation is carried out, and the results are consistent with the analytical results. Numerical results demonstrate that the traffic flow can be efficiently improved by accounting for the traffic interruption probability on a gradient highway.     

道路交通的流体物理模型与粒子仿真方法

针对受多种因素影响的复杂道路交通系统问题,基于颗粒动力学理论,结合传统的Lighthill-WhithamRichards物理模型,建立道路交通系统的流体物理模型,采用无网格粒子与网格相结合的方法进行数值仿真,并应用于典型道路交通问题的求解.在新模型中,将车辆比拟为硬颗粒,车辆的跟车比拟为颗粒间的碰撞相互作用,已知道路情况对驾驶员操作车辆的影响比拟为流-粒两相系统中的外部流体驱动力作用,不同车道间车辆的影响比拟为颗粒间的黏性作用,从而在颗粒动力学理论的基础上,推导建立了道路交通系统拟流体模型;引入光滑离散颗粒流体动力学(SDPH)对车辆系统模型进行离散,建立"SDPH车辆"与真实车辆之间的一一对应关系,再结合有限体积方法,对道路交通构建的双流体模型进行求解,建立求解交通流体物理模型的新型仿真方法.最后,采用所建立的模型和方法对车辆汇入以及机非混合对交通系统的影响过程进行了数值仿真,所得结果与实测值符合较好,表明新的模型和方法有效性好、可靠性高,为道路交通问题的解决提供了一条全新的途径.     

Analyses of driver’s anticipation effect in sensing relative flux in a new lattice model for two-lane traffic system

In this paper, a new lattice hydrodynamic traffic flow model is proposed by considering the driver’s anticipation effect in sensing relative flux (DAESRF) for two-lane system. The effect of anticipation parameter on the stability of traffic flow is examined through linear stability analysis and shown that the anticipation term can significantly enlarge the stability region on the phase diagram. To describe the phase transition of traffic flow, mKdV equation near the critical point is derived through nonlinear analysis. The theoretical findings have been verified using numerical simulation which confirms that traffic jam can be suppressed efficiently by considering the anticipation effect in the new lattice model for two-lane traffic.     

Phase transition on speed limit traffic with slope

Through introducing a generalized optimal speed function to consider spatial position, slope grade and variable safe headway, the effect of slope in a single-lane highway on the traffic flow is investigated with the extended optimal speed model. The theoretical analysis and simulation results show that the flux of the whole road with the upgrade （or downgrade） increases linearly with density, saturates at a critical density, then maintains this saturated value in a certain density range and finally decreases with density. The value of saturated flux is equal to the maximum flux of the upgrade （or downgrade） without considering the slight influence of the driver＇s sensitivity. And the fundamental diagrams also depend on sensitivity, slope grade and slope length. The spatiotemporal pattern gives the segregation of different traffic phases caused by the rarefaction wave and the shock wave under a certain initial vehicle number. A comparison between the upgrade and the downgrade indicates that the value of saturated flux of the downgrade is larger than that of the upgrade under the same condition. This result is in accordance with the real traffic.     

交叉口混合交通流元胞自动机模型及仿真研究

本文以右转机动车和直行自行车为对象研究交叉口混合交通流特性.基于交叉口机非干扰特性,将机动车元胞模型和自行车元胞模型进行了耦合,建立了考虑自行车穿越机动车延时、机动车穿越自行车间隙和冲突区占据处置等规则的交叉口混合交通流元胞自动机模型(NS-BCA).对右转机动车与直行自行车混合交通流进行了仿真,从流量-车辆到达率关系、交通流相位相变、交通流相位-到达率-混合交通流状态等方面研究了交叉口混合交通流的机非干扰机理.     

A Macro Model for Traffic Flow with Consideration of Static Bottleneck

In this paper, we develop a macro model for traffic flow with consideration of static bottleneck to explore the impacts of static bottleneck on traffic flow. The analytical and numerical results show that the proposed model can qualitatively describe the equilibrium flux, uniform flow and small perturbation under the action of a static bottleneck.     

A Macro Model for Traffic Flow with Consideration of Static Bottleneck

In this paper, we develop a macro model for traffic flow with consideration of static bottleneck to explore the impacts of static bottleneck on traffic flow. The analytical and numerical results show that the proposed model can qualitatively describe the equilibrium flux, uniform flow and small perturbation under the action of a static bottleneck.     

The KdV–Burgers equation in a new continuum model with consideration of driverʼs forecast effect and numerical tests

A new continuum traffic flow model is proposed based on an improved car-following model, which takes the driver?s forecast effect into consideration. The backward travel problem is overcome by our model and the neutral stability condition of the new model is obtained through the linear stability analysis. Nonlinear analysis shows clearly that the density fluctuation in traffic flow leads to a variety of density waves and the Korteweg–de Vries–Burgers (KdV–Burgers) equation is derived to describe the traffic flow near the neutral stability line. The corresponding solution for traffic density wave is also derived. Finally, the numerical results show that our model can not only reproduce the evolution of small perturbation, but also improve the stability of traffic flow.     

Traffic Flow States in a Freeway with Bottleneck

The system of mixture of single lane and double lane is studied by a cellular automata model, which is developed by us based on the Nagel and Schreckenberg's models. We justify that the model can reach a stable states quickly. The density distributions of the stable state is presented for several cases, which illustrate the manner of the congestion. The relationship between the outflow rate and the total number of vehicles and that between the outflow rate and the density just before the bottleneck are both given. Comparing with the relationship that occurring in the granular flow, we conclude that the transition from the free traffic flow to the congested traffic flow can also be attributed to the abrupt variation through unstable flow state, which can naturally explain the discontinuities and the complex time variation behavior observed in the traffic flow experiments.     

A new lattice model of traffic flow with the consideration of the traffic interruption probability

In this paper, we present a new lattice model which involves the effects of traffic interruption probability to describe the traffic flow on single lane freeways. The stability condition of the new model is obtained by the linear stability analysis and the modified Korteweg-de Vries (KdV) equation is derived through nonlinear analysis. Thus, the space will be divided into three regions: stable, metastable and unstable. The simulation results also show that the traffic interruption probability could stabilize traffic flow.     

The KdV-Burgers equation in a modified speed gradient continuum model

Based on the full velocity difference model, Jiang et al. put forward the speed gradient model through the micromacro linkage （Jiang R, Wu Q S and Zhu Z J 2001 Chin. Sci. Bull 46 345 and Jiang R, Wu Q S and Zhu Z J 2002 Trans. Res. B 36 405）. In this paper, the Taylor expansion is adopted to modify the model. The backward travel problem is overcome by our model, which exists in many higher-order continuum models. The neutral stability condition of the model is obtained through the linear stability analysis. Nonlinear analysis shows clearly that the density fluctuation in traffic flow leads to a variety of density waves. Moreover, the Korteweg-de Vries-Burgers （KdV-Burgers） equation is derived to describe the traffic flow near the neutral stability line and the corresponding solution for traffic density wave is derived. The numerical simulation is carried out to investigate the local cluster effects. The results are consistent with the realistic traffic flow and also further verify the results of nonlinear analysis.     

A new lattice model of traffic flow with the anticipation effect of potential lane changing

A new lattice model of traffic flow is presented by taking into account the anticipation of potential lane changing on front site on single lane. The stability condition of the extended model is obtained by using the linear stability theory. The modified KdV equation near the critical point is constructed and solved through nonlinear analysis. And the phase space of traffic flow in the density-sensitivity space could be divided into three regions: stable, metastable and unstable ones, respectively. Numerical simulation also shows that the consideration of lane changing probability in lattice model can stabilize traffic flow, which implies that the new consideration has an important effect on traffic flow in lattice models.     

Effect of driver over-acceleration on traffic breakdown in three-phase cellular automaton traffic flow models

Based on simulations with cellular automaton (CA) traffic flow models, a generic physical feature of the three-phase models studied in the paper is disclosed. The generic feature is a discontinuous character of driver over-acceleration caused by a combination of two qualitatively different mechanisms of over-acceleration: (i) Over-acceleration through lane changing to a faster lane, (ii) over-acceleration occurring in car-following without lane changing. Based on this generic feature a new three-phase CA traffic flow model is developed. This CA model explains the set of the fundamental empirical features of traffic breakdown in real heterogeneous traffic flow consisting of passenger vehicles and trucks. The model simulates also quantitative traffic pattern characteristics as measured in real heterogeneous flow.     

随机计及相对速度的交通流跟驰模型

从研究微观个体车辆行为出发，考虑车辆加速过程的不确定性，提出了随机计及相对速度的 交通流跟驰模型(SR-OV模型).对随机相对速度的跟驰模型的动力学方程进行稳定性分析，得 到与Bando跟驰模型不同的稳定性判据，其稳定性优于Bando模型.运用摄动理论分析交通过 程中密度波的变化，结果表明，在发生交通阻塞相变时，交通密度波以mKdV方程描述的扭结 -反扭结波演化.对随机相对速度跟驰模型进行数值模拟和分析，结果发现车流速度的变化小 于Bando模型的速度变化，而且与随机概率有关，当随机考虑相对速度的概率增大时，初始 的小扰动不会放大对车流产生影响，甚至长时间就消失，这与Bando模型完全不同.数值模拟 所得到的相图与解析解相符合,而且交通流稳定区域大于Bando模型.从车间距-速度演化图上 ，随着随机概率的增大，SR-OV模型在初始时存在的滞后现象，随着时间的增长，趋于稳定 状态后，滞后曲线收敛于一小区域，滞后效应被削弱.这完全不同于Bando模型，在Bando模 型中，滞后曲线由一点向外扩散，滞后曲线区域越来越大，车流趋于不稳定状态. 关键词： 交通流 跟驰模型 稳定性判据 相对速度     

具有加权顾前势的交通流模型

交通流随机行为的研究对于理解交通系统的内在演化规律具有重要作用. 基于元胞自动机模型和顾前势模型, 提出了一种考虑加权顾前势的交通流模型. 通过引入顾前势加权系数及对越靠近自身车辆的相互作用势赋予越大的权重, 使得建模过程更符合实际交通中司机根据前面车辆和环境情况进行随机决策的过程. 通过数值模拟, 再现了丰富的高密度交通行为. 仿真结果表明, 加权系数在高密度情况下作用明显, 更有利于在保持较高交通密度的同时, 具有较高的交通流量和道路通行能力. 关键词： 交通流 顾前势 随机模型 加权