Relative velocity difference model for the car-following theory

To explore and evaluate the impacts of relative velocity difference (RVD) with memory on the dynamic characteristics and fuel economy of traffic flow in the intelligent transportation environment, we first analyze the linkage between RVD with different-step memory and the following car’s behaviors with the measured car-following (CF) data in cities by using the gray correlation analysis method and then present a RVD model based on the previous CF models in the literatures and calibrate it. Finally, we conduct several numerical simulations in the adaptive cruise control (ACC) strategy to explore how RVD with memory affects car’s velocity fluctuation and fuel consumptions, and find that the RVD model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion, and that considering RVD with memory in modeling CF behaviors and designing the advanced ACC strategy can improve the stability and fuel economy of traffic flow.     

Phase transitions in the two-lane density difference lattice hydrodynamic model of traffic flow

In this paper, we derive the KdV equation from the two-lane lattice hydrodynamic traffic model considering density difference effect. The soliton solution is obtained from the KdV equation. Under periodical boundary, the KdV soliton of traffic flow is demonstrated by numerical simulation. The numerical simulation result is consistent with the nonlinear analytical result. Under open system, the density fluctuation of the downstream last one lattice is designed to explore the empirical congested traffic states. A phase diagram is presented which includes free traffic, moving localized cluster, triggered stop-and-go traffic, oscillating congested traffic, and homogeneous congested traffic. Finally, the spatiotemporal evolution of all the traffic states described in phase diagram are reproduced. Results suggest that the two-lane density difference hydrodynamic traffic model is suitable to describe the actual traffic.     

A new lattice hydrodynamic model for two-lane traffic with the consideration of density difference effect

A new lattice hydrodynamic model for two-lane traffic flow is proposed by introducing the density difference effect (DDE). Using linear stability theory, stability condition of the presented model is obtained. Jamming transitions among the freely moving phase, the coexisting phase, and the uniform congested phase are investigated by employing nonlinear analysis. The modified KdV (mKdV) equation near the critical point is derived and the kink-antikink soliton solutions are obtained. Numerical simulations are presented to verify analytical results, showing that DDE can improve the stability of traffic flow effectively.     

A velocity matching car-following model on a closed ring in which overtaking is allowed

Car-following models seek to describe the behaviour of a group of vehicles as they move along a stretch of road. In such models the behaviour of each vehicle is taken to be dependant on the motion of the vehicle in front and overtaking is not permitted. In this paper the effect of removing this ‘no-overtaking’ restriction is investigated. The resulting model is described in terms of a set of coupled time delay differential equations and these are solved numerically to analyse their post-transient behaviour under a periodic perturbation. For certain parameter choices this behaviour is found to be chaotic, and the degree of chaos is estimated using the Grassberger–Procaccia dimension.     

TDGL and mKdV equations for an extended car-following model

In this paper, we construct an improved car-following model by accounting for the effect of the optimal velocity difference and a two-velocity difference. The effect of this model is examined through the linear stability analysis. The TDGL equation and the mKdV equation are derived from nonlinear analysis. Then, the energy consumption and the stability in car-following models considering the optimal velocity difference and a two-velocity difference are discussed. Moreover, numerical simulation shows that the new model can improve the stability of traffic flow, which is consistent with the theoretical analysis.     

A new car-following model accounting for varying road condition

In this paper, we develop a new car-following model with consideration of varying road condition based on the empirical data. Firstly, we explore the effects of road condition on uniform flow from analytical and numerical perspectives. The results indicate that road condition has great influences on uniform flow, i.e., good road condition can enhance the velocity and flow and their increments will increase when road condition becomes better; bad road conditions will reduce the velocity and flow and their reductions will increase when road condition turns worse. Secondly, we study the effects of road conditions on the starting and braking processes. The numerical results show that good road condition will speed up the two processes and that bad road condition will slow down the two processes. Finally, we study the effects of road condition on small perturbation. The numerical results indicate that the stop-and-go phenomena resulted by small perturbation will become more serious when the road condition becomes better.     

An extended delayed feedback control method for the two-lane traffic flow

This study extended a delayed feedback control method for the two-lane car-following model. In order to suppress the traffic jams more actually in the two-lane vehicle groups with lane-changing behavior, we introduced the delayed time of receiving the longitudinal and lateral interaction information in the controller into the feedback signals for the control scheme. The stability conditions for different cases were derived, respectively, according to the delayed time by the theory analysis. And the delayed time in the controller was found to instigate the traffic oscillations when the feedback gains were designed improper, which showed that the longer delayed time induces worse traffic jams. The numerical simulation results were found consistent with the theoretical findings as well. Finally, we further presented a comparative study of the proposed control method by a comparison with one existing controller which did not consider the delayed time. And it showed that the delayed time in the controller also affects the traffic flow and performance of control method.     

稀薄流非线性模型方程离散速度坐标法有限差分解

从一般非线性Bo ltzm ann方程出发,发展并实现了一套适于大范围K nudsen数稀薄流问题数值模拟的统一算法。采用BGK模型和Shakov模型近似碰撞项,进而引入两个二速度无量纲简化分布函数,通过关于分子速度第三分量取矩积分,将三速度单一模型方程变换为二速度微分方程组。基于G auss-H erm ite积分公式和正交多项式G auss积分公式,借助离散速度坐标法消除简化模型方程对分子速度空间的连续依赖性,从相空间到物理空间得到一组带源项双曲守恒离散方程,并给出其显式和隐式二阶迎风TVD有限差分解。以二维圆柱A r气体超声速绕流算例,验证了数值算法的有效性,比较分析了漫反射和镜面反射两种气体分子壁面反射模型的计算结果。     

An extended car-following model accounting for the honk effect and numerical tests

In this paper, an extended car-following model is proposed to simulate traffic flow by considering the honk effect. The stability condition of this model is obtained by using the linear stability analysis. The phase diagram shows that the honk effect plays an important role in improving the stabilization of traffic system. The mKdV equation near the critical point is derived to describe the evolution properties of traffic density waves by applying the reductive perturbation method. Furthermore, the numerical simulation is carried out to validate the analytical results and indicates that the traffic jam can be suppressed efficiently via taking into account the honk effect.     

A new car-following model with consideration of inter-vehicle communication

In this paper, we construct a new car-following model with inter-vehicle communication (IVC) to study the driving behavior under an accident. The numerical results show that the proposed model can qualitatively describe the effects of IVC on each vehicle’s speed, acceleration, movement trail, and headway under an accident and that the new model can overcome the full velocity difference (FVD) model’s shortcoming that collisions occur under an accident, which illustrates that the new model can better describe the driving behavior under an accident than the FVD model.     

Continuum modeling for two-lane traffic flow

In this paper, we study the continuum modeling of traffic dynamics for two-lane freeways. A new dynamics model is proposed, which contains the speed gradient-based momentum equations derived from a car-following theory suited to two-lane traffic flow. The conditions for securing the linear stability of the new model are presented. Numerical tests are carried out and some nonequilibrium phenomena are observed, such as small disturbance instability, stop-and-go waves, local clusters and phase transition. The project supported by the National Natural Science Foundation of China (70521001) The English text was polished by Yunming Chen.     

A continuum traffic flow model with the consideration of coupling effect for two-lane freeways

A new higher-order continuum model is proposed by considering the coupling and lane changing effects of the vehicles on two adjacent lanes. A stability analysis of the proposed model provides the conditions that ensure its linear stability. Issues related to lane changing, shock waves and rarefaction waves, local clustering and phase transition are also investigated with numerical experiments. The simulation results show that the proposed model is capable of providing explanations to some particular traffic phenomena commonly observable in real traffic flows.