Density waves in a traffic flow model with reaction-time delay

Density waves are investigated analytically and numerically in the optimal velocity model with reaction-time delay of drivers. The stability condition of this model is obtained by using the linear stability theory. The results show that the decrease of reaction-time delay of drivers leads to the stabilization of traffic flow. The Burgers, Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations are derived to describe the density waves in the stable, metastable and unstable regions respectively. The triangular shock waves, soliton waves and kink-antikink waves appearing respectively in the three distinct regions are derived to describe the traffic jams. The numerical simulations are given.     

Modeling U-turn traffic flow

Median U-turns are sometimes installed to improve the traffic flow at busy intersections by eliminating left turns. Using a microscopic traffic model, we confirmed the presence of transitions from free flow to congested flow with increasing car inflow density. In addition, our proposed rules inside a U-turn curve, which accounted for safety issues and an asymmetric lane changing behavior (outer-to-inner vs. inner-to-outer lane transitions), predicted the speed distribution of cars after the U-turn curve. We found that U-turn curves installed for improving traffic flow at busy intersections produced their desired effects only when there is minimal interaction between cars.     

The difference of drivers' anticipation behaviors in a new macro model of traffic flow and numerical simulation

A valuable consideration is inserted into car-following theory to investigate the difference of drivers' anticipation. Furthermore, a fresh macro traffic model involving the difference of the drivers' anticipation is deduced from the car-following model by applying transformation relationship from micro to macro variables. And this effect resulted from the difference of the drivers' anticipation is observed via numerical simulation. The results show that the difference of drivers' anticipation has a negligible impact on traffic flow.     

Impact of the honk effect on the stability of traffic flow

In this paper, we propose an extended car-following model which takes into account the honk effect. The analytical and numerical results show that the honk effect improves the stability of traffic flow. The dependence of the stability on the properties of the honk effect is investigated in this paper.     

Analysis of the stability and density waves for traffic flow

In this paper, the optimal velocity model of traffic is extended to take into account the relative velocity. The stability and density waves for traffic flow are investigated analytically with the perturbation method. The stability criterion is derived by the linear stability analysis. It is shown that the triangular shock wave, soliton wave and kink wave appear respectively in our model for density waves in the three regions: stable, metastable and unstable regions. These correspond to the solutions of the Burgers equation, Korteweg－de Vries equation and modified Korteweg－de Vries equation. The analytical results are confirmed to be in good agreement with those of numerical simulation. All the results indicate that the interaction of a car with relative velocity can affect the stability of the traffic flow and raise critical density.     

Effect of looking backward on traffic flow in an extended multiple car-following model

In this paper, a new car-following model is proposed by incorporating the backward looking effect under certain conditions and multiple information of preceding cars in traffic flow. And the neutral stability condition of this model can be obtained by using the linear stability theory. Numerical simulation shows that the proposed model is theoretically an improvement over previous ones.     

Numerical study of urban traffic flow with dedicated bus lane and intermittent bus lane

Based on the cellular automaton traffic flow model and the concept of public transport priority, a two-lane traffic model with an intermittent bus lane is proposed and the properties of urban traffic flow are studied. The cases of traffic with a dedicated bus lane (DBL), an intermittent bus lane (IBL) and an ordinary two-lane traffic are simulated, and comparisons in the form of the fundamental diagrams and the velocity-density profiles are made between them. It is shown that the DBL has the advantage of freeing buses from traffic interference and also has the disadvantage of disrupting traffic, the IBL is more efficient in improving the bus flow than ordinary two-lane traffic and maintaining the car flow at a higher level at the same time than the DBL, while the ordinary two-lane traffic suppresses public transportation and is not advantageous in easing urban traffic congestion. Also it is indicated that the DBL is only appropriate for low traffic flow in a two-lane traffic system, and this limitation can be partly overcome by opening the bus lane to general traffic intermittently when the bus lane is not in use by buses.     

The stabilization effect of the density difference in the modified lattice hydrodynamic model of traffic flow

A modified lattice hydrodynamic model of traffic flow is proposed by introducing the density difference between the leading and the following lattice. The stability condition of the modified model is obtained through the linear stability analysis. The results show that considering the density difference leads to the stabilization of the system. The Burgers equation and mKdV equation are derived to describe the density waves in the stable and unstable regions respectively. Numerical simulations show that considering the density difference not only could stabilize traffic flow but also makes the lattice hydrodynamic model more realistic.     

Soliton and kink jams in traffic flow with open boundaries

Soliton density wave is investigated numerically and analytically in the optimal velocity model (a car-following model) of a one-dimensional traffic flow with open boundaries. Soliton density wave is distinguished from the kink density wave. It is shown that the soliton density wave appears only at the threshold of occurrence of traffic jams. The Korteweg-de Vries (KdV) equation is derived from the optimal velocity model by the use of the nonlinear analysis. It is found that the traffic soliton appears only near the neutral stability line. The soliton solution is analytically obtained from the perturbed KdV equation. It is shown that the soliton solution obtained from the nonlinear analysis is consistent with that of the numerical simulation.     

The theoretical analysis of the lattice hydrodynamic models for traffic flow theory

The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but also connected with the microscopic car following model closely. The modified Korteweg-de Vries (mKdV) equation related to the density wave in a congested traffic region has been derived near the critical point since Nagatani first proposed it. But the Korteweg-de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail for the car following model. We devote ourselves to obtaining the KdV equation from the original lattice hydrodynamic models and the KdV soliton solution to describe the traffic jam. Especially, we obtain the general soliton solution of the KdV equation and the mKdV equation. We review several lattice hydrodynamic models, which were proposed recently. We compare the modified models and carry out some analysis. Numerical simulations are conducted to demonstrate the nonlinear analysis results.     

边界高密度下低杂波耦合的数值模拟

采用STEP＋RAMP的模型模拟低杂波与等离子体耦合。在该模型中,等离子体边界密度一开始就处于一个比较高的值(大于截     

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.     

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     

Multiple car-following model of traffic flow and numerical simulation

On the basis of the full velocity difference (FVD) model, an improved multiple car-following (MCF) model is proposed by taking into account multiple information inputs from preceding vehicles. The linear stability condition of the model is obtained by using the linear stability theory. Through nonlinear analysis, a modified Korteweg-de Vries equation is constructed and solved. The traffic jam can thus be described by the kink--antikink soliton solution for the mKdV equation. The improvement of this new model over the previous ones lies in the fact that it not only theoretically retains many strong points of the previous ones, but also performs more realistically than others in the dynamical evolution of congestion. Furthermore, numerical simulation of traffic dynamics shows that the proposed model can avoid the disadvantage of negative velocity that occurs at small sensitivity coefficients λ in the FVD model by adjusting the information on the multiple leading vehicles. No collision occurs and no unrealistic deceleration appears in the improved model.     

对流梯形微通道内气液两相流动的数值研究

采用VOF方法,对梯形微通道内不可压缩气液两相流动进行了数值模拟研究,详细分析了气泡形成过程,以及当量直径、截面形状、液体表面张力和粘度等对气泡液柱形成过程和长度的影响,拟合出微通道气泡液柱长度计算公式。结果表明:气泡液柱的长度受表观气速和表观液速的影响较大;表面张力对气泡尺寸的影响较小,当液体粘度增加为水粘度的10倍时,形成的气泡形状不规则。增大表面张力,形成气泡的时间增加;增大粘度,形成气泡的时间减小。     

考虑车辆相对运动速度的交通流演化过程的数值模拟

提出考虑了车辆相对运动速度的最佳速度跟车模型,对该模型稳定性进行了分析.对其所描述的交通流的演化过程进行了数值模拟,并与未考虑相对运动速度的最佳速度跟车模型作了比较. 关键词： 交通流 最佳速度 跟车模型 相对运动速度     

Effect of adaptive cruise control systems on mixed traffic flow near an on-ramp

Mixed traffic flow consisting of vehicles equipped with adaptive cruise control (ACC) and manually driven vehicles is analyzed using car-following simulations. Simulations of merging from an on-ramp onto a freeway reported in the literature have not thus far demonstrated a substantial positive impact of ACC. In this paper cooperative merging for ACC vehicles is proposed to improve throughput and increase distance traveled in a fixed time. In such a system an ACC vehicle senses not only the preceding vehicle in the same lane but also the vehicle immediately in front in the other lane. Prior to reaching the merge region, the ACC vehicle adjusts its velocity to ensure that a safe gap for merging is obtained. If on-ramp demand is moderate, cooperative merging produces significant improvement in throughput (20%) and increases up to 3.6 km in distance traveled in 600 s for 50% ACC mixed flow relative to the flow of all-manual vehicles. For large demand, it is shown that autonomous merging with cooperation in the flow of all ACC vehicles leads to throughput limited only by the downstream capacity, which is determined by speed limit and headway time.     

Phase diagrams of noisy traffic states in the presence of a bottleneck

The traffic states are investigated for the noisy traffic flow in the presence of a bottleneck under the open boundary condition. The phase diagrams of the different kinds of congested traffic are presented for different values of sensitivity (the inverse of delay time). It is shown that the five different types of traffic states appear below the critical point: the free traffic with a pinned localized cluster, the weak standing shock, the moving localized cluster, the oscillatory congested traffic, and the strong standing shock. Above the critical point, the moving localized cluster and oscillatory congested traffic do not occur. Also, in the traffic flow without noise, the moving localized cluster and oscillatory congested traffic do not appear.     

A new car-following model with consideration of roadside memorial

In this Letter, a car-following model with consideration of roadside memorial is proposed. The numerical results show that the proposed model can qualitatively describe the impacts of roadside memorial on traffic flow and the traffic risk coefficient. It is also shown that roadside memorial can enhance the traffic safety.     

Explaining traffic patterns at on-ramp vicinity by a driver perception model in the framework of three-phase traffic theory

In traffic system, driving behaviors change with the surrounding traffic perceived by drivers, resulting in the complex spatio-temporal traffic patterns. Accordingly, in the majority of traffic models, vehicle accelerations are described by dynamic equations based on driving behavior, system dynamics and some underlying steady-state velocity-gap (bumper-to-bumper spacing) relation in order to guarantee the realistic human behavior. This paper proposes a deterministic car-following model based on a multi-branch fundamental diagram with each branch representing a particular category of driving style. Furthermore, an additional dynamic perception equation is introduced to reflect the driving style adaptation in response to the change in surrounding traffic situations. With simulation based on the proposed “driver perception model” (DP model), empirical findings of traffic breakdown and observed spatio-temporal patterns at on-ramp vicinity are reproduced. Furthermore, comparison results show the consistency between numerical simulation and the real traffic data of Beijing urban freeway.