A New Macro Model for Traffic Flow on a Highway with Ramps and Numerical Tests

In this paper, we present a new macro model for traffic flow on a highway with ramps based on the existing models. We use the new model to study the effects of on-off-ramp on the main road traffic during the morning rush period and the evening rush period. Numerical tests show that, during the two rush periods, these effects are often different and related to the status of the main road traffic. If the main road traffic flow is uniform, then ramps always produce stop-and-go traffic when the main road density is between two critical values, and ramps have little effect on the main road traffic when the main road density is less than the smaller critical value or greater than the larger critical value. If a small perturbation appears on the main road, ramp may lead to stop-and-go traffic, or relieve or even eliminate the stop-and-go traffic, under different circumstances. These results are consistent with real traffic, which shows that the new model is reasonable.     

Analysis of the wave properties of a new two-lane continuum model with the coupling effect

A multilane extension of the single-lane anisotropic continuum model (GK model) developed by Gupta and Katiyar for traffic flow is discussed with the consideration of the coupling effect between the vehicles of different lanes in the instantaneous traffic situation and the lane-changing effect. The conditions for securing the linear stability of the new model are presented. The shock and the rarefaction waves, the local cluster effect and the phase transition are investigated through simulation experiments with the new model and are found to be consistent with the diverse nonlinear dynamical phenomena observed in a real traffic flow. The analysis also focuses on empirically observed two-lane phenomena, such as lane usage inversion and the density dependence of the number of lane changes. It is shown that single-lane dynamics can be extended to multilane cases without changing the basic properties of the single-lane model. The results show that the new multilane model is capable of explaining some particular traffic phenomena and is in accordance with real traffic flow.     

Three-lane changing behaviour simulation using a modified optimal velocity model

In real urban traffic, roadways are usually multilane and are divided into fast, medium and slow lanes according to different velocity restrictions. Microscopic modelling of single lane has been studied widely using discrete cellular automata and continuous optimal velocity models. In this paper, we extend the continuous single-lane models (OV model and FVD model) to simulate the lane-changing behaviour on an urban roadway that consists of three lanes. Considering headway difference, velocity difference, safety distance, and the probability of lane-changing intention, a comprehensive lane-changing rule set is constructed. We analyse the fundamental diagram and reveal the “faster-is-slower” effect in urban traffic induced by lane-changing behaviour. We also investigate the effect of lane-changing behaviour on the distribution of vehicles, velocity, flow and headway. Asymmetrical phenomenon with symmetrical rules on urban roadway and density inversion on the slow lane were also found. The simulation results indicate that lane-changing behaviour is not advisable on crowded urban roadway. It is hoped that information from this study may be useful for traffic control and individual moving strategy on urban roadway.     

Effects of the number of on-rampson the ring traffic flow

Since ramp is an important composition of traffic system and there often exist multi ramps in a traffic system, the number of ramps can have great effects on main road traffic and produce some complex phenomena. In this paper, we employ the model presented by Tang \textit{et al}. [2009 {\em Communications in Theoretical Physics} {\bf 51}({1}) 71] to further study the effects of the number of on-ramps on the stability of traffic flow on a ring road. The numerical results show that this model can reproduce some complex traffic phenomena resulting from multi on-ramps on the ring road and the effects of the number of on-ramps on traffic flow, but the phenomena and the effects are both related to the initial density of the main road.     

Assigning on-ramp flows to maximize highway capacity

In this paper, we study the capacity of a highway with two on-ramps by using a cellular automata traffic flow model. We investigate how to improve the system capacity by assigning traffic flow to the two ramps. The system phase diagram is presented and different regions are classified. It is shown that in region I, in which both ramps are in free flow and the main road upstream of the ramps is in congestion, assigning a higher proportion of the demand to the upstream on-ramp could improve the overall flow, which is consistent with previous studies. This is explained through studying the spatiotemporal patterns and analytical investigations. In contrast, optimal assignment has not been observed in other regions. We point out that our result is robust and model independent under certain conditions.     

Simulation of multilane freeway traffic with detailed rules deduced from microscopic driving behavior

A simulation to model traffic on a multilane freeway is introduced starting from microscopic driving rules. The model takes each individual car into account with its individual features and actual situations, so that a distribution of parameters as well as different behaviors can easily be analyzed. Therefore, a detailed study of certain situations, driving tactics, vehicle properties, and their influence on the global traffic flow can be performed. The model is discussed, as are first results such as the influence of driver behavior on the fundamental diagram and, in addition, the dynamics of microscopic, individual quantities like separation and difference in speed between successive cars. It turns out that a hysteresis in the reaction of the driver for speeding up and slowing down plays an important role, and effects macroscopic quantities like the shape of the fundamental diagram, e.g., the metastable behavior around the maximum flow and on the speed of observed jams running backward. Furthermore, microscopic time resolved characteristics are strongly influenced, e.g., oscillations in the distance and relative speed between successive cars.     

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     

Mitigation of congestion at a traffic bottleneck with diversion and lane restrictions

Mitigation of congestion on a two-lane highway with an off-ramp and an on-ramp is simulated with three-phase traffic theory. Advanced travel information-the average velocity of vehicles near the bottleneck at an on-ramp-is used to divert vehicles at an upstream off-ramp. If enough vehicles divert, previously expanding synchronous flow congestion can be stalled and isolated to the region between the ramps. The introduction of lane restrictions (forbidding lane changing on the portion of highway between the ramps) in addition to diversion substantially reduces and essentially eliminates the congestion, restoring flow to nearly free-flow conditions.     

Staggered car-following induced by lateral separation effects in traffic flow

This Letter develops a new staggered car-following model taking into consideration lateral separation effects. Time-to-collision, calculated using visual angle variables, is introduced to describe the lateral separation distance and improve the optimal velocity model. The analytical and numerical results show that the stability of traffic flow can gradually be enhanced with the increase of lateral separation effects. The asymmetry property of traffic flow is also investigated using the new model. The results imply that incorporating lateral separation effects into the car-following model leads to the suppression of traffic jams and greatly enhances the realism of the model.     

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.     

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.     

固定闭塞系统中列车流的特性分析

在NS模型的基础上，针对轨道交通的特点，本文提出一种用于模拟四显示固定闭塞系统的元胞自动机模型.应用该模型模拟四显示固定闭塞系统中的列车延迟的交通现象，分析了四显示固定闭塞系统中的发车时间间隔、客货车比例、车站停靠时间、停靠站台数量等因素对列车平均延迟时间的影响.结果表明：客、货车混行时，货车对后行客车的运行会产生抑制作用，调整客、货车在车站的停靠时间可有效缓解这种抑制作用，减少客车的延迟时间；增加停靠站台的数量可提高线路上的车流密度，缓解车流延误，但在较大的发车时间间隔时，站台的利用率会降低. 关键词： 元胞自动机 固定自动闭塞系统 列车延迟     

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     

Phases of scaling and cross-correlation behavior in traffic

While many microscopic models of traffic flow describe transitions between different traffic phases, such transitions are difficult to quantify in measured traffic data. Here we study long-term traffic recordings consisting of ≈2900$\approx 2900$ days of flow, density, and velocity time series with minute resolution from a Spanish motorway. We calculate fluctuations, cross-correlations, and long-term persistence properties of these quantities in the flow–density diagram. This leads to a data-driven definition of (local) traffic states based on the dynamical properties of the data, which differ from those given in standard guidelines. We find that detrending techniques must be used for persistence analysis because of non-stationary daily and weekly traffic flow patterns. We compare our results for the measured data with analysis results for a microscopic traffic model, finding good agreement in most quantities. However, the simulations cannot easily reproduce the congested traffic states observed in the data. We show how fluctuations and cross-correlations in traffic data may be used for prediction, i.e., as indications of increasing or decreasing velocities.     

Traffic states and jamming transitions induced by a bus in two-lane traffic flow

We study the traffic states and jamming transitions induced by a bus (slow car) in a two-lane traffic of cars. We use the dynamic model which is an extended one of the optimal velocity model to take into account the lane changing. The fundamental (flow-density) diagram is presented. The fundamental diagram changes highly by introducing a bus on a two-lane roadway. It is found that there are the six distinct states for the two-lane traffic flow including a bus. The spatio-temporal patterns are presented for the distinct traffic states. The dynamical state of traffic changes with density of cars. It is shown that the dynamical transitions among the distinct traffic states occur at some values of density. The phase diagram (region map) is shown for the two-lane traffic flow including a bus.     

The KdV-Burgers equation in speed gradient viscous continuum model

Based on the microscopic two velocity difference model, a macroscopic model called speed viscous continuum model is developed to describe traffic flow. The relative velocities are added to the motion equation, which leads to viscous effects in continuum model. The viscous continuum model overcomes the backward travel problem, which exists in many higher-order continuum models. Nonlinear analysis shows that the density fluctuation in traffic flow leads to density waves. Near the onset of instability, a small disturbance could lead to solitons described by the Korteweg-de Vries-Burgers (KdV-Burgers) equation, which is seldom found in other traffic flow models, and the soliton solution is derived.     

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.     

智能交通系统的元胞自动机交通流模型

在Nagel-Schreckenberg(NS)模型的基础上，提出一种可应用智能交通系统（ITS）信息的新的交通流元胞自动机模型. 其中考虑了有效间距及刹车灯的作用，并引入了可变安全间距的新概念. 数值模拟表明：对于这种改进的ITS元胞自动机模型，道路交通量有了显著提高，体现了智能交通的优越性——有效地扩大交通流量，减少阻塞生成. 当考虑快车和慢车的混合交通流时，发现即使少量的慢车也会导致交通流量大幅度下降，说明了严格实施快慢道行驶的必要性. 关键词： 交通流 智能交通系统（ITS） 元胞自动机模型 刹车灯 可变安全间距     

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     

Disorder effect on the traffic flow behavior

The effects of some disorders, on the traffic flow behavior, are studied numerically. Especially, the effect of mixture of vehicles of different velocities and/or lengths, the effects of different drivers reactions, the position and the extraction rate of off-ramp in the free way. Using a generalized optimal velocity model, for a mixture of fast and slow vehicles, we have investigated the effect of delay times τ _f and τ _s on the fundamental diagram. It is Found that the small delay times have almost no effect, while, for sufficiently large delay time τ _s , the current profile displays qualitatively five different forms, depending on τ _f , τ _s and the fractions f _f and f _s of the fast and slow cars, respectively. The velocity (current) exhibits first-order transitions at low and/or high densities, from freely moving phase to the congested state, and from congested state to a jamming one, respectively. The minimal current appears in intermediate values of τ _s . Furthermore there exist, a critical value of τ _f above which the meta-stability and hysteresis appear. The effects of disorder due to drivers behaviors have been introduced through a random delay time τ allowing the car to reach its optimal velocity traffic flow models with open boundaries. In the absence of the variation of the delay time Δτ, it is found that the transition from unstable to meta-stable and from meta-stable to stable state occur under the effect of the injecting and the extracting rate probabilities α and β respectively. Moreover, the perturbation of the traffic flow behavior due to the off-ramp has been studied using numerical simulations in the one dimensional cellular automaton traffic flow model with open boundaries. When the off-ramp is located between two critical positions i _c1 and i _c2 the current remains constant (plateau) for β_0c1 < β₀ < β_0c2, and the density undergoes two successive first order transitions: from high density to plateau current phase and from average density to the low one. In the case of two off-ramps, these transitions occur only when the distance between ramps, is smaller than a critical value.