Stabilisation analysis of multiple car-following model in traffic flow

An improved multiple car-following model is proposed by considering the arbitrary number of preceding cars, which includes both the headway and the velocity difference of multiple preceding cars. The stability condition of the extended model is obtained by using the linear stability theory. The modified Korteweg--de Vries equation is derived to describe the traffic behaviour near the critical point by applying the nonlinear analysis. Traffic flow can be also divided into three regions: stable, metastable and unstable regions. Numerical simulation is accordance with the analytical result for the model. And numerical simulation shows that the stabilisation of traffic is increasing by considering the information of more leading cars and there is unavoidable effect on traffic flow from the multiple leading cars' information.     

New insights into traffic dynamics: a weighted probabilistic cellular automaton model

From the macroscopic viewpoint for describing the acceleration behaviour of drivers, a weighted probabilistic cellular automaton model （the WP model, for short） is proposed by introducing a kind of random acceleration probabilistic distribution function. The fundamental diagrams, the spatiotemporal patterns, are analysed in detail. It is shown that the presented model leads to the results consistent with the empiricaZ data rather well, nonlinear flow-density relationship existing in lower density regions, and a new kind of traific phenomenon called neo-synchronized flow. Furthermore, we give the criterion for distinguishing the high-speed and low-speed neo-synchronized flows and clarify the mechanism of this kind of traffic phenomenon. In addition, the result that the time evolution of distribution of headways is displayed as a normal distribution further validates the reasonability of the neo-synchronized flow. These findings suggest that the diversity and the randomicity of drivers and vehicles have indeed a remarkable effect on traffic dynamics.     

Non-lane-based full velocity difference car following model

In order to describe car following behavior in real world, this paper presents a non-lane-based car following model by incorporating the effects of the lane width in traffic. The stability condition of the model is obtained by using the linear stability theory. And numerical simulation is carried out to validate the analytic results. The property of the model is investigated, and it is found that the proposed model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion. The results implied that incorporating the lane width effects in car following model not only stabilize traffic flow and suppress the traffic jam, but also lower critical headway and increase capacity. Thus, the lateral separation effects greatly enhance the realism of car following models.     

The effects of reaction delay in the Nagel-Schreckenberg traffic flow model

This paper studies a new model, which considers the effects of drivers reaction delay in the Nagel-Schreckenberg model. We studied the traffic flow properties in the new model under both periodic and open boundary conditions. The fundamental diagram, spatio-temporal patterns, density-density correlation functions, relaxation time, and distance headway distribution are investigated. Several interesting results are reported, for example, (i) the jam becomes less condensed when the delay effect is considered; (ii) the distance headway of the new model exhibits a multi-peak distribution when randomization p is small; (iii) for large p, the distribution of distance headway follows a power law in the new model; (iv) under open boundary conditions, the existence of a stationary jam near the left boundary will lower the flow rate.     

Synchronized Flow in a Cellular Automaton Model with Time Headway Dependent Randomization

We propose another possible mechanism of synchronized flow, i,e. that a time headway dependent randomization can exhibit synchronized flow. Based on this assumption, we present a new cellular automaton （CA） model for traffic flow, in which randomization effect is enhanced with the decrease of time headway. We study fundamental diagram and spatial-temporal diagrams of the model and perform microscopic analysis of time series data, which shows the model could reproduce synchronized flow as expected. It is also shown that a spontaneous transition from synchronized flow to jam could be observed by incorporating slow-to-start effect into the model. We expect that our work could contribute to the understanding of the real origin of synchronized flow.     

优先随机慢化及预测间距对交通流的影响

在周期性边界条件下，通过引入预测车辆间距对Noise-First模型进行改进，数值模拟了不同参数下的交通情形. 研究表明：引入预测间距的Noise-First模型更能真实地反映实际交通状况，不仅再现了启止波、同步流，而且出现了亚稳态，非平衡相变等与实际道路交通一致的非线性现象. 关键词： 交通流 元胞自动机 同步流 亚稳态     

基于多尺度熵的交通流复杂性分析

交通流演化复杂性的研究有助于深刻理解交通系统的内在演化规律,为交通流的预测和控制提供理论依据.多尺度熵方法在生理时间序列和计算机网络流量的分析中得到了广泛的应用.考虑到交通流中的车辆到达和计算机网络中的分组到达具有类似特性,本文以刹车灯模型的车头时距为分析对象,利用多尺度熵方法来分析交通流演化的复杂性.分析结果表明:1)车头时距的复杂性随着时间尺度的增加而降低,反映了交通流的短时间难预测性;2)当时间尺度较小时,车头时距复杂性在自由流时和同步流时差异不大,但是,随着时间尺度的增加,自由流时车头时距的熵值迅速下降,而同步流时车头时距的熵值下降较慢.这一特性对于识别自由流中是否产生了同步流有非常重要的参考价值.本文的研究可以为揭示交通流演化的复杂性提供新的思路和方法.     

A macroscopic traffic model for heterogeneous flow

A new macroscopic heterogeneous traffic flow model is proposed in this paper. Driver anticipation is developed using analogies from Darcy's law and is based on the time and lateral distance headways. An equilibrium velocity distribution for heterogeneous traffic based on traffic alignment is employed. The performance of the Extended Speed Gradient (ESG), Zhang and proposed models is compared for the same traffic conditions using the Roe decomposition technique. The results obtained show the significance of the time and lateral distance headways on the evolution of traffic flow. Further, the proposed model provides a more realistic characterization of traffic flow than the ESG and Zhang models.     

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.     

Regularity of traffic noise signals

The flexibility of the filtered renewal process compared with the filtered Poisson process as a model for traffic noise is demonstrated. This is done by proving that for the family of gamma distributed headways with coefficient of variation less than one the variance of the traffic noise signal never exceeds that of the corresponding filtered Poisson process. Furthermore it is proved that the inverse inequality holds for the family of completely monotone distributions, which includes all finite mixtures of exponential distributions. The theory is illustrated by some numerical calculations.     

Delays,inaccuracies and anticipation in microscopic traffic models

We generalize a wide class of time-continuous microscopic traffic models to include essential aspects of driver behaviour not captured by these models. Specifically, we consider (i) finite reaction times, (ii) estimation errors, (iii) looking several vehicles ahead (spatial anticipation), and (iv) temporal anticipation. The estimation errors are modelled as stochastic Wiener processes and lead to time-correlated fluctuations of the acceleration.We show that the destabilizing effects of reaction times and estimation errors can essentially be compensated for by spatial and temporal anticipation, that is, the combination of stabilizing and destabilizing effects results in the same qualitative macroscopic dynamics as that of the, respectively, underlying simple car-following model. In many cases, this justifies the use of simplified, physics-oriented models with a few parameters only. Although the qualitative dynamics is unchanged, multi-anticipation increase both spatial and temporal scales of stop-and-go waves and other complex patterns of congested traffic in agreement with real traffic data. Remarkably, the anticipation allows accident-free smooth driving in complex traffic situations even if reaction times exceed typical time headways.     

A new car-following model with the consideration of anticipation optimal velocity

In this paper, a new anticipation optimal velocity model (AOVM) is proposed by considering anticipation effect on the basis of the full velocity difference model (FVDM) for car-following theory on single lane. The linear stability condition is derived from linear stability analysis. Starting and braking process is investigated for the car motion under a traffic signal, which shows that the results accord with empirical traffic values. Especially AOVM can avoid the disadvantage of the unrealistically high deceleration appearing in FVDM. Furthermore, numerical simulation shows that AOVM might avoid the disadvantage of negative velocity and headway that occur at small sensitivity coefficients in the FVDM since the anticipation effect is taken into account in AOVM, which means that collision disappears with the consideration of an appropriate anticipation parameter.     

Stability analysis of traffic flow with extended CACC control models

To further investigate car-following behaviors in the cooperative adaptive cruise control(CACC) strategy,a comprehensive control system which can handle three traffic conditions to guarantee driving efficiency and safety is designed by using three CACC models.In this control system,some vital comprehensive information,such as multiple preceding cars' speed differences and headway,variable safety distance(VSD) and time-delay effect on the traffic current and the jamming transition have been investigated via analytical or numerical methods.Local and string stability criterion for the velocity control(VC) model and gap control(GC) model are derived via linear stability theory.Numerical simulations are conducted to study the performance of the simulated traffic flow.The simulation results show that the VC model and GC model can improve driving efficiency and suppress traffic congestion.     

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.     

A stochastic multi-cluster model of freeway traffic

A stochastic approach based on the Master equation is proposed to describe the process of formation and growth of car clusters in traffic flow in analogy to usual aggregation phenomena such as the formation of liquid droplets in supersaturated vapour. By this method a coexistence of many clusters on a one-lane circular road has been investigated. Analytical equations have been derived for calculation of the stationary cluster distribution and related physical quantities of an infinitely large system of interacting cars. If the probability per time (or p) to decelerate a car without an obvious reason tends to zero in an infinitely large system, our multi-cluster model behaves essentially in the same way as a one-cluster model studied before. In particular, there are three different regimes of traffic flow (free jet of cars, coexisting phase of jams and isolated cars, highly viscous heavy traffic) and two phase transitions between them. At finite values of p the behaviour is qualitatively different, i.e., there is no sharp phase transition between the free jet of cars and the coexisting phase. Nevertheless, a jump-like phase transition between the coexisting phase and the highly viscous heavy traffic takes place both at and at a finite p. Monte-Carlo simulations have been performed for finite roads showing a time evolution of the system into the stationary state. In distinction to the one-cluster model, a remarkable increasing of the average flux has been detected at certain densities of cars due to finite-size effects. Received 17 September 1999     

A new car-following model with consideration of the traffic interruption probability

In this paper, we present a new car-following model by taking into account the effects of the traffic interruption probability on the car-following behaviour of the following vehicle. The stability condition of the model is obtained by using the linear stability theory. The modified Korteweg--de Vries (KdV) equation is constructed and solved, and three types of traffic flows in the headway sensitivity space---stable, metastable, and unstable---are classified. Both the analytical and simulation results show that the traffic interruption probability indeed has an influence on driving behaviour, and the consideration of traffic interruption probability in the car-following model could stabilize traffic flow.     

Computer simulation model for the prediction of traffic noise levels

This paper describes a computer simulation model capable of predicting the noise levels generated by traffic passing through road intersections controlled by roundabouts where departures from free-flow traffic conditions occur. The model depends for its operation on the acoustical and flow characteristics of single vehicles travelling on a road from which the overall noise generated by traffic streams can be deduced using a sampling/integration technique. Distance effects, ground cover, vehicle type, velocity and headway characteristics, etc. are taken into account in the model and the simplest possible input parameters are used deliberately to facilitate the eventual use of the model by highway and planning authorities. Good agreement has been achieved between measured and predicted L₁₀ values for freely flowing traffic negotiating roundabouts. Further applications of the model involving road intersections controlled by traffic lights and the effect of traffic queues are nearing completion.     

高速车随机延迟逐步加速交通流元胞自动机模型

提出介于Nagel-Schreckenberg(NS)模型和Fukui-Ishibashi(FI)模型之间的一种新的一维交通流元胞自动机模型. 此模型采用NS模型中的车辆逐步加速方式,和FI模型中的仅最大速车可随机减速的车辆延迟方式.证明新模型的基本图,即车流渐近稳态的平均速度与道路上的车辆密度之间的函数关系与FI模型的完全相同.这也就是说,只允许最高速车辆可发生延迟的FI交通流模型,如果将其突然无限制加速方式(车辆可在一个时步内从零速加速到最高速限M或车头距离所允许的最大速度),改变为车辆的逐步有限加速 关键词： 交通流 元胞自动机模型 相变基本图 Nagel-Schreckenberg模型 Fukui-Ishibashi模型