Simulating synchronized traffic flow and wide moving jam based on the brake light rule

A new cellular automaton (CA) model based on brake light rules is proposed, which considers the influence of deterministic deceleration on randomization probability and deceleration extent. To describe the synchronized flow phase of Kerner’s three-phase theory in accordance with empirical data, we have changed some rules of vehicle motion with the aim to improve speed and acceleration vehicle behavior in synchronized flow simulated with earlier cellular automaton models with brake lights. The fundamental diagrams and spatial–temporal diagrams are analyzed, as well as the complexity of the traffic evolution, the emergence process of wide moving jam. Simulation results show that our new model can reproduce the three traffic phases: free flow, synchronized flow and wide moving jam. In addition, our new model can well describe the complexity of traffic evolution: (1) with initial homogeneous distribution and large densities, the traffic will evolve into multiple steady states, in which the numbers of wide moving jams are not invariable. (2) With initial homogeneous distribution and the middle range of density, the wide moving jam will emerge stochastically. (3) With initial mega-jam distribution and the density close to a point with the low value, the initial mega-jam will disappear stochastically. (4) For the cases with multiple wide moving jams, the process is analyzed involving the generation of narrow moving jam due to “pinch effect”, which leads to wide moving jam emergence.     

Synchronized traffic flow simulating with cellular automata model

The synchronized flow traffic phase of Kerner’s three-phase traffic theory can be well reproduced by the model proposed by Jiang and Wu [R. Jiang, Q.S. Wu, J. Phys. A: Math. Gen. 36 (2003) 381]. But in the Jiang and Wu model, the rule for brake light-after switching on, the brake light will not set off until the vehicle accelerates-is obviously unrealistic. Thus we improved the model by considering the difference in accelerating and decelerating performance under different driving conditions. The fundamental diagram and spatial-temporal diagrams are analyzed. We confirmed that the new model could reproduce the synchronized flow by two methods, i.e. the traffic flow interruption effect and performing microscopic analysis of time series data. Simulation results show that the decelerating difference is an important factor to reproduce the synchronized flow. We expect that our work could make contributions to understanding the mechanism of the synchronized flow.     

The influence of nonmonotonic synchronized flow branch in a cellular automaton traffic flow model

In this paper we study the congested patterns upstream of an isolated on-ramp in a cellular automaton traffic flow model, which is proposed in our previous paper [Cheng-Jie Jin, Wei Wang, Rui Jiang, Kun Gao, J. Stat. Mech (2010) P03018]. The simulation results under open boundary conditions are presented by spatiotemporal diagrams. Our diagram of congested patterns is quite similar to that of the cellular automaton models within Kerner’s three-phase traffic theory, while some differences in the “moving synchronized flow pattern” (MSP) should be noted. In our model the upstream front of MSP propagates not only upstream, but also downstream. The propagation direction depends on the flow rates and densities of free flow and synchronized flow. Besides, in our model the outflow of wide moving jams or bottlenecks could be free flow or synchronized flow, as reported in many empirical data. In the dissolving of congestions, the form of free flow may be hindered and stable synchronized flow may emerge. This phenomenon can help us understand more about the outflow. All the interesting characteristics of our model are due to the nonmonotonic structure of synchronized flow branch in the fundamental diagram, which has not been found in previous models.     

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.     

考虑延迟概率因素对混合车辆敏感驾驶交通流模型的研究

在交通流NS模型的基础上，考虑混合车辆之间存在的速度差异，不同车辆的驾驶员在对前车的敏感驾驶随机减速行为过程中其延迟概率是不同的，从而提出了一维多速混合车辆敏感驾驶元胞自动机交通流模型. 通过计算机数值模拟得到了混合车辆在不同参数下的 基本图.结果表明，与NS模型、SDNS模型相比，道路交通流量有较大的提高，而且还展现出 了亚稳态、相分离等复杂的实际交通行为现象.结合实际情况，对混合交通的特性进行了分析和讨论. 关键词： 元胞自动机 混合交通流模型 亚稳态 相分离 计算机模 拟     

考虑动态车间距的一维元胞自动机交通流模型

基于NaSch元胞自动机交通流模型, 考虑司机复杂的性格特征和驾驶行为差异, 引入相邻车辆的动态车间距, 提出了一个改进的单车道元胞自动机交通流模型. 通过数值模拟得到了流量-密度关系, 在中高密度区域呈现出一种弥散分布的状态而非惟一确定的关系, 再现了交通系统中的自由流、同步流及宽幅运动阻塞, 表明道路上即使没有交通瓶颈也会出现同步流和拥挤交通, 同时揭示了在同步流中存在的车辆高速跟驰现象, 高速跟驰率与交通实测结果较为符合.     

An Extended Optimal Velocity Model with Consideration of Honk Effect

Based on the OV （optimal velocity） model, we in this paper present an extended OV model with the consideration of the honk effect. The analytical and numerical results illustrate that the honk effect can improve the velocity and flow of uniform flow but that the increments are relevant to the density.     

A New Lattice Model of Two-Lane Traffic Flow with the Consideration of the Honk Effect

In this paper, a new lattice model of two-lane traffic flow with the honk effect term is proposed to study the influence of the honk effect on wide moving jams under lane changing. The linear stability condition on two-lane highway is obtained by applying the linear stability theory. The modified Korteweg-de Vries (KdV) equation near the critical point is derived and the coexisting curves resulted from the modified KdV equation can be described, which shows that the critical point, the coexisting curve and the neutral stability line decrease with increasing the honk effect coefficient. A wide moving jam can be conceivably described approximately in the unstable region. Numerical simulation is performed to verify the analytic results. The results show that the honk effect could suppress effectively the congested traffic patterns about wide moving jam propagation in lattice model of two-lane 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.     

On the modeling of synchronized flow in cellular automaton models

In this paper,we further analyze our cellular automaton(CA)traffic flow model.By changing some parameters,the characteristics of our model can be significantly varied,ranging from the features of phase transitions to the number of traffic phases.We also review the other CA models based on Kerner’s three-phase traffic theory.By comparisons,we find that the core concepts for modeling the synchronized flow in these models are similar.Our model can be a good candidate for modeling the synchronized flow,since there is enough flexibility in our framework.     

An extended car-following model considering the appearing probability of truck and driver's characteristics

In this paper, the appearing probability of truck is introduced and an extended car-following model is presented to analyze the traffic flow based on the consideration of driver's characteristics, under honk environment. The stability condition of this proposed model is obtained through linear stability analysis. In order to study the evolution properties of traffic wave near the critical point, the mKdV equation is derived by the reductive perturbation method. The results show that the traffic flow will become more disorder for the larger appearing probability of truck. Besides, the appearance of leading truck affects not only the stability of traffic flow, but also the effect of other aspects on traffic flow, such as: driver's reaction and honk effect. The effects of them on traffic flow are closely correlated with the appearing probability of truck. Finally, the numerical simulations under the periodic boundary condition are carried out to verify the proposed model. And they are consistent with the theoretical findings.     

The phase diagram and the pathway of phase transitions for traffic flow in a circular one-lane roadway

This paper demonstrates that patient driving habits lead to homogenous congested flow while impatient driving habits lead to wide-moving jam flow in the high density region based on the numerical simulation of the intelligent driver model proposed by M.Treiber [M. Treiber, A.Hennecke, D. Helbing, Phys. Rev. E 62 (2) (2000), 1805-1824]. In a circular one lane traffic system which includes homogeneous drivers, we obtain the stable condition of homogenous flow and the phase diagram of traffic flow based on the linearization analysis. The phase diagram shows three possible pathways of phase transition along with the increase of global density: from the homogenous free flow to the homogenous congested flow directly, from the homogenous free flow to the synchronized flow then to the homogenous congested flow, or from the homogenous free flow to synchronized flow then to the wide-moving jam flow. The paper also analyzes the traffic flow including heterogenous drivers, and the results indicate that homogenous congested flow will lose its stability when the proportion of impatient drivers reaches a critical value and some new kinds of traffic flow emerge: wide-moving jam flow or a mixture of synchronized flow and wide-moving jam flow.     

A modified NaSch model with density-dependent randomization for traffic flow

Based on the Nagel-Schreckenberg (NaSch) model of traffic flow, a modified cellular automaton (CA) traffic model with the density-dependent randomization (abbreviated as the DDR model) is proposed to simulate traffic flow. The fundamental diagram obtained by simulation shows the ability of this modified NaSch model to capture the essential features of traffic flow, e.g., synchronized flow, metastable state, hysteresis and phase separation at higher densities. Comparisons are made between this DDR model and the NaSch model, also between this DDR model and the VDR model. And the underlying mechanism is analyzed. All these results indicate that the presented model is reasonable and more realistic.     

A traffic flow cellular automaton model to considering drivers’ learning and forgetting behaviour

It is known that the commonly used NaSch cellular automaton (CA) model and its modifications can help explain the internal causes of the macro phenomena of traffic flow.However,the randomization probability of vehicle velocity used in these models is assumed to be an exogenous constant or a conditional constant,which cannot reflect the learning and forgetting behaviour of drivers with historical experiences.This paper further modifies the NaSch model by enabling the randomization probability to be adjusted on the bases of drivers’ memory.The Markov properties of this modified model are discussed.Analytical and simulation results show that the traffic fundamental diagrams can be indeed improved when considering drivers’ intelligent behaviour.Some new features of traffic are revealed by differently combining the model parameters representing learning and forgetting behaviour.     

考虑车与车互联通讯技术的交通流跟驰模型

基于Newell跟驰模型,建立考虑车与车互联(vehicle-to-vehicle,V2V)通讯技术的单车道跟驰模型.根据V2V技术的特征,引入参数α以表征驾驶员在收到V2V技术所提供的实时交通信息后的提前反应程度.根据线性稳定分析方法,得到V2V跟驰模型的中性稳定条件.通过计算机的模拟,研究V2V技术对交通流运行的影响,分析小扰动下V2V跟驰模型对参数变化的敏感性,研究不同α取值下交通流密度波及迟滞回环的变化.研究发现:1)与全速度差跟驰模型相比,在引入V2V后,交通流在加速起步、减速刹车及遇到突发事件时,车辆运行的安全性和舒适性均得到不同程度的提升;2)V2V跟驰模型对参数α及T的变化较为敏感,且在交通流较为拥堵时,V2V技术的引入可以提升交通流的平均速度;3)参数α的增大、T的减小可以有效提升V2V跟驰模型在不同交通环境下的运行稳定性.由于可以实时地获取交通流运行的状态并针对性地改变车辆自身的运行,V2V交通流跟驰模型提升了交通流运行的稳定性.     

Cellular automata model for traffic flow with safe driving conditions

In this paper, a recently introduced cellular automata （CA） model is used for a statistical analysis of the inner micro-scopic structure of synchronized traffic flow. The analysis focuses on the formation and dissolution of clusters or platoons of vehicles, as the mechanism that causes the presence of this synchronized traffic state with a high flow. This platoon formation is one of the most interesting phenomena observed in traffic flows and plays an important role both in manual and automated highway systems （AHS）. Simulation results, obtained from a single-lane system under periodic boundary conditions indicate that in the density region where the synchronized state is observed, most vehicles travel together in pla- toons with approximately the same speed and small spatial distances. The examination of velocity variations and individual vehicle gaps shows that the flow corresponding to the synchronized state is stable, safe and highly correlated. Moreover, results indicate that the observed platoon formation in real traffic is reproduced in simulations by the relation between vehicle headway and velocity that is embedded in the dynamics definition of the CA model.     

考虑驾驶员特性的一维元胞自动机交通流模型

在一维元胞自动机交通流WWH模型和SDNaSch模型的基础上,建立了一种考虑驾驶员特性的元胞自动机交通流模型(Driver-SDNaSch模型).该模型将驾驶员分为激进型、保守型和中立型三类,根据其不同的驾驶特性制定了各自的演化规则,并以此对其进行状态更新;同时考虑了前车速度为0的情况,引入安全减速概率.通过计算机对Driver-SDNaSch模型进行模拟,给出了由三类驾驶员按不同比例组成的混合交通流的速度-密度图和流量-密度图,并对此类混合交通流的特性进行了分析和讨论.与NaSch模型和SDNaSch模 关键词： 交通流 元胞自动机 驾驶员特性 计算机数值模拟     

An improved cellular automaton model considering the effect of traffic lights and driving behaviour

This paper proposes an improved cellular automaton model to describe the urban traffic flow with the consideration of traffic light and driving behaviour effects. Based on the model,the characteristics of the urban traffic flow on a single-lane road are investigated under three different control strategies,i.e.,the synchronized,the green wave and the random strategies. The fundamental diagrams and time-space patterns of the traffic flows are provided for these strategies respectively. It finds that the dynamical transition to the congested flow appears when the vehicle density is higher than a critical level. The saturated flow is less dependent on the cycle time and the strategies of the traffic light control,while the critical vehicle density varies with the cycle time and the strategies. Simulated results indicate that the green wave strategy is proven to be the most effective one among the above three control strategies.     

The effect of stochastic accelerating and delay probability with the velocity and the gap between vehicles on traffic flow

This paper proposes a new combined cellular automaton (CA) model considering the driver behavior of stochastic acceleration and delay with the velocity of the preceding vehicle and the gap between the successive vehicles based on the WWH model and the noise-first NaSch model. It introduces the delay probability varying with the gap, adds the anticipation headway and increases the acceleration with a certain probability. Through these simulations, not only can the metastable state and start--stop wave be obtained but also the synchronized flow which the wide moving jam results in. Moreover, the effect of stochastic acceleration and delay on traffic flow is discussed by analyzing the correlation of traffic data. This indicates that synchronized flow easily emerges in the critical area between free flow and synchronized flow when acceleration and delay are synchronized or their probability is close to 0.5.