A Cellular Automaton Model for Two-Lane Traffic

We present some long time limit properties of a cellular automaton that models traffic of cars on a (infinite) two-lane road. This model, called TL184, is a natural generalization of the cellular automaton classified as 184 by Wolfram (to be abbreviated by CA184) and studied before as a model for one-lane traffic. TL184 models cars' motions on each lane by particles that interact via the CA184 rules, and cars' lane changes by a possibility for particles to flip from one CA184 to another. We calculate the infinite-time limit of the particle current in TL184, starting from a translation invariant measure, and use this result to show how the possibility of lane changes may enhance the current of cars in TL184 compared to that in a corresponding model of two non-interacting one-lane roads. We provide examples which demonstrate that even though the rules that regulate lane changes are completely symmetric, the system does not evolve to an equipartition of cars among both lanes from a given initially asymmetric distribution; moreover, the asymptotic car velocities and currents may be different on different lanes. We also show that, for a particular class of initial distributions, the asymptotic car density on a lane may be a non-monotonic function of the initial car density on this lane. Finally, we derive the current-density relation for an extended continuous-time version of TL184 with asymmetric lane-changing rules.     

考虑行车状态的一维元胞自动机交通流模型

在Nagel Schrekenberg单车道元胞自动机交通流模型（简称NS模型）的基础上，考虑车辆之间的相对运动薛郁等提出了一种改进的单车道元胞自动机交通流模型（简称改进的NS模型）.通过两种情况列出了改进的NS模型存在不尽周严的地方，随之在新模型中引入了行车状态 变量和反馈规则，从而控制车辆出现倒车和刹车过急等现象.通过计算机对新模型进行模拟 ，发现减速概率和车流密度对车流状态的演化影响很大，当减速概率高（如道路条件差）时 ，即使车流密度低，车流也会出现局部堵塞状态；而当减速概率一定时，随着车流密度增加 ，车流的运动相与堵塞相发生了全局性的交替出现，此时类似于波的波峰和波谷的传播.与 改进的NS模型相比较，新模型模拟的车流量较高，说明新模型减少了车流的总体停滞状态. 关键词： 交通流 元胞自动机 行车状态 反馈规则     

The Stability of Multi-modal Traffic Network

There is an explicit and implicit assumption in multimodal traffic equilibrium models, that is, if the equilibrium exists, then it will also occur. The assumption is very idealized; in fact, it may be shown that the quite contrary could happen, because in multimodal traffic network, especially in mixed traffic conditions the interaction among traffic modes is asymmetric and the asymmetric interaction may result in the instability of traffic system. In this paper, to study the stability of multimodal traffic system, we respectively present the travel cost function in mixed traffic conditions and in traffic network with dedicated bus lanes. Based on a day-to-day dynamical model, we study the evolution of daily route choice of travelers in multimodal traffic network using 10000 random initial values for different cases. From the results of simulation, it can be concluded that the asymmetric interaction between the cars and buses in mixed traffic conditions can lead the traffic system to instability when traffic demand is larger. We also study the effect of travelers' perception error on the stability of multimodal traffic network. Although the larger perception error can alleviate the effect of interaction between cars and buses and improve the stability of traffic system in mixed traffic conditions, the traffic system also become instable when the traffic demand is larger than a number. For all cases simulated in this study, with the same parameters, traffic system with dedicated bus lane has better stability for traffic demand than that in mixed traffic conditions. We also find that the network with dedicated bus lane has higher portion of travelers by bus than it of mixed traffic network. So it can be concluded that building dedicated bus lane can improve the stability of traffic system and attract more travelers to choose bus reducing the traffic congestion.     

The Stability of Multi-modal Traffic Network

There is an explicit and implicit assumption in multimodal traffic equilibrium models, that is, if the equilibrium exists, then it will also occur. The assumption is very idealized; in fact, it may be shown that the quite contrary could happen, because in multimodal traffic network, especially in mixed traffic conditions the interaction among traffic modes is asymmetric and the asymmetric interaction may result in the instability of traffic system. In this paper, to study the stability of multimodal traffic system, we respectively present the travel cost function in mixed traffic conditions and in traffic network with dedicated bus lanes. Based on a day-to-day dynamical model, we study the evolution of daily route choice of travelers in multimodal traffic network using 10000 random initial values for different cases. From the results of simulation, it can be concluded that the asymmetric interaction between the cars and buses in mixed traffic conditions can lead the traffic system to instability when traffic demand is larger. We also study the effect of travelers' perception error on the stability of multimodal traffic network. Although the larger perception error can alleviate the effect of interaction between cars and buses and improve the stability of traffic system in mixed traffic conditions, the traffic system also become instable when the traffic demand is larger than a number. For all cases simulated in this study, with the same parameters, traffic system with dedicated bus lane has better stability for traffic demand than that in mixed traffic conditions. We also find that the network with dedicated bus lane has higher portion of travelers by bus than it of mixed traffic network. So it can be concluded that building dedicated bus lane can improve the stability of traffic system and attract more travelers to choose bus reducing the traffic congestion.     

Effect of driver over-acceleration on traffic breakdown in three-phase cellular automaton traffic flow models

Based on simulations with cellular automaton (CA) traffic flow models, a generic physical feature of the three-phase models studied in the paper is disclosed. The generic feature is a discontinuous character of driver over-acceleration caused by a combination of two qualitatively different mechanisms of over-acceleration: (i) Over-acceleration through lane changing to a faster lane, (ii) over-acceleration occurring in car-following without lane changing. Based on this generic feature a new three-phase CA traffic flow model is developed. This CA model explains the set of the fundamental empirical features of traffic breakdown in real heterogeneous traffic flow consisting of passenger vehicles and trucks. The model simulates also quantitative traffic pattern characteristics as measured in real heterogeneous flow.     

Instability control in two dimensional traffic flow model

Chaos control in two dimensional traffic flow model taking into account the effect of overpasses, asymmetric distribution of cars and blockage of cars moving in the same direction is performed using parameter change method for discrete dynamical systems.     

Vehicular motion in counter traffic flow through a series of signals controlled by a phase shift

We study the dynamical behavior of counter traffic flow through a sequence of signals (traffic lights) controlled by a phase shift. There are two lanes for the counter traffic flow: the first lane is for east-bound vehicles and the second lane is for west-bound vehicles. The green-wave strategy is studied in the counter traffic flow where the phase shift of signals in the second lane has opposite sign to that in the first lane. A nonlinear dynamic model of the vehicular motion is presented by nonlinear maps at a low density. There is a distinct difference between the traffic flow in the first lane and that in the second lane. The counter traffic flow exhibits very complex behavior on varying the cycle time, the phase difference, and the split. Also, the fundamental diagram is derived by the use of the cellular automaton (CA) model. The dependence of east-bound and west-bound vehicles on cycle time, phase difference, and density is clarified.     

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.     

Cellular automata simulation of traffic including cars and bicycles

As ‘greening’ of all aspects of human activity becomes mainstream, transportation science is also increasingly focused around sustainability. Modal co-existence between motorised and non-motorised traffic on urban networks is, in this context, of particular interest for traffic flow modelling. The main modelling problems here are posed by the heterogeneity of vehicles, including size and dynamics, and by the complex interactions at intersections. Herein we address these with a novel technique, based on one-dimensional cellular automata components, for modelling network infrastructure and its occupancy by vehicles. We use this modelling approach, together with a corresponding vehicle behaviour model, to simulate combined car and bicycle traffic for two elemental scenarios—examples of components that would be used in the building of an arbitrary network. Results of simulations performed on these scenarios, (i) a stretch of road and (ii) an intersection causing conflict between cars and bicycles sharing a lane, are presented and analysed.     

Continuum modeling for two-lane traffic flow with consideration of the traffic interruption probability

Considering the effects that the probability of traffic interruption and the friction between two lanes have on the car-following behaviour,this paper establishes a new two-lane microscopic car-following model.Based on this microscopic model,a new macroscopic model was deduced by the relevance relation of microscopic and macroscopic scale parameters for the two-lane traffic flow.Terms related to lane change are added into the continuity equations and velocity dynamic equations to investigate the lane change rate.Numerical results verify that the proposed model can be efficiently used to reflect the effect of the probability of traffic interruption on the shock,rarefaction wave and lane change behaviour on two-lane freeways.The model has also been applied in reproducing some complex traffic phenomena caused by traffic accident interruption.     

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.     

瓶颈处车辆横纵向行为建模与分析

车辆的横向偏移现象在现实的交通流中广泛存在, 交通瓶颈处的横向偏移现象往往更加显著. 车辆间横纵向的运动相互干扰, 使得瓶颈交通流组织十分混乱, 通行能力受到显著影响. 为了研究瓶颈处车辆横纵向行为规律及其对交通流的影响, 提出一个考虑横向偏移特征的车辆行为模型: 通过引入目标转向角概念,并结合经典优化速度模型, 给出了用于描述车辆的横纵向运动规律的运动方程, 同时通过分析车辆横向偏移特征, 制定了基于车辆行驶状态划分的目标转向角确定规则集. 数值模拟结果表明: 车辆的横向偏移会对交通流的运行产生影响, 在一定的横向偏移反应阈值下, 瓶颈处横向干扰于交通流的影响随着密度的增加而增加; 同时观察到了实际城市交通瓶颈的宏观及微观现象, 验证了模型的有效性. 关键词： 交通流 瓶颈 车辆行为 横向偏移特征     

Simon-Gutowitz bidirectional traffic model revisited

The Simon-Gutowitz bidirectional traffic model [P.M. Simon, H.A. Gutowitz, Phys. Rev. E 57 (1998) 2441] is revisited in this Letter. We found that passing cars get stuck with oncoming cars before returning to their home lanes. This provokes the occurrence of wide jams on both lanes. We have rectified the rules for lane changing. Then, the wide jams disappear and the revisited model can describe well the realistic bidirectional traffic.     

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.     

A study on the effects of the transit parking time on traffic flow based on cellular automata theory

This paper mainly deals with the effects of transit stops on vehicle speeds and conversion lane numbers in a mixed traffic lane.Based on thorough research of traffic flow and cellular automata theory,it calibrates the cellular length and the running speed.Also,a cellular automata model for mixed traffic flow on a two-lane system under a periodic boundary condition is presented herewith,which also takes into consideration the harbour-shaped transit stop as well.By means of computer simulation,the article also studies the effects of bus parking time on the traffic volume,the transit speed and the fast lane speed at the same time.The results demonstrate that,with the increase of the bus parking time,the traffic volume of the transit stop and the transit speed decrease while the fast lane speed increases.This result could help calculate the transit delay correctly and make arrangements for transit routes reasonably and scientifically.     

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

In this paper, the viscous continuum traffic flow model for a single lane is extended to the traffic flow for two-lane freeways. The proposed model is a higher-order continuum model considering the coupling and lane changing effects of the vehicles on two adjacent lanes. It results from integrating the Taylor series expansion of the viscous continuum traffic flow model proposed by Ge (2006 Physica A 371 667) into the multi-lane model presented by Daganzo (1997 Transpn. Res. B 31 83). Our proposed model may be used to describe non-anisotropic behaviour because of lane changing in multi-lane traffic. A linear stability analysis is given and the neutral stability condition is obtained. Also, issues related to lane changing, shock waves and rarefaction waves, local clustering and phase transition are investigated through a simulation experiment. The simulation results show that the proposed model is capable of explaining some particular traffic phenomena commonly observable in real world traffic flow.     

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     

考虑驾驶方式改变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SDNS模型的基础上,建立了考虑驾驶方式改变的元胞自动机模型（Change-CA模型）.具体描述为驾驶员可根据交通环境选择不同的驾驶方式在道路上驾车行驶,以各自的演化规则进行状态更新,同时定义了驾驶方式更新原则.通过计算机数值模拟,发现驾驶方式可变时,模型模拟得到的混合交通流流量较大;保守型驾驶方式对交通流变化的影响随改变概率增大而减少.并且在演化过程中,驾驶方式改变频率的变化趋势与改变概率、安全概率密切相关.与NS模型和SDNS模型相比,Change-CA模型减少了车流 关键词： 交通流 元胞自动机 驾驶方式 计算机数值模拟     

A new traffic model with the consideration of coupling effect with two lanes

This paper introduces a new two-lane high-order continuum model by embedding the two delay time scales continuum traffic model presented by Xue (2003 Phys. Rev. E 68 066123) into the multi-lane model proposed by Daganzo (1997 Transpn. Res. B 31 83) with the consideration of the coupling effect between the vehicles of two lanes in instantaneous traffic situation and lane-change effect. In the novel model, the coupling effect of two lanes and phenomena of lane change, which were not discussed in Daganzo's model and Xue's model, are taken into account. Numerical simulation shows that it is in accordance with real traffic flow. This obviously indicates that the new phenomenon and behaviour are analogous results as single lane presented by Xue, and the proposed model is more reasonable on two lanes. Furthermore, the generation rate between two lanes is also investigated. The results show that the formation and diffusion of traffic shock wave can be better simulated on two lanes.     

Analysis of the influence of occupation rate of public transit vehicles on mixing traffic flow in a two-lane system

Based on the existing classical cellular automaton model of traffic flow, a cellular automaton traffic model with different-maximum-speed vehicles mixed on a single lane is proposed, in which public transit and harbour-shaped bus stops are taken into consideration. Parameters such as length of cellular automaton, operation speed and random slow mechanism are re-demarcated. A harbour-shaped bus stop is set up and the vehicle changing lane regulation is changed. Through computer simulation, the influence of occupation rate of public transit vehicles on mixed traffic flow and traffic capacity is analysed. The results show that a public transport system can ease urban traffic congestion but creates new jams at the same time, and that the influence of occupation rate of public transit vehicles on traffic capacity is considerable. To develop urban traffic, attention should be paid to the occupation rate of public transit vehicles and traffic development in a haphazard way should be strictly avoided.