Multifractal chaotic attractors in a system of delay-differential equations modeling road traffic

We study a system of delay-differential equations modeling single-lane road traffic. The cars move in a closed circuit and the system's variables are each car's velocity and the distance to the car ahead. For low and high values of traffic density the system has a stable equilibrium solution, corresponding to the uniform flow. Gradually decreasing the density from high to intermediate values we observe a sequence of supercritical Hopf bifurcations forming multistable limit cycles, corresponding to flow regimes with periodically moving traffic jams. Using an asymptotic technique we find approximately small limit cycles born at Hopf bifurcations and numerically preform their global continuations with decreasing density. For sufficiently large delay the system passes to chaos following the Ruelle-Takens-Newhouse scenario (limit cycles-two-tori-three-tori-chaotic attractors). We find that chaotic and nonchaotic attractors coexist for the same parameter values and that chaotic attractors have a broad multifractal spectrum. (c) 2002 American Institute of Physics.     

Study of the Arc and of the Interaction between Arc and Operating Mechanism in SF6 Puffer Breakers

The article deals with studies of the arcing performance of SF6 puffer breakers at currents of up to 80 kA and voltages of up to 200 kV, using an interrupter unit fitted with viewing windows. The studies are mainly concerned with the behavior of the arc at current zero and with restrike phenomena under various conditions. In addition to measurements of the electrical variables and the pressure variation, the tests cover the use of high-speed cameras, spectroscopic diagnostic methods, and schlieren methods. The density fields and flow fields derived from the latter are used to optimize the gas flow. On the basis of the breaker data and those of its operating mechanism a method for computing the essential variables, e.g., pressure, gas flow, back pressure, and contact travel, is developed. The variation of these parameters as a function of the interrupter data for various currents and with due allowance for the interaction between the arc and the operating mechanism must be known if the breaker design is to be optimized. The method uses simplified equations for the gas flow and the arc. The relationship between the gas data (e. g., density, enthalpy, speed of sound, electrical conductivity, and dielectric strength) and the temperature is taken into account by using approximation functions. The temperature of the arc core is matched to the test results.     

速度限制对交通流的影响

运用元胞自动机模型研究单车道路面上设立限速区对交通流的影响.计算机模拟结果显示,在交通流与密度的基本图中存在饱和交通流量,其大小取决于限速区的最大速度.限速区的设立导致不同相的分离.在确定性的模型中,当车辆密度较低时,存在两种不同的自由流相;而当车辆密度较高时,出现最大交通流相和自由流相.在随机模型中,车辆密度较高时,出现最大交通流相-堵塞相-自由流.对交通流以及临界密度等量给出一些解析结果.     

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.     

Jam formation in traffic flow on a highway with some slowdown sections

We study the traffic jams appearing on a single-lane highway with a few slowdown sections. At low density, the flow (current) increases linearly with density, while it saturates at some values of intermediate density. In such case that some slowdown sections have the same speed limit, when the flow begins to saturate, a single discontinuous front (stationary shock wave) occurs before a slowdown section or some discontinuous fronts appear before some slowdown sections. For the case of different speed limits, the discontinuous front occurs before the section of strongest slowdown. The saturated flow is given by the maximal value of the current of the strongest slowdown section. The relationship between the densities is derived before and after the discontinuity. The dependence of jam lengths on density is derived numerically and analytically.     

Biham–Middleton–Levine model with four-directional traffic

We study the four-directional traffic flow on a two-dimensional lattice. In the case of discrete densities, we assume equal number of vehicles in each lane. Except for the minimum density, the gridlock emerges swiftly. Two kinds of gridlock have been observed. The global gridlock dominates the system when the density is twice the minimum value. At higher densities, the system is pervaded by local gridlocks. We also analyze the time evolution of average speed. In the case of continuous densities, the vehicle numbers vary from lane to lane. The global gridlock is then destroyed by the fluctuations; while the local gridlock can still be observed.     

Perturbed Arcs in Turbulent Axial Gas Flow IV. Thermal Reignition Experiments

By means of the short-circuiting of electric arcs burning in turbulent axial gas coolant flow and their reaction on a (recovering) voltage ramp the reignition in circuit breakers is modelled. Strong stochasticity of thermal reignition is demonstrated even under relatively weak conditions. Channels or nozzles showing flow detachment are further deteriorated by that. Corresponding low-current test experiments are recommended for in-scale circuit breaker development tests.     

A macro traffic flow model accounting for road capacity and reliability analysis

Based on existing traffic flow models, in this paper we develop a macro traffic flow model taking into consideration road capacity to study the impact of the road capacity on traffic flow. The numerical results show that the road capacity destroys the stability of uniform flow and produces stop-and-go traffic under a moderate density and that the road capacity enhances the traffic risk coefficient and reduces the traffic system’s reliability. In addition, the numerical results show that properly improving the road condition can enhance the road capacity, reduce the traffic risk coefficient and enhance the traffic system’s reliability.     

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.     

交叉口进口道换道行为研究及建模

为了对信号交叉口上游车辆换道行为进行分析,以元胞自动机交通流理论为基础,结合自由换道模型及强制换道模型提出了进口道附近路段的综合换道模型,并对原有强制换道模型进行改进.通过对综合换道模型进行模拟,得出进口道附近交通流的时空关系及密度关系图.模拟结果表明,车流密度在[0,0.2]及[0.4,0.6]范围时,进口道换道率变化率较高;同时在中低密度下,随着换道率的增加,平均车速逐渐降低,但在高密度下,车速随换道率变化并不显著.     

基于安全驾驶的元胞自动机交通流模型

针对Nagel-Schreckenberg模型(NaSch模型)中存在的高速车辆可能发生追尾事故的不安全性，考虑了前车速度为零的情况，提出一种新的强调驾驶安全性的一维元胞自动机交通流模型：安全驾驶模型，并对该模型进行了数值模拟.由于安全概率的引入，使得系统在临界密度附近出现低速的同步相，而不是完全的堵塞相，减小了追尾事故发生的可能性，提高了高密度时道路的通行能力.模拟结果显示出了亚稳态、非平衡相变以及滞后效应等实际交通所具有的特性. 关键词： 交通流 安全驾驶 元胞自动机 同步流     

Phase diagram of speed gradient model with an on-ramp

In this paper, phase transitions are investigated in speed gradient model with an on-ramp. Phase diagrams of traffic flow composed of manually driven vehicles and adaptive cruise control (ACC) vehicles are studied, respectively. The traffic flow composed of ACC vehicles is modeled by enhancing propagation speed of small disturbance. The phase diagram of traffic flow composed of manually driven vehicles is similar to that in previous works, in which such states as pinned localized cluster (PLC), moving localized cluster (MLC), triggered stop-and-go traffic (TSG), oscillatory congested traffic (OCT), and homogeneous congested traffic (HCT) are reproduced. In the phase diagram of traffic flow composed of ACC vehicles, traffic stability is enhanced and such states as PLC, MLC, and TSG disappear. Furthermore, some interesting phenomena, such as stationary OCT upstream of on-ramp and appearance of second OCT in HCT, are identified.     

决定论性逐步加速交通流模型的渐近稳态行为

研究Nagel-Schreckenberg(NS)交通流元胞自动机模型在不考虑车辆随机延迟情况下的决定论性模型的基本图,即渐近稳态的车流平均速度作为车辆密度的函数关系．证明决定论性NS模型,在车流的自组织作用下,其渐近稳态的基本图,与决定论性Fukui-Ishibashi(FI)交通流模型的基本图完全相同．这个结果表明,若把FI交通流模型中的车辆突然加速方式（即车辆速度可以在仅仅一个时步内加速到其最高速限M或前方空距所允许的最大速度）,改变为车辆逐步加速方式（车辆速度在每一时步中最多仅能增加一个速度单位）,则车辆的自组织相互作用,并不会改变其车流的长时间渐近稳态行为． 关键词：     

Two-dimensional city traffic model with periodically placed blocks

A new two-dimensional cellular automaton traffic model is proposed, where blocks are placed periodically. The present model includes the model of two crossing roads in the limit of maximum sized blocks and the BML model in the limit of zero sized blocks. New phases of traffic flow appear between the free flow phase and the jam phase in the BML model. The boundaries between these phases come closer as the size of the block decreases and converge into one phase boundary at a density around 0.19, which is in fair agreement with the critical density in the BML model.     

Impact of the Next-Nearest-Neighbor Interaction on Traffic Flow of Highway with Slopes

In this paper,we study the motion course of traffic flow on the slopes of a highway by applying a microscopic traffic model,which takes into account the next-nearest-neighbor interaction in an intelligent transportation system environment.Three common gradients of the highway,which are sag terrain,uphill terrain,and downhill terrain on a single-lane roadway,are selected to clarify the impact on the traffic flow by the next-nearest-neighbor interaction in relative velocity.We obtain the current-density relation for traffic flow on the sag,the uphill and the downhill under the next-nearest-neighbor interaction strategy.It is observed that the current saturates when the density is greater than a critical value and the current decreases when the density is greater than another critical value.When the density falls into the intermediate range between the two critical densities it is also found that the oscillatory jam,easily leads to traffic accidents,often appears in the downhill stage,and the next-nearest-neighbor interaction in relative velocity has a strong suppressing effect on this kind of dangerous congestion.A theoretical analysis is also presented to explain this important conclusion.     

A cellular automata model for urban traffic with multiple roundabouts

Urban transportation with multiple roundabouts is facing significant challenges such as traffic congestion, gridlock and traffic accidents. In order to understand these behaviors, we propose a two-dimensional cellular automata (CA) model, where all streets are two-way, with one lane in each direction. To allow the turning movement, a roundabout is designed for each intersection where four roads meet. The distance between each pair of roundabouts is configured with the parameter K while the turning behavior of drivers is modeled by a parameter γ. To study the impact of these different parameters on the urban traffic, several traffic metrics are considered such as traffic flow, average velocity, accident probability and waiting time at the entrance of roundabout. Our simulation results show that the urban traffic is in free flow state when the vehicle’s density is low enough. However, when the density exceeds a critical density ρ_c, the urban traffic will be in gridlock state whenever γ is nonzero. In the case where $\gamma =0,$ the urban traffic presents a phase transition between free flow and congested state. Furthermore, detailed analysis of the traffic metrics shows that the model parameters (γ, K) have a significant effects on urban traffic dynamics.     

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     

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.