Dynamics of traffic networks: From microscopic and macroscopic perspectives

Considering the microscopic characteristics (vehicle speed, road length etc.) of links and macroscopic behaviors of traffic systems, we derive the critical flow generation rate in scale-free networks. And the dynamics of traffic congestion is studied numerically in this paper. It is shown that the queue length increases with microscopic characteristics of links. Additionally, the critical flow generation rate decreases with increase of the network size N, maximum speed v_max and parameter τ. The significance of this finding is that, in order to improve the traffic environment, both the local information for the single link and behaviors of the whole network must be analyzed simultaneously in a traffic system design.     

On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models

Daganzo’s criticisms of second-order fluid approximations of traffic flow [C. Daganzo, Transpn. Res. B. 29, 277 (1995)] and Aw and Rascle’s proposal how to overcome them [A. Aw, M. Rascle, SIAM J. Appl. Math. 60, 916 (2000)] have stimulated an intensive scientific activity in the field of traffic modeling. Here, we will revisit their arguments and the interpretations behind them. We will start by analyzing the linear stability of traffic models, which is a widely established approach to study the ability of traffic models to describe emergent traffic jams. Besides deriving a collection of useful formulas for stability analyses, the main attention is put on the characteristic speeds, which are related to the group velocities of the linearized model equations. Most macroscopic traffic models with a dynamic velocity equation appear to predict two characteristic speeds, one of which is faster than the average velocity. This has been claimed to constitute a theoretical inconsistency. We will carefully discuss arguments for and against this view. In particular, we will shed some new light on the problem by comparing Payne’s macroscopic traffic model with the Aw-Rascle model and macroscopic with microscopic traffic models.     

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.     

道路交通的流体物理模型与粒子仿真方法

针对受多种因素影响的复杂道路交通系统问题,基于颗粒动力学理论,结合传统的Lighthill-WhithamRichards物理模型,建立道路交通系统的流体物理模型,采用无网格粒子与网格相结合的方法进行数值仿真,并应用于典型道路交通问题的求解.在新模型中,将车辆比拟为硬颗粒,车辆的跟车比拟为颗粒间的碰撞相互作用,已知道路情况对驾驶员操作车辆的影响比拟为流-粒两相系统中的外部流体驱动力作用,不同车道间车辆的影响比拟为颗粒间的黏性作用,从而在颗粒动力学理论的基础上,推导建立了道路交通系统拟流体模型;引入光滑离散颗粒流体动力学(SDPH)对车辆系统模型进行离散,建立"SDPH车辆"与真实车辆之间的一一对应关系,再结合有限体积方法,对道路交通构建的双流体模型进行求解,建立求解交通流体物理模型的新型仿真方法.最后,采用所建立的模型和方法对车辆汇入以及机非混合对交通系统的影响过程进行了数值仿真,所得结果与实测值符合较好,表明新的模型和方法有效性好、可靠性高,为道路交通问题的解决提供了一条全新的途径.     

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.     

A quantum mechanics-based approach to model incident-induced dynamic driver behavior

A better understanding of the psychological factors influencing drivers, and the resulting driving behavior responding to incident-induced lane traffic phenomena while passing by an incident site is vital to the improvement of road safety. This paper presents a microscopic driver behavior model to explain the dynamics of the instantaneous driver decision process under lane-blocking incidents on adjacent lanes. The proposed conceptual framework decomposes the corresponding driver decision process into three sequential phases: (1) initial stimulus, (2) glancing-around car-following, and (3) incident-induced driving behavior. The theorem of quantum mechanics in optical flows is applied in the first phase to explain the motion-related perceptual phenomena while vehicles approach the incident site in adjacent lanes, followed by the incorporation of the effect of quantum optical flows in modeling the induced glancing-around car-following behavior in the second phase. Then, an incident-induced driving behavior model is formulated to reproduce the dynamics of driver behavior conducted in the process of passing by an incident site in the adjacent lanes. Numerical results of model tests using video-based incident data indicate the validity of the proposed traffic behavior model in analyzing the incident-induced lane traffic phenomena. It is also expected that such a proposed quantum-mechanics based methodology can throw more light if applied to driver psychology and response in anomalous traffic environments in order to improve road safety.     

宏观交通流模型的能耗研究

本文在几种典型的宏观交通流模型的基础上,导出能量耗散的计算公式,宏观交通流模型能耗不同于元胞自动机交通模型,其能耗不仅考虑车流速度减少,而且还要计及通过路段的车流通量引起的能耗.通过对满足黎曼初始条件的道路能耗和道路交通瓶颈处能耗的计算和理论分析,表明交通拥堵处,能量耗散比较高,而且能量耗散的变化也能反映交通拥堵产生及消散的情况.     

Density viscous continuum traffic flow model

A new traffic flow model called density viscous continuum model is developed to describe traffic more reasonably. The two delay time scales are taken into consideration, differing from the model proposed by Xue and Dai [Phys. Rev. E 68 (2003) 066123]. Moreover the relative density is added to the motion equation from which the viscous term can be derived, so we obtain the macroscopic continuum model from microscopic car following model successfully. The condition for stable traffic flow is derived. Nonlinear analysis shows that the density fluctuation in traffic flow induces density waves. Near the onset of instability, a small disturbance could lead to solitons determined by the Korteweg-de-Vries (KdV) equation, and the soliton solution is derived. The results show that local cluster effects can be obtained from the new model and are consistent with the diverse nonlinear dynamical phenomena observed in the freeway traffic.     

A two-channel model for transport across high T c bicrystal grain boundary junctions

This paper describes an investigation of the microscopic configuration of the barrier which exists at the boundary in high T _c grain boundary junctions. A model for describing the properties of bicrystal and biepitaxial grain boundary junctions is proposed. Two channels for transport currents are assumed, the supercurrent being carrier by one channel only. The measurable macroscopic parameters of a junction, (critical current density and normal state resistance) are computed in terms of the microscopic parameters that appear in this model. The model well describes major features of the characteristics observed for high T _c bicrystal junctions.     

The Korteweg-de Vries soliton in the lattice hydrodynamic model

The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but is also closely connected with the microscopic car following model. The modified Korteweg-de Vries (mKdV) equation about the density wave in congested traffic has been derived near the critical point since Nagatani first proposed it. But the Korteweg-de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail in the car following model. So we devote ourselves to obtaining the KdV equation from the lattice hydrodynamic model and obtaining the KdV soliton solution describing the traffic jam. Numerical simulation is conducted, to demonstrate the nonlinear analysis result.     

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.     

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     

Multiscale analysis of a spatially heterogeneous microscopic traffic model

The microscopic Optimal Velocity (OV) model is posed on an inhomogeneous ring-road, consisting of two spatial regimes which differ by a scaled OV function. Parameters are chosen throughout for which all uniform flows are linearly stable. The large time behaviour of this discrete system is stationary and exhibits three types of macroscopic traffic pattern, each consisting of plateaus joined together by sharp interfaces. At a coarse level, these patterns are determined by simple flow and density balances, which in some cases have non-unique solutions. The theory of characteristics for the classical Lighthill-Whitham PDE model is then applied to explain which pattern the OV model selects. A global analysis of a second-order PDE model is then performed in an attempt to explain some qualitative details of interface structure. Finally, the full microscopic model is analysed at the linear level to explain features which cannot be described by the present macroscopic approaches.     

考虑信号灯影响的交通流模型与数值模拟

基于信号灯交通系统中跟车行为的特点,改进了现有跟车方程,提出一个考虑信号影响的交通流模型.数值计算结果表明,该模型可以很好地再现车流的聚集与消散、停车波和启动波的演化规律及传播特性,证明模型是合理有效的. 关键词： 交通流模型 信号灯 停车波 启动波     

考虑自适应巡航车辆影响的上匝道系统混合交通流模型

在考虑自适应巡航(adaptive cruise control, ACC)车辆的交通流模型的基础上, 建立了考虑ACC车辆影响的上匝道系统混合交通流模型, 研究ACC车辆引入对上匝道交通系统交通流的影响. 为了描述ACC车辆和手动驾驶车辆在交通流运行中的差异, 分别构建了基于常车头时距原则的ACC 车辆跟驰子模型和手动驾驶车辆MCD元胞自动机子模型; 基于上匝道车辆合流驶入主线的需求, 建立了换道子模型, 引入了表征驾驶员换道心理的参数λ. 通过对混合交通流模型进行数值模拟发现, ACC车辆的混入可以有效改善上匝道系统交通流的运行, 降低合流等事件对于交通流运行的影响, 抑制交通拥堵的时空范围及拥堵强度, 提高交通流的平均速度和流量. 此外在混合交通流模型中, ACC车辆期望车头时距H_d的减小与换道心理参数λ 的增大均可以提高混合交通流运行的速度和流量, 而合流区长度l_w对混合交通流影响则因上匝道车辆驶入概率的不同而存在差异.     

信号灯控制下的主道双车道入匝道系统交通流特性研究

采用元胞自动机模型研究了具有信号灯控制的主道为双车道的入匝道系统交通流特性.将信号灯设置在入匝道口处,通过信号灯来引导主道和匝道上的车辆通行.分析了信号灯控制对主道与匝道的车流量、系统通行能力以及入匝道口处的车流平均速度的影响.通过相图比较,说明信号灯控制的双车道入匝道系统能模拟出比信号灯控制的单车道入匝道系统更加符合实际的交通流特性.与姜锐提出的模型［Jiang R 2003 J. Phys. A 36 11713］结果相比,信号灯控制下的匝道系统的交通流状态得到改善并且道路通行能力有所提 关键词： 交通流 元胞自动机 入匝道系统 信号灯     

弯道交通流跟驰建模与稳定性分析

为发现弯道道路条件下交通流的演化特性及稳定条件,在全速度差最优模型的基础上,研究了弯道情况下的交通流跟驰模型表达式,并以状态空间法和控制系统的稳定性判据对其进行了稳定性分析,得到弯道情况下交通流的稳定条件,最后进行了数值模拟,验证了模型稳定条件的正确性.研究结果表明在相同的初始交通流密度情况下,弯道道路随着道路弧度的增大,交通流稳定性逐渐降低.     

双车道元胞自动机NS和WWH交通流混合模型的研究

考虑不同车辆的驾驶员有不同的驾驶方式和习惯，具体表现为不同的驾驶员采用适合自己行车特点的交通流模型在道路上驾车行驶，在一维元胞自动机交通流NS模型和WWH模型的基础上，建立了双车道元胞自动机NS和WWH交通流混合模型. 通过计算机模拟，给出了混合比例系数f_NS对混合交通流的速度-密度和流量-密度图以及车辆转道频率影响的结果. 关键词： 双车道 元胞自动机 混合交通流模型 计算机数值模拟     

Thermal Fields as Causal Fluids

In a previous paper we investigated a divergence-type theory (DDT) describing the dissipative interaction between a field and a fluid. In this paper we compare the macroscopic view of DDT with a microscopic special case, an O(N) scalar field to leading order in the large N approximation and its thermal fluctuations. Our aim is to compare within a simple model the two approaches.     

The theoretical analysis of the lattice hydrodynamic models for traffic flow theory

The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but also connected with the microscopic car following model closely. The modified Korteweg-de Vries (mKdV) equation related to the density wave in a congested traffic region has been derived near the critical point since Nagatani first proposed it. But the Korteweg-de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail for the car following model. We devote ourselves to obtaining the KdV equation from the original lattice hydrodynamic models and the KdV soliton solution to describe the traffic jam. Especially, we obtain the general soliton solution of the KdV equation and the mKdV equation. We review several lattice hydrodynamic models, which were proposed recently. We compare the modified models and carry out some analysis. Numerical simulations are conducted to demonstrate the nonlinear analysis results.