基于驾驶行为细致分析的交通流建模和模拟
|
摘要
交通科学基础研究的目的是建立交通流模型,通过分析和仿真,发现制约交通系统的基本规律和内在机理,用以指导交通工程实践。本文的工作旨在研究道路交通流理论的若干前沿性问题,在综合分析各种现有的交通流模型的基础上,提出更为符合实际的模型,并通过理论分析和数值模拟,探索交通系统中的各种非线性现象。全文的主要工作如下:
一.基于NaSch元胞自动机模型,考虑局部密度和司机的延迟反应对随机减速概率的影响,以及司机的个性特征和车辆密度对随机减速概率的影响,提出了两个改进的元胞自动机模型。
在NaSch元胞自动机交通流模型的基础上,考虑到车辆的随机减速概率不仅要受到车辆速度的影响,还要受到局部密度和司机延迟反应的影响,当车辆的局部密度较大时,随机减速概率会增大,反之则减小,为此提出了一个新的模型(简称为DDR模型),认为随机减速概率依赖于前一时刻的局部密度。数值模拟显示,该模型能够再现真实交通中的复杂现象,如时走时停交通、亚稳态和回滞现象,且得到的道路最大流量比NaSch模型更接近于实测值,更重要的是,当r≥7时,模型能够模拟出真实交通中的自由流、均匀流和宽幅运动阻塞。此外,通过考虑车辆密度和司机个人行为的差异对随机减速概率产生的影响,提出了另一个元胞自动机新模型,简称为IBDR模型。模型同样能够再现时走时停交通、亚稳态和回滞现象,也得到了比NaSch模型更接近于实测值的最大流量,同时发现司机的个性特征对最大流量的影响要比密度的影响更大一些,当道路上有一些比较谨慎的司机在驾驶车辆时,随机减速概率就大,道路的流量明显下降,这也从一个方面证明了设置快慢车道的必要性。本章提出的两个模型能部分地描述真实交通现象,可以为交通流理论的发展提供一定的参考。
二.在Chowdhury等人提出的双车道元胞自动机模型的基础上,通过数值模拟研究了存在事故车瓶颈时混合交通流的非线性动力学特性。
利用Chowdhury等人提出的双车道元胞自动机模型,对含有事故车交通瓶颈的混合交通流的特性进行了分析研究。通过数值模拟,得到了基本图和车辆的时空演化图,证实当道路上没有事故车瓶颈和其它瓶颈,慢车对交通流特性有很大的影响。当采用不同的换道规则以及事故车出现在不同的车道时,不同车道上的基本图呈现出不同的特点。在中低密度区,当右车道(慢车道)上存在事故车时,采用非对称换道规则比用对称性换道规则更易缓解本车道的拥堵,当左车道(快车道)上存在事故车时,则采用对称换道规则时本车道有较大的流量。从时空斑图上可以看到,事故车瓶颈不仅会引起本车道的交通拥堵,而且会对邻道的交通产生严重的影响。基本图中表现出来的特点与车辆的时空演化图中表现出来的拥堵特性较为吻合。同时发现,在混合交通情况下,或者道路上存在事故车瓶颈时,就会发生频繁的换道,而采用非对称性换道规则时的换道概率更是要大于采用对称性换道规则时的换道概率,当道路上的车辆都有相同的最大速度,又没有事故车时,车辆换道的概率最小。
三.提出了一个改进的跟驰模型,分别考虑司机的反应延迟与车辆的运动延迟,并研究了该模型在亚稳态区域和不稳定区域密度波的非线性特征。
基于Nagatani提出的差分形式的跟驰模型和Bando等人提出的优化速度函数,对单车道周期性边界条件下的交通流进行了数值模拟,再现了孤立波、扭结—反扭结波的时空演化图,得到了向后传播的密度波。再次论证了不管是周期性边界条件还是开放式边界条件,在中性稳定线附近总是出现孤立波,并且当初始车头间距小于安全间距时,孤立波呈现正立波型,反之,当初始车头间距大于安全间距时,孤立波呈现倒置波型。同时对扭结-反扭结波幅值的理论解和数值解进行了比较,发现幅值的变化趋势是相同的,即随着敏感度.a的增大而减小,并且当a＞2.3时,两者在数值上吻合也较好,而当a＜2.3时,数值解稍大于理论解。我们认为,差异的原因在于理论解在非线性分析时忽略了高阶小量。另外,数值模拟显示,交通流的最大流量随着安全间距的减小而增大。数值结果与解析解较为符合。
在上述模型的基础上,提出了一个改进的跟驰模型,把司机的反应延迟与车辆的运动延迟分开考虑,通过线性分析得到了该模型的中性稳定线和临界点,进一步通过摄动分析得到了KdV方程和mKdV方程,分别用来描述中性稳定线和临界点附近的交通现象。当司机的反应延迟与总的延迟时间具有不同的比例n时,给出了中性稳定线和共存曲线在车头间距—敏感度相图中的分布情况,并发现随着n值的增大,稳定区域缩小。这意味着当司机的敏感性越差,即司机反应延迟的时间越长,就越容易产生交通阻塞。数值模拟还给出了孤立波和扭结—反扭结波的时空演化图,它们都呈现向后传播的特性,同时随着n值的增大,扭结—反扭结波显得更密一些。结果表明司机的反应延迟在交通拥堵的形成过程中起着重要的作用,此延迟时间越长,越易造成交通阻塞。该模型从微观的角度揭示了交通拥堵形成的部分机理。
四.提出了一个考虑司机反应延迟的格子流体力学模型,并对模型进行了线性和非线性的理论分析。
在Nagatani提出的单车道格子流体力学模型的基础上,结合第四章的研究内容,提出了两个改进的格子流体力学模型(模型Ⅰ和模型Ⅱ),在模型中分别考虑司机的反应延迟与车辆的运动延迟。经由线性分析得到了模型的中性稳定曲线和临界点,采用摄动理论对临界点附近的交通流现象进行了非线性分析,得到了mKdV方程,当司机的反应延迟与总的延迟时间具有不同的比例n时,给出了中性稳定线和共存曲线在车头间距—敏感度相图中的分布情况。图中显示出模型Ⅰ的临界点、中性稳定曲线和共存曲线都低于模型Ⅱ的相应值,这一点与Nagatani的结论一致。在同一个模型中,随着司机反应延迟的增加,交通流的稳定区域不断缩小,这表明:当司机的反应延迟时间增加的时候,更容易产生交通拥堵,拥堵也更难以消散,这一结论与第四章的跟驰模型的结论一致。因此从宏观模型的角度再次表明,司机的反应延迟在交通拥堵的形成过程中起着重要的作用,延迟时间越长越易造成交通阻塞。同时也说明了格子流体力学模型能够发现交通中的本质现象,是一种有效的交通分析工具。
最后,对我国道路交通流的进一步研究做了分析和展望,并对今后的工作提出了初步的设想。
The aim of the fundamental research for traffic science is to find the basic regulations governing traffic systems through modeling, simulating and analyzing real traffic. In this dissertation, based on an overview of the existing models for traffic flows, several modified mathematical models of traffic flow in accordance with empirical observations are proposed. The theoretical analysis and numerical simulation are performed in order to explore the nonlinear phenomena in traffic systems.
This dissertation consists of the following four main parts:
Ⅰ. Based on the NaSch model of traffic flow, two novel cellular automaton traffic models are presented. One takes into account the effects of local density and the driver response delay on the randomization, and the other includes the effects of road density and drivers' individual behavior on the randomization.It is claimed that the randomization probability in the cellular automaton model is affected not only by the vehicle velocity, but also by the local density and drivers' delay in response. The randomization increases as the local density increases. Besides, a driver can usually sense the local density at previous time step and adjust the vehicle velocity at the present time step. So a modified NaSch model, i.e., the density dependent randomization model (abbreviated as the DDR model), is proposed, in which the randomization probability is assumed to depend on the local density at the preceding time step. The simulation results indicate that this model can reproduce the complicated behavior of real traffic, such as the stop and go traffic, metastable state and hysteresis. The fundamental diagram obtained by numerical simulation shows that the resulted road capacity is close to the empirical data compared with that by the NaSch model. And it is of greater importance that the DDR model can reproduce the free flow, the homogeneous flow and the traffic jam. Furthermore, another modified NaSch model, i.e., the individual behavior dependent randomization model (abbreviated as the IBDR model), is established by considering the effects of road density and the drivers' individual behavior on the randomization. The model can also reproduce the stop and go traffic, metastable state, the hysteresis and the larger value of maximum flow which is close to the observed data compared with that obtained from the NaSch model. Besides, it is found that the driving feature of the individual driver has more appreciable influence on the maximum traffic flow than density does. When there are some vehicles owned by the conservative drivers in traffic flow, the random deceleration probability is larger and the road capacity is reduced apparently. For practical use, this fact indicates that it is meaningful and essential to distinguish clearly fast lanes from slow traffic lanes. In summary, the two modified NaSch model proposed herein can capture some respects of the real traffic, even though not the entire. And they can be contributed to the development of the traffic flow theory.
Ⅱ. Based on the two-lane CA model proposed by Chowdhury et al, the nonlinear dynamics of the mixed traffic flow with a bottleneck caused by a traffic accident is studied via numerical simulation.
The property of the mixed traffic flow with a bottleneck caused by an accident vehicle is studied by using the two-lane cellular automaton model proposed by Chowdhury et al. The results of the numerical study, i.e., the fundamental diagrams and the macroscopic features of spatial-temporal traffic patterns at the blockage, are given by applying both symmetric and asymmetric lane changing rules. It is shown that when there is no accident on the road, the presence of slow vehicles has a strong influence on the dynamics of traffic flow. And the fundamental diagrams for the different lanes exhibit different properties when the different lane changing rules are adopted and the accident car appears on the different lanes. In the low and moderate density regions, if the prection of slower cars is 10%, the asymmetric lane changing rule is more advantageous in reducing jam than the symmetric lane changing rule when there is a blockage on the right lane (the slow lane); and in the contrary, the symmetric lane changing rule is superior provided that there is a blockage on the left lane (the fast lane). The spatial-temporal diagrams show that the accident not only causes the local jam in the lane with the accident, but also causes vehicle cluster in the bypass lane. The results also indicate that when traffic is inhomogeneous with different types of vehicles and even with an accident or other defeats, the vehicles will change lane more frequently. In addition, the maximum lane changing rate using the asymmetric rule is lager than that using the symmetric rule. And as there is no slow vehicle and no accident, the corresponding lane changing rate is the lowest.
Ⅲ. An extended car following model is proposed by taking into account the delay of the driver response in sensing headway and the delay of car motion respectively, and the nonlinear properties of the density waves are studied in the metastable and unstable regions.
The soliton and kink-antikink density waves in the traffic flows are simulated with periodic boundaries, by adding a small disturbance in the initial condition on a single-lane road based on the car-following model proposed by Nagatani et al and the optimal velocity function proposed by Bando et al. The waves are reproduced in the form of the spatial-temporal evolution of headway, and both of the density waves propagate backwards. It is found that the solitons appear only near the neutral stability line regardless of the open boundary conditions or periodic boundary conditions, and they exhibit upward form when the initial headway is smaller than the safety distance, otherwise they exhibit downward form. Comparison is made between the numerical and analytical results about the amplitude of kink-antikink wave, and the result shows that the varying tendency of the amplitude is the same, i.e., the amplitude decreases with the increase of the sensitivityα. However, asαis smaller (α<2.3), the numerical results of amplitude are greater than the analytical ones, and then they exhibit a good agreement asα> 2.3. The underlying mechanism is analyzed and this difference is related to the neglected higher-order terms in the nonlinear analysis. Besides, it is shown that the maximal flow increases with the decrease of the safety distance. The numerical simulation shows a good agreement with the analytical results.
Based on the above model, an extended car-following model is proposed by taking into account the delay of drivers' response in sensing headway and the delay of car motion respectively. The neutral stability line and the critical point are obtained by using the linear stability theory. Furthermore, the KdV equation and mKdV equation are derived to describe traffic behavior near the neutral stability line and the critical point respectively by applying the reductive perturbation method. The phase diagrams for the headway and sensitivity with neutral stability lines and coexisting curves are given for different values of n, which denotes the proportion of drivers' delay in response to the total delay. It can be found that the stability regions decrease with the increase of n. This means that the traffic jams will appear easily when the delay of drivers' response in sensing headway increases. The numerical results reproduce the soliton-type density waves and kink-antikink density waves in the form of the spatial-temporal evolution of headway, and both of them propagate backwards. Furthermore, the wave number of kink-antikinks increases with the increase of n. Meanwhile the results show that the delay of drivers' response in sensing headway plays an important role in phase transition, i.e., the longer the delay of driver response is, the easier the formation of the traffic jam is. This model elucidates the mechanism of the traffic jam to some extent from a microscopic viewpoint.
Ⅳ. Two lattice hydrodynamic models for the traffic flow are constructed and the linear and nonlinear analyses are conducted.
Based on the lattice hydrodynamic models proposed by Nagatani et al and incorporated with the results obtained with the car-following model in this dissertation, two lattice hydrodynamic models (model I and model II) for the traffic flow are proposed by taking into account the delay of drivers' response in sensing headway and the delay of car motion respectively. The neutral stability lines and the critical points for the two models are obtained by using the linear stability theory. The mKdV equations near the critical point are derived to describe the traffic jam by using the reductive perturbation method, and the kink-antikink soliton solutions related to the traffic density waves are given. The phase diagrams in the headway-sensitivity plane with neutral stability lines and coexisting curves are given for different values of n . The corresponding critical points, neutral stability lines and coexisting curves in model I are lower than those in model II. And this coincides with the result of Nagatani et al. It can be found that the stability regions decrease with increasing n in both the models and the propagation velocity in model II also decreases with increasing n. It indicates that the traffic jams will be easy to appear and difficult to disperse as the drivers' delay in response increases, and this coincides with the result of study with the car-following model. Then the study indicates the fact that the delay of drivers' response in sensing headway plays an important role in jamming formation from the macroscopic viewpoint. Meanwhile it indicates that the lattice hydrodynamic models can capture the intrinsic properties in traffic flows, and are effective in traffic analysis.
The final chapter of this dissertation is devoted to an analysis and prospect of further study for the traffic flow in our country.
一.基于NaSch元胞自动机模型,考虑局部密度和司机的延迟反应对随机减速概率的影响,以及司机的个性特征和车辆密度对随机减速概率的影响,提出了两个改进的元胞自动机模型。
在NaSch元胞自动机交通流模型的基础上,考虑到车辆的随机减速概率不仅要受到车辆速度的影响,还要受到局部密度和司机延迟反应的影响,当车辆的局部密度较大时,随机减速概率会增大,反之则减小,为此提出了一个新的模型(简称为DDR模型),认为随机减速概率依赖于前一时刻的局部密度。数值模拟显示,该模型能够再现真实交通中的复杂现象,如时走时停交通、亚稳态和回滞现象,且得到的道路最大流量比NaSch模型更接近于实测值,更重要的是,当r≥7时,模型能够模拟出真实交通中的自由流、均匀流和宽幅运动阻塞。此外,通过考虑车辆密度和司机个人行为的差异对随机减速概率产生的影响,提出了另一个元胞自动机新模型,简称为IBDR模型。模型同样能够再现时走时停交通、亚稳态和回滞现象,也得到了比NaSch模型更接近于实测值的最大流量,同时发现司机的个性特征对最大流量的影响要比密度的影响更大一些,当道路上有一些比较谨慎的司机在驾驶车辆时,随机减速概率就大,道路的流量明显下降,这也从一个方面证明了设置快慢车道的必要性。本章提出的两个模型能部分地描述真实交通现象,可以为交通流理论的发展提供一定的参考。
二.在Chowdhury等人提出的双车道元胞自动机模型的基础上,通过数值模拟研究了存在事故车瓶颈时混合交通流的非线性动力学特性。
利用Chowdhury等人提出的双车道元胞自动机模型,对含有事故车交通瓶颈的混合交通流的特性进行了分析研究。通过数值模拟,得到了基本图和车辆的时空演化图,证实当道路上没有事故车瓶颈和其它瓶颈,慢车对交通流特性有很大的影响。当采用不同的换道规则以及事故车出现在不同的车道时,不同车道上的基本图呈现出不同的特点。在中低密度区,当右车道(慢车道)上存在事故车时,采用非对称换道规则比用对称性换道规则更易缓解本车道的拥堵,当左车道(快车道)上存在事故车时,则采用对称换道规则时本车道有较大的流量。从时空斑图上可以看到,事故车瓶颈不仅会引起本车道的交通拥堵,而且会对邻道的交通产生严重的影响。基本图中表现出来的特点与车辆的时空演化图中表现出来的拥堵特性较为吻合。同时发现,在混合交通情况下,或者道路上存在事故车瓶颈时,就会发生频繁的换道,而采用非对称性换道规则时的换道概率更是要大于采用对称性换道规则时的换道概率,当道路上的车辆都有相同的最大速度,又没有事故车时,车辆换道的概率最小。
三.提出了一个改进的跟驰模型,分别考虑司机的反应延迟与车辆的运动延迟,并研究了该模型在亚稳态区域和不稳定区域密度波的非线性特征。
基于Nagatani提出的差分形式的跟驰模型和Bando等人提出的优化速度函数,对单车道周期性边界条件下的交通流进行了数值模拟,再现了孤立波、扭结—反扭结波的时空演化图,得到了向后传播的密度波。再次论证了不管是周期性边界条件还是开放式边界条件,在中性稳定线附近总是出现孤立波,并且当初始车头间距小于安全间距时,孤立波呈现正立波型,反之,当初始车头间距大于安全间距时,孤立波呈现倒置波型。同时对扭结-反扭结波幅值的理论解和数值解进行了比较,发现幅值的变化趋势是相同的,即随着敏感度.a的增大而减小,并且当a＞2.3时,两者在数值上吻合也较好,而当a＜2.3时,数值解稍大于理论解。我们认为,差异的原因在于理论解在非线性分析时忽略了高阶小量。另外,数值模拟显示,交通流的最大流量随着安全间距的减小而增大。数值结果与解析解较为符合。
在上述模型的基础上,提出了一个改进的跟驰模型,把司机的反应延迟与车辆的运动延迟分开考虑,通过线性分析得到了该模型的中性稳定线和临界点,进一步通过摄动分析得到了KdV方程和mKdV方程,分别用来描述中性稳定线和临界点附近的交通现象。当司机的反应延迟与总的延迟时间具有不同的比例n时,给出了中性稳定线和共存曲线在车头间距—敏感度相图中的分布情况,并发现随着n值的增大,稳定区域缩小。这意味着当司机的敏感性越差,即司机反应延迟的时间越长,就越容易产生交通阻塞。数值模拟还给出了孤立波和扭结—反扭结波的时空演化图,它们都呈现向后传播的特性,同时随着n值的增大,扭结—反扭结波显得更密一些。结果表明司机的反应延迟在交通拥堵的形成过程中起着重要的作用,此延迟时间越长,越易造成交通阻塞。该模型从微观的角度揭示了交通拥堵形成的部分机理。
四.提出了一个考虑司机反应延迟的格子流体力学模型,并对模型进行了线性和非线性的理论分析。
在Nagatani提出的单车道格子流体力学模型的基础上,结合第四章的研究内容,提出了两个改进的格子流体力学模型(模型Ⅰ和模型Ⅱ),在模型中分别考虑司机的反应延迟与车辆的运动延迟。经由线性分析得到了模型的中性稳定曲线和临界点,采用摄动理论对临界点附近的交通流现象进行了非线性分析,得到了mKdV方程,当司机的反应延迟与总的延迟时间具有不同的比例n时,给出了中性稳定线和共存曲线在车头间距—敏感度相图中的分布情况。图中显示出模型Ⅰ的临界点、中性稳定曲线和共存曲线都低于模型Ⅱ的相应值,这一点与Nagatani的结论一致。在同一个模型中,随着司机反应延迟的增加,交通流的稳定区域不断缩小,这表明:当司机的反应延迟时间增加的时候,更容易产生交通拥堵,拥堵也更难以消散,这一结论与第四章的跟驰模型的结论一致。因此从宏观模型的角度再次表明,司机的反应延迟在交通拥堵的形成过程中起着重要的作用,延迟时间越长越易造成交通阻塞。同时也说明了格子流体力学模型能够发现交通中的本质现象,是一种有效的交通分析工具。
最后,对我国道路交通流的进一步研究做了分析和展望,并对今后的工作提出了初步的设想。
The aim of the fundamental research for traffic science is to find the basic regulations governing traffic systems through modeling, simulating and analyzing real traffic. In this dissertation, based on an overview of the existing models for traffic flows, several modified mathematical models of traffic flow in accordance with empirical observations are proposed. The theoretical analysis and numerical simulation are performed in order to explore the nonlinear phenomena in traffic systems.
This dissertation consists of the following four main parts:
Ⅰ. Based on the NaSch model of traffic flow, two novel cellular automaton traffic models are presented. One takes into account the effects of local density and the driver response delay on the randomization, and the other includes the effects of road density and drivers' individual behavior on the randomization.It is claimed that the randomization probability in the cellular automaton model is affected not only by the vehicle velocity, but also by the local density and drivers' delay in response. The randomization increases as the local density increases. Besides, a driver can usually sense the local density at previous time step and adjust the vehicle velocity at the present time step. So a modified NaSch model, i.e., the density dependent randomization model (abbreviated as the DDR model), is proposed, in which the randomization probability is assumed to depend on the local density at the preceding time step. The simulation results indicate that this model can reproduce the complicated behavior of real traffic, such as the stop and go traffic, metastable state and hysteresis. The fundamental diagram obtained by numerical simulation shows that the resulted road capacity is close to the empirical data compared with that by the NaSch model. And it is of greater importance that the DDR model can reproduce the free flow, the homogeneous flow and the traffic jam. Furthermore, another modified NaSch model, i.e., the individual behavior dependent randomization model (abbreviated as the IBDR model), is established by considering the effects of road density and the drivers' individual behavior on the randomization. The model can also reproduce the stop and go traffic, metastable state, the hysteresis and the larger value of maximum flow which is close to the observed data compared with that obtained from the NaSch model. Besides, it is found that the driving feature of the individual driver has more appreciable influence on the maximum traffic flow than density does. When there are some vehicles owned by the conservative drivers in traffic flow, the random deceleration probability is larger and the road capacity is reduced apparently. For practical use, this fact indicates that it is meaningful and essential to distinguish clearly fast lanes from slow traffic lanes. In summary, the two modified NaSch model proposed herein can capture some respects of the real traffic, even though not the entire. And they can be contributed to the development of the traffic flow theory.
Ⅱ. Based on the two-lane CA model proposed by Chowdhury et al, the nonlinear dynamics of the mixed traffic flow with a bottleneck caused by a traffic accident is studied via numerical simulation.
The property of the mixed traffic flow with a bottleneck caused by an accident vehicle is studied by using the two-lane cellular automaton model proposed by Chowdhury et al. The results of the numerical study, i.e., the fundamental diagrams and the macroscopic features of spatial-temporal traffic patterns at the blockage, are given by applying both symmetric and asymmetric lane changing rules. It is shown that when there is no accident on the road, the presence of slow vehicles has a strong influence on the dynamics of traffic flow. And the fundamental diagrams for the different lanes exhibit different properties when the different lane changing rules are adopted and the accident car appears on the different lanes. In the low and moderate density regions, if the prection of slower cars is 10%, the asymmetric lane changing rule is more advantageous in reducing jam than the symmetric lane changing rule when there is a blockage on the right lane (the slow lane); and in the contrary, the symmetric lane changing rule is superior provided that there is a blockage on the left lane (the fast lane). The spatial-temporal diagrams show that the accident not only causes the local jam in the lane with the accident, but also causes vehicle cluster in the bypass lane. The results also indicate that when traffic is inhomogeneous with different types of vehicles and even with an accident or other defeats, the vehicles will change lane more frequently. In addition, the maximum lane changing rate using the asymmetric rule is lager than that using the symmetric rule. And as there is no slow vehicle and no accident, the corresponding lane changing rate is the lowest.
Ⅲ. An extended car following model is proposed by taking into account the delay of the driver response in sensing headway and the delay of car motion respectively, and the nonlinear properties of the density waves are studied in the metastable and unstable regions.
The soliton and kink-antikink density waves in the traffic flows are simulated with periodic boundaries, by adding a small disturbance in the initial condition on a single-lane road based on the car-following model proposed by Nagatani et al and the optimal velocity function proposed by Bando et al. The waves are reproduced in the form of the spatial-temporal evolution of headway, and both of the density waves propagate backwards. It is found that the solitons appear only near the neutral stability line regardless of the open boundary conditions or periodic boundary conditions, and they exhibit upward form when the initial headway is smaller than the safety distance, otherwise they exhibit downward form. Comparison is made between the numerical and analytical results about the amplitude of kink-antikink wave, and the result shows that the varying tendency of the amplitude is the same, i.e., the amplitude decreases with the increase of the sensitivityα. However, asαis smaller (α<2.3), the numerical results of amplitude are greater than the analytical ones, and then they exhibit a good agreement asα> 2.3. The underlying mechanism is analyzed and this difference is related to the neglected higher-order terms in the nonlinear analysis. Besides, it is shown that the maximal flow increases with the decrease of the safety distance. The numerical simulation shows a good agreement with the analytical results.
Based on the above model, an extended car-following model is proposed by taking into account the delay of drivers' response in sensing headway and the delay of car motion respectively. The neutral stability line and the critical point are obtained by using the linear stability theory. Furthermore, the KdV equation and mKdV equation are derived to describe traffic behavior near the neutral stability line and the critical point respectively by applying the reductive perturbation method. The phase diagrams for the headway and sensitivity with neutral stability lines and coexisting curves are given for different values of n, which denotes the proportion of drivers' delay in response to the total delay. It can be found that the stability regions decrease with the increase of n. This means that the traffic jams will appear easily when the delay of drivers' response in sensing headway increases. The numerical results reproduce the soliton-type density waves and kink-antikink density waves in the form of the spatial-temporal evolution of headway, and both of them propagate backwards. Furthermore, the wave number of kink-antikinks increases with the increase of n. Meanwhile the results show that the delay of drivers' response in sensing headway plays an important role in phase transition, i.e., the longer the delay of driver response is, the easier the formation of the traffic jam is. This model elucidates the mechanism of the traffic jam to some extent from a microscopic viewpoint.
Ⅳ. Two lattice hydrodynamic models for the traffic flow are constructed and the linear and nonlinear analyses are conducted.
Based on the lattice hydrodynamic models proposed by Nagatani et al and incorporated with the results obtained with the car-following model in this dissertation, two lattice hydrodynamic models (model I and model II) for the traffic flow are proposed by taking into account the delay of drivers' response in sensing headway and the delay of car motion respectively. The neutral stability lines and the critical points for the two models are obtained by using the linear stability theory. The mKdV equations near the critical point are derived to describe the traffic jam by using the reductive perturbation method, and the kink-antikink soliton solutions related to the traffic density waves are given. The phase diagrams in the headway-sensitivity plane with neutral stability lines and coexisting curves are given for different values of n . The corresponding critical points, neutral stability lines and coexisting curves in model I are lower than those in model II. And this coincides with the result of Nagatani et al. It can be found that the stability regions decrease with increasing n in both the models and the propagation velocity in model II also decreases with increasing n. It indicates that the traffic jams will be easy to appear and difficult to disperse as the drivers' delay in response increases, and this coincides with the result of study with the car-following model. Then the study indicates the fact that the delay of drivers' response in sensing headway plays an important role in jamming formation from the macroscopic viewpoint. Meanwhile it indicates that the lattice hydrodynamic models can capture the intrinsic properties in traffic flows, and are effective in traffic analysis.
The final chapter of this dissertation is devoted to an analysis and prospect of further study for the traffic flow in our country.
引文
[1]王晶,北京市交通社会成本的评估,交通环保,2005,2:31-33
[2]林广宇,魏朗,汽车节能与环保分析,交通节能与环保,2006,3:31-33
[3]中国尴尬的世界第一:交通死亡事故占全球15%,http://www.pcauto.com.cn/playcar/saft/info/0511/348730.html,2005-11-4
[4]王炜,项乔君,常玉林等,城市交通系统能源消耗与环境影响分析方法,科学出版社,2002
[5]戴世强,冯苏苇,顾国庆,交通流动力学:它的内容、方法和意义,自然杂志,1997,19(4):196-201
[6]戴世强,薛郁,交通流的建模和仿真,见《交通流与颗粒流》(唐孝威,张训生,陆坤权主编),杭州:浙江大学出版社,2004,66-125
[7]Chowdhury D.,Santen L.,Schadschneider A.,Statistical physics of vehicular traffic and some related systems,Phys.Rep.,2000,329:199-329
[8]Nagel K.,Rickert M.,Parallel implementation of the TRANSIMS micro-simulation,Parallel Comput.,2001,27:1611-1639
[9]Helbing D.,Hennecke A.,Shvetsov V.,et al.MASTER:macroscopic traffic simulation based on a gas-kinetic,non-local traffic model.Transp.Res.B,2001,35:183-211
[10]雷丽,城市高架路—匝道—地面交通的交互作用及交通流特性研究,博士学位论文,上海:上海大学,2004
[11]Wardrop J.G.,Charlesworth G.,A method of Estimating speed and flow of traffic from a moving vehicle,Proc.of the Inst.of Civil Engineers,Part Ⅱ,1954,3:158-171
[12]Wright C.,A theoretical analysis of the moving observer method,Trans.Res.7,TRB,NRC,Washington DC:293-311
[13]李志鹏,交通流建模及城市路网交通状态分析,博士学位论文,上海:上海交通大学,2007
[14]贾斌,高自友,李克平,李新刚,基于元胞自动机的交通系统建模与模拟,北京:科学出版社,2007
[15]Knospe W.,Single-vehicle data of highway traffic:Microscopic description of traffic phases, Phys. Rev. E, 2002, 65: 056133
[16] Helbing D., Traffic and related self-driven many particle systems, Rev. Mod. Phy., 2001,73(4): 1067-1141
[17] Kerner B.S., Empirical macroscopic features of spatial-temporal traffic patterns at highway bottlenecks, Phys. Rev. E, 2002, 65: 046138
[18] Greenshields B.D., A study of traffic capacity, Proc. Highway Res. Board, 1934, 14: 448-477
[19] Kerner B.S. and Rehborn H., Experimental features and characteristics of traffic jam, Phys. Rev. E, 1996, 53: R1297-R1300
[20] Kerner B.S. and Konhauser P., Experimental properties of phase transition in traffic flow, Phys. Rev. Lett, 1997, 79: 4030-4033
[21] Kerner B.S., Rehborn, H., Experimental properties of complexity in traffic flow, Phys. Rev. E, 1996,53 :R4275-R4278
[22] Kerner B.S., Three-phase traffic theory and highway capacity, Physica A, 2004, 333: 379-440
[23] Kerner B.S., Experimental features of self-organization in traffic flow, Phys. Rev. Lett, 1998, 81:3797-3800
[24] Kinzer J.P., Application of the theory of probability to problems of highway traffic, B.C.E. thesis, Polytechnic Institute of Brooklyn (July 1, 1933); also Proc. 1st. Traffic Eng. 5, 118-124
[25] Adams W.F., Road traffic considered as a random series, J. hist. Civil Eng., 1936, (4): 121-130
[26] Greenshields B.D., Shapiro D., Ericksen E.L., Traffic performance at urban street intersections, Tech. Rep. No. 1, Yale Bureau of Highway Traffic, New Haven, Corn, 1947
[27] Hoogendoorn S.P., State-of-the-art of Vehicular Traffic Flow Modelling, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 2001,215(4):283-303
[28] Pipes L.A., An operational analysis of traffic dynamics, J. of App. Phys., 1953, 24: 274-281
[29]Chandler R.E.,et al,Traffic dynamics:studies in car following,Oper.Res.,1958,6:165-184
[30]Herman R.,Potts R.B.,Single lane traffic theory and experiment,In Proceeding:Symposium on theory of traffic flow,Elsevier,New York,1961
[31]Gazis D.C.,Herman R.,Rothery R.W.,Nonlinear follow the leader models of traffic flow,Oper.Res.,1961,9:545-567
[32]Newell G.F.,Nonlinear effects in the dynamics of car following,Oper.Res.,1961,9:209-229
[33]Bando M.,et al,Dynamical model of traffic congestion and numerical simulation,Phys.Rev.E,1995,51:1035-1042
[34]Helbing D.,Tilch B.,Generalized force model of traffic dynamics,Phys.Rev.E,1998,58:133-138
[35]Jiang R.,Wu Q.S.,Zhu Z.J.,Full velocity difference model for a car-following theory,Phys.Rev.E,2001,64:017101
[36]姜锐,交通流复杂动态特性的微观和宏观模式研究,博士学位论文,合肥:中国科学技术大学,2002
[37]Bando M.,Hasebe K.,Nakanishi K.,Nakayama A.,Analysis of optimal velocity model with explicit delay,Phys.Rev.E,1998,58(5):5429-5435
[38]Del Castillo J.M.,Benitez EG.,On the functional form of the speed-density relationship—Ⅰ:General theory;Ⅱ:Empirical investigation,Trans.Res.B,1995,29:373-406
[39]葛红霞,基于诱导信息的交通流动力学特性与非线性密度波研究,博士学位论文,上海:上海大学,2006
[40]Dong L.Y.,Meng Q.X.,Effect of the relative velocity on the Optimal Velocity Model,J.Shanghai Univ.,2005,9(4):283-285
[41]Treiber M.,et al,Congested traffic states in empirical observations and microscopic simulation,Phys.Rev.E,2000,62:1805-1824
[42]薛郁,董力耘,袁以武,戴世强,考虑车辆相对运动速度的交通流演化过程的数值模拟,物理学报,2002,51(3):492-495
[43]Nagatani T.,Stabilization and enhancement of traffic flow by the next-nearest-neighbor interaction,Phys.Rev.E,1999,60:6359
[44]Lenz H.,Wagner C.K.and Sollacher R.,Multi-anticipative car-following model,Eur.Phys.J.B,1999,7:331
[45]Ge H.X.,Dai S.Q.,Dong L.Y.,Xue Y.,Stabilization effect of traffic flow in an extended car-following model based on an intelligent transportation system application,Phys.Rev.E,2004,70:066134
[46]Cremer M.,Ludwig J.,A fast simulation model for traffic flow on the basis of Boolean operations,J.Math.Comp.Simul.,1986,28:297-303
[47]Wolfram S.,Theory and Application of Cellular Automata,World Scientific,Singapore,1986
[48]Nagel K.,Schreckenberg M.,A cellular automaton model for freeway traffic,J.Phys.I(France),1992,2:2221-2233
[49]Nagel K.,Paczuski M.,Emergent traffic jams,Phys.Rev.E,1995,51:2909-2918
[50]Takayasu M.,Takayasu H.,1/f noise in a traffic model,Fractals,1993,1:860-866
[51]Benjamin S.C.,Johnson N.F.,Hui P.M.,Cellular automaton models of traffic flow along a highway containing a junction,J.Phys.A,1996,29:3119-3127
[52]Barlovic R.,Santen L.,Schreckenburg A.,Metastable states in cellular automata for traffic flow,Eur.Phys.J.B,1998,5:793-800
[53]Kemer B.S.,et al.,Cellular automata approach to three-phase traffic theory,J.Phys.A,2002,35:9971-10013
[54]Knospe W.,et al.,Towards a realistic microscopic description of highway traffic,J.Phys.A,2000,33:L477-L485
[55]胡永涛,改进的元胞自动机模型及其应用,硕士学位论文,上海:上海大学,1999
[56]薛郁,董力耘,戴世强,一种改进的一维元胞自动机交通流模型及减速概率的影响,物理学报,2001,50(3):445-449
[57]Li X.B.,Wu Q.S.,Jiang R.,Cellular automaton model considering the velocity effect of a car on the successive car,Phy.Rev.E,2001,64:066128
[58]董力耘,薛郁,戴世强,基于跟驰思想的一维元胞自动机交通流模型,应用数学和力学,2002,23(4):331-337
[59]雷丽,薛郁,戴世强,交通流的一维元胞自动机敏感驾驶模型,物理学报,2003,52(9):2121-2126
[60]Ge H.X.,Dong L.Y.,Lei L.,Dai S.Q.,A modified cellular automaton model for traffic flow,J.Shahghai Univ.,2004,8(1):1-3
[61]谭惠丽,刘慕仁,孔令江,开放边界条件下改进的Nagel-Schreckenberg交通流模型的研究,物理学报,2002,51(12):2713-2718
[62]Fukui M.,Ishibashi Y.,Traffic flow in 1D cellular automaton model including cars moving with high speed,J.Phys.Soc.Japan,1996,65(6):1868-1870
[63]Wang B.H.,et al.,Analytical results for the steady state of traffic flow models with stochastic delay,Phy.Rev.E,1998,58:2876-2882
[64]王雷,一维交通流元胞自动机模型中自组织临界性及相变行为研究,博士学位论文,合肥:中国科学技术大学,2000
[65]Wang L.,Wang B.H.,Hu B.,Cellular automaton traffic flow model between the Fukui-Ishibashi and Nagel-Schreckenberg models,Phys.Rev.E,2001,63:056117
[66]Schadschneider A.,Schreckenberg M.,Cellular-automaton models and traffic flow,J.Phys.A,1993,26:L679-L683
[67]Schadschneider A.,Schreckenberg M.,Car-oriented mean-field theory for traffic flow models,J.Phys.A,1997,30:L69-L75
[68]Rickert M.,Nagel K.,Schreckenberg M.,Latour A.,Two lane traffic simulations using cellular automata,Physica A,1996,231:534-550
[69]Chowdhury D.,Wolf D.E.,Schreckenberg M.,Particle hopping models for two-lane traffic with two kinds of vehicles:effects of lane changing rules,Physica A,1997,235:417-439
[70]Nagel K.,et al.,Two-lane traffic rules for cellular automata:A systematic approach,Phy.Rev.E,1998,58:1425-1437
[71]Wagner P.,Nagel K.,Wolf D.E.,Realistic multi-lane traffic rules for cellular automata,Physica A,1997,234:687-698
[72]Chowdhury D.,Wolf D.E.and Schreckenberg M.,Particle hopping models for two-lane traffic with two kinds of vehicles:effects of lane changing rules,Physica A,1997,235:417-439
[73]Knospe W.,Santen L.,Schadschneider A.,Schreckenberg M.,Disorder effects in cellular automata for two-lane traffic,Physica A,1999,265:614-633
[74]Knospe W.,Santen L.,Schadschneider A.,Schreckenberg M.,A realistic two-lane traffic model for highway traffic,J.Phys.A,2002,35:3369-3388
[75]贾斌,交通瓶颈处车流复杂动态特性的元胞自动机模拟,博士学位论文,合肥:中国科学技术大学,2003
[76]Meng J.P.,Dai S.Q.,Dong L.Y.,Zhang J.F.,Cellular automaton model for mixed traffic flow with motorcycles.Physica A,2007,380:470-480
[77]Kerner B.S.,Klenov S.L.,Spatial-temporal patterns in heterogeneous traffic flow with a variety of driver behavioral characteristics and vehicle parameters,J.Phys.A,2004,37:8753-8788
[78]Jia B.,Jiang R.,Gao Z.Y.and Zhao X.M.,The effect of mixed vehicles on traffic flow in two lane cellular automata model,Int.J.Mod.Phys.C,2005,16(10):1617-1626
[79]Wahle J.,et al,A cellular automaton traffic flow model for online simulation of traffic,Parallel Comput.,2001,27:719-735
[80]Rickert M.,Nagal K.,Experiences with a simplified microsimulation for the Dallas/Fort-Worth area,Int.J.Mod.Phys.,1997,C8:483-503
[81]Kauman O.,et al,On-line simulation of the freeway network of North Rhine Westphatia,Helbing D.,Herrmann M.,Schreckenberg M.,Wolf D.E.(Eds.),In:Traffic and Granular Flow 99,Springer,Berlin,2000:351-356
[82]Biham O.,Middleton A.A.,Levine D.A.,Self-organization and a dynamical transition in traffic flow models,Phys.Rev.A,1992,46:R6124-R6127
[83]Nagatani T.,Effect of traffic accident on jamming transition in traffic flow model,J.Phys.A,1993,26:1015-1020
[84]Gu G.Q.,Chung K.H.,Hui P.M.,Two-dimensional traffic flow problems in inhomogeneous lattice,Physica A,1995,217:339-347
[85]Chung K.H.,Hui P.M.,Gu G.Q.,Two-dimensional traffic problems with faulty traffic lights,Phys.Rev.E,1995,56(1):772-774
[86]冯苏苇,戴世强,交通灯的数学建模与数值模拟,现代数学和力学(MMM-Ⅶ),上海大学出版社,1997:390-392
[87]Feng S.W.,Gu G.Q.,Dai S.Q.,Effects of traffic lights on CA traffic model,Comm.in Nonli.Sci.and Numer.Simul.,1997,2(2):70-74
[88]Chowdhury D.,Schadschneider A.,Self-organization of traffic jams in cities:Effects of stochastic dynamics and signal periods,Phys.Rev.E,1999,59:R131 l-R1314
[89]薛郁,戴世强,顾国庆,元胞自动机的交通立体模型与相变,第14届全国水动力学研讨会,周连第主编,海洋出版社,2000:1-7
[90]Xue Y.,Dai S.Q.,Gu G.Q.,Analysis of phase transition of traffic flow in a two-layer network via cellular automaton model,ICNM-IV(ed.by WZ Chien et al),Shanghai University Press,2002:913-918
[91]Emmerich H.,Rank E.,Investigating traffic flow in the presence of hindrances by cellular automata,Physica A,1995,216:435-444
[92]Pottmeier A.,et al.,Localized defects in a cellular automaton model for traffic flow with phase separation,Physica A,2002,308:471-482
[93]Campari E.G.,Levi G.,A cellular automata model for highway traffic,Eur.Phys.J.B,2000,17:159-166
[94]Pederson M.M.,Ruhoff P.T.,Entry ramps in the Nagel-Schreckenberg model,Phys.Rev.E,2002,65:056705
[95]Jiang R.,Wu Q.S.,Wang B.H.,Cellular automata model simulating traffic interactions between on-ramp and main road,Phys.Rev.E,2002,66:036104
[96]高自友,李克平,城市平面交叉路口辅助信号灯控制系统,专利授权号:200410006109.2,授权日期:2005.11.23
[97]Jia B.,Jiang R.,Wu Q.S.,The traffic bottleneck effects caused by the lane closing in the cellular automata model,Int.J.Mod.Phys.C,2003,14(10):1295-1303
[98] Huang D. W., Huang W. N., The influence of tollbooths on highway traffic, Physica A, 2002, 312:597-608
[99] Lighthill M.J., Whitham J.B., On Kinematic Waves. I: Flow movement in long rivers; II: A theory of traffic flow on long crowded roads, Proc. Royal Soc. A, 1955, 229: 281-345
[100] Richards P.I., Shockwaves on the highway, Oper. Res., 1956,4: 42-51
[101] Daganzo C.F., Requiem for second-order fluid approximations of traffic flow, Trans. Res., 1995, 29B: 277-286
[102] Bick J.H., Newell G.F., A continuum model for two-directional traffic flow, Q. App. Math., 1960, 18(2): 191-204
[103] Rorbech R., Determining the length of the approach lanes required at signal-controlled intersections on through highways—An application of the shock wave theory of Lighthill and Whitham, Trans. Res., 1968, 2: 283-291
[104] Michalopoulos P.G., Stephanopoulos G, Pisharody V.B., Modeling of traffic flow at signalized links, Trans. Sci., 1980, 14: 9-41
[105] Michalopoulos P.G., Beskos D.E., Lin J.K., Analysis of interrupted traffic flow by finite difference methods, Trans. Res., 1984, 18B: 409-421
[106] Ansorge R., What does the entropy condition mean in traffic flow theory? Trans. Res., 1990, 24B: 133-143
[107] Leo C.J., Pretty R., Numerical simulation of macroscopic continuum traffic models, Trans. Res., 1992,26B: 207-220
[108] Edie L.C., Bavarez E., Generation and propagation of stop-start traffic waves, In: Edie L.C., Herman R., Roghery R.(Eds.), Vehicular Traffic Science, Elsevier, Amsterdam, 1967: 26-37
[109] Payne H.J., Models of freeway traffic and control, In: Bekey GA.(ed.), Mathematical Methods of Public Systems, 1971, 1(1): 51-61
[110] Whitham G.B., Linear and nonlinear waves, John Wiley and Sons, 1974
[111] Payne H.J., FREFLO: A macroscopic simulation model of freeway traffic, Trans. Res. Rec, 1979,772:68-75
[112] Payne H.J., A critical review of a macroscopic freeway model, Proc. Research Directions in Computer Control of Urban Traffic Systems,ASCE,New York,1979:251-265
[113]Rathi A.K.,Lieberman E.B.,Yedlin M.,Enhanced FREFLO program:Simulation of congested environments,TRR,1987,1112:67-71
[114]Ross P.,Traffic dynamics,Trans.Res.,1988,22B:421-435
[115]Papageorgiou M.,Blosseville J.,Hadj-Salem H.,Macroscopic modeling of traffic flow on the Boulevard Peripherique in Paris,Trans.Res.,1989,23B:29-47
[116]Hauer E.,Hurdle V.E,Discussions in Payne H.J.,"FREFLO:a macroscopic simulation model of freeway traffic",TRR,1979:722
[117]Leo C.H.,Pretty R.L.,Numerical simulation of macroscopic continuum traffic models,Trans.Res.,1992,26B:207-220
[118]Papageorgiou M.,A hierarchical control system for freeway traffic,Trans.Res.,1983,17B:251-261
[119]Kerner B.S.,Konhauser P.,Cluster effect in initially homogeneous traffic flow,Phys.Rev.E,1993,48:R2335-2338
[120]Kemer B.S.,Konhauser P.,Structure and parameters of clusters in traffic flow,Phys.Rev.E,1994,50(1):54-83
[121]冯苏苇,低速混合型城市交通流的建模、实测与模拟,博士学位论文,上海:上海大学,1997
[122]Zhang H.M.,A nonequilibrium traffic model devoid of gas-like behavior,Trans.Res.,2002,36B:275-290
[123]Jiang R.,Wu Q.S.,Zhu Z.J.,A new continuum model for traffic flow and numerical tests,Trans.Res.,2002,36B:405-419
[124]Xue Y.,Dai S.Q.,Continuum traffic model with the consideration of two delay time scales,Phy.Rev.E,2003,68:066123
[125]薛郁,交通流的建模、数值模拟及其临界相变行为的研究,博士学位论文,上海:上海大学,2002
[126]Nagatani T.,Modified KdV equation for jamming transition in the continuum models of traffic,Physica A,1998,261:599-607
[127]Nagatani T.,TDGL and MKdV equations for jamming transition in the lattice models for traffic,Physica A,1999,264:581-592
[128]Nagatani T.,Jamming transitions and the modified Korteweg-de Vries equation in a two-lane traffic flow,Physica A,1999,265:297-310
[129]Nagatani T.,Jamming transition in a two-dimensional traffic flow model,Phys.Rev.E,1999,59(5):4857-4921
[130]薛郁,优化车流的交通流格子模型,物理学报,2004,53:25-30
[131]Ge H.X.,Dai S.Q.,Xue Y.and Dong L.Y.,Phase transition and modified KdV equation in a cooperative driving system,Phys.Rev.E,2005,71:066119
[132]Ge H.X.,Dai S.Q.,Dong L.Y.and Xue Y.,Two novel lattice traffic models with ITS consideration,MMM-Ⅸ,2004:475
[133]Prigogine I.,In:Herman R.(Eds.),Theory of Traffic Flow,Elsevier,Amsterdam,1961:158
[134]Prigogine I.,Herman R.,Kinetic Theory of Vehicular Traffic,American Elsevier,New York,1971:17-54
[135]Phillips W.F.,A new continuum traffic model obtained from kinetic theory,IEEE Trans.Autom.Control.,1978,AC-23:1032-1036
[136]Paveri-Fontana S.L.,On Boltzmann-like treatments for traffic flow:a critical review of the basic model and an alternative proposal for dilute traffic analysis.Trans.Res.,1975,9B:225-235
[137]Helbing D.,Greiner A.,Modeling and simulation of multilane traffic flow,Phys.Rev.E,1997,55:5498-5508
[138]Nagatani T.,Kinetic segregation in a multilane highway traffic flow,Physica A,1997,237:67-74
[139]Hoogendoorn S.P.,Bovy P.H.L.,Continuum modeling ofmulticlass traffic flow,Trans.Res.,2000,34B:123-146
[140]Hoogendoorn S.P.,Bovy P.H.L.,Genetic gas-kinetic traffic systems modeling with applications to vehicular traffic flow,Trans.Res.,2001,35B:317-336
[141]Helbing D.,Treiber M.,Gas-kinetic-based traffic model explaining observed hysteretic phase transition, Phys. Rev. Letters, 1998, 81(14): 3042-3045
[142] Treiber M., Hennecke A., Helbing D., Derivation, properties, and simulation of a gas-kinetic-based, nonlocal traffic model, Phys. Rev. E, 1999, 59(1): 239-253
[143] Zhu H.B., Ge H.X., Dong L.Y., Dai S.Q., A modified NaSch model with density-dependent randomization for traffic flow, Eur. Phys. J. B, 2007, 57: 103-108
[144] Zhu H.B., Dai S.Q., New cellular automaton traffic model with density-dependent randomization, Proceedings of the 5th International Conference on Nonlinear Mechanics (ICNM-V), Shanghai, June 2007: 1210-1214
[145] Zhu H.B., Ge H.X., Dai S.Q., A new cellular automaton model for traffic flow with different probability for drivers, International Journal of Modern Physics C, 2007, 18(5): 773-782
[146] Zhu H.B., Dai S.Q., Numerical simulation of soliton and kink density waves in traffic flow with periodic boundaries, Physica A, 2008, 387: 4367-4375
[147] Zhu H.B., Dai S.Q., Analysis of car-following model considering driver's physical delay in sensing headway, Physica A, 2008, 387: 3290-3298
[148] Whitham G.B., Exact solutions for a discrete system arising in traffic flow, Proc. R. Soc. London, Ser. A, 1990,428: 49
[149] Nagatani T., Nakanishi K.., Emmerich H., Phase transition in a difference equation model of traffic flow, J. Phys. A, 1998,31: 5431
[150] Treiterer J., Investigation of traffic dynamics by aerial photogrammetry techniques, Techn. Rep. B, 1975, 246094, Columbus, OH
[151] Wagner P., in Traffic and Granular Flow, edited by Wolf D.E., Schreckenberg M. and Bachem A., 1996, World Scientific, Singapore, 139
[152] Nagatani T., Self-organization and phase-transition in traffic-flow model of a 2-lane roadway, J. Phys. A, 1993, 26: L781-L787
[153] Nagatani T., Dynamical jamming transition induced by a car accident in traffic-flow model of a 2-lane roadway, Physica A, 1994, 202: 449-458
[154] Nagei K., Stretz P., Pieck M., et al. Los Alamos National Laboratory Report No. LA-UR 97～3530, 1997 (unpublished). See http:// transims. Tsasa.lanl.gov/research-team/
[155]Yang X.Q.,Ma Y.Q.,Zhao Y.M.,Effects of quenched randomness induced by car accidents on traffic flow in a cellular automata model,Phys.Rev.E,2004,70:046121
[156]Ge H.X.,Cheng R.J.,Dai S.Q.,KdV and kink-antikink solitons in car-following models,Physica A,2005,357:466-476
[157]Muramatsu M.,Nagatani T.,Soliton and kink jams in traffic flow with open boundaries,Phys.Rev.E,1999,60:180-187
[158]Liu MR,Lattics Boltzmann Method for one dimensional traffic flow,In:Meng QG eds.Proceedings of the Conference of Yong Scholars on New Directions of Fliud Mechanics,Hangzhou,1998,113-118(in Chinese)
[159]吕晓阳,孔令江,刘幕仁,一维元胞自动机随机交通流模型的宏观方程的分析,物理学报,2001,50(7):1255
[160]Kurtze D.A.,Hong D.C.,Traffic jams,granular flow,and soliton selection,Phys.Rev.E,1995,52:218-221
[161]戴世强,科学引路 畅通有日,科学时报,2004
[2]林广宇,魏朗,汽车节能与环保分析,交通节能与环保,2006,3:31-33
[3]中国尴尬的世界第一:交通死亡事故占全球15%,http://www.pcauto.com.cn/playcar/saft/info/0511/348730.html,2005-11-4
[4]王炜,项乔君,常玉林等,城市交通系统能源消耗与环境影响分析方法,科学出版社,2002
[5]戴世强,冯苏苇,顾国庆,交通流动力学:它的内容、方法和意义,自然杂志,1997,19(4):196-201
[6]戴世强,薛郁,交通流的建模和仿真,见《交通流与颗粒流》(唐孝威,张训生,陆坤权主编),杭州:浙江大学出版社,2004,66-125
[7]Chowdhury D.,Santen L.,Schadschneider A.,Statistical physics of vehicular traffic and some related systems,Phys.Rep.,2000,329:199-329
[8]Nagel K.,Rickert M.,Parallel implementation of the TRANSIMS micro-simulation,Parallel Comput.,2001,27:1611-1639
[9]Helbing D.,Hennecke A.,Shvetsov V.,et al.MASTER:macroscopic traffic simulation based on a gas-kinetic,non-local traffic model.Transp.Res.B,2001,35:183-211
[10]雷丽,城市高架路—匝道—地面交通的交互作用及交通流特性研究,博士学位论文,上海:上海大学,2004
[11]Wardrop J.G.,Charlesworth G.,A method of Estimating speed and flow of traffic from a moving vehicle,Proc.of the Inst.of Civil Engineers,Part Ⅱ,1954,3:158-171
[12]Wright C.,A theoretical analysis of the moving observer method,Trans.Res.7,TRB,NRC,Washington DC:293-311
[13]李志鹏,交通流建模及城市路网交通状态分析,博士学位论文,上海:上海交通大学,2007
[14]贾斌,高自友,李克平,李新刚,基于元胞自动机的交通系统建模与模拟,北京:科学出版社,2007
[15]Knospe W.,Single-vehicle data of highway traffic:Microscopic description of traffic phases, Phys. Rev. E, 2002, 65: 056133
[16] Helbing D., Traffic and related self-driven many particle systems, Rev. Mod. Phy., 2001,73(4): 1067-1141
[17] Kerner B.S., Empirical macroscopic features of spatial-temporal traffic patterns at highway bottlenecks, Phys. Rev. E, 2002, 65: 046138
[18] Greenshields B.D., A study of traffic capacity, Proc. Highway Res. Board, 1934, 14: 448-477
[19] Kerner B.S. and Rehborn H., Experimental features and characteristics of traffic jam, Phys. Rev. E, 1996, 53: R1297-R1300
[20] Kerner B.S. and Konhauser P., Experimental properties of phase transition in traffic flow, Phys. Rev. Lett, 1997, 79: 4030-4033
[21] Kerner B.S., Rehborn, H., Experimental properties of complexity in traffic flow, Phys. Rev. E, 1996,53 :R4275-R4278
[22] Kerner B.S., Three-phase traffic theory and highway capacity, Physica A, 2004, 333: 379-440
[23] Kerner B.S., Experimental features of self-organization in traffic flow, Phys. Rev. Lett, 1998, 81:3797-3800
[24] Kinzer J.P., Application of the theory of probability to problems of highway traffic, B.C.E. thesis, Polytechnic Institute of Brooklyn (July 1, 1933); also Proc. 1st. Traffic Eng. 5, 118-124
[25] Adams W.F., Road traffic considered as a random series, J. hist. Civil Eng., 1936, (4): 121-130
[26] Greenshields B.D., Shapiro D., Ericksen E.L., Traffic performance at urban street intersections, Tech. Rep. No. 1, Yale Bureau of Highway Traffic, New Haven, Corn, 1947
[27] Hoogendoorn S.P., State-of-the-art of Vehicular Traffic Flow Modelling, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 2001,215(4):283-303
[28] Pipes L.A., An operational analysis of traffic dynamics, J. of App. Phys., 1953, 24: 274-281
[29]Chandler R.E.,et al,Traffic dynamics:studies in car following,Oper.Res.,1958,6:165-184
[30]Herman R.,Potts R.B.,Single lane traffic theory and experiment,In Proceeding:Symposium on theory of traffic flow,Elsevier,New York,1961
[31]Gazis D.C.,Herman R.,Rothery R.W.,Nonlinear follow the leader models of traffic flow,Oper.Res.,1961,9:545-567
[32]Newell G.F.,Nonlinear effects in the dynamics of car following,Oper.Res.,1961,9:209-229
[33]Bando M.,et al,Dynamical model of traffic congestion and numerical simulation,Phys.Rev.E,1995,51:1035-1042
[34]Helbing D.,Tilch B.,Generalized force model of traffic dynamics,Phys.Rev.E,1998,58:133-138
[35]Jiang R.,Wu Q.S.,Zhu Z.J.,Full velocity difference model for a car-following theory,Phys.Rev.E,2001,64:017101
[36]姜锐,交通流复杂动态特性的微观和宏观模式研究,博士学位论文,合肥:中国科学技术大学,2002
[37]Bando M.,Hasebe K.,Nakanishi K.,Nakayama A.,Analysis of optimal velocity model with explicit delay,Phys.Rev.E,1998,58(5):5429-5435
[38]Del Castillo J.M.,Benitez EG.,On the functional form of the speed-density relationship—Ⅰ:General theory;Ⅱ:Empirical investigation,Trans.Res.B,1995,29:373-406
[39]葛红霞,基于诱导信息的交通流动力学特性与非线性密度波研究,博士学位论文,上海:上海大学,2006
[40]Dong L.Y.,Meng Q.X.,Effect of the relative velocity on the Optimal Velocity Model,J.Shanghai Univ.,2005,9(4):283-285
[41]Treiber M.,et al,Congested traffic states in empirical observations and microscopic simulation,Phys.Rev.E,2000,62:1805-1824
[42]薛郁,董力耘,袁以武,戴世强,考虑车辆相对运动速度的交通流演化过程的数值模拟,物理学报,2002,51(3):492-495
[43]Nagatani T.,Stabilization and enhancement of traffic flow by the next-nearest-neighbor interaction,Phys.Rev.E,1999,60:6359
[44]Lenz H.,Wagner C.K.and Sollacher R.,Multi-anticipative car-following model,Eur.Phys.J.B,1999,7:331
[45]Ge H.X.,Dai S.Q.,Dong L.Y.,Xue Y.,Stabilization effect of traffic flow in an extended car-following model based on an intelligent transportation system application,Phys.Rev.E,2004,70:066134
[46]Cremer M.,Ludwig J.,A fast simulation model for traffic flow on the basis of Boolean operations,J.Math.Comp.Simul.,1986,28:297-303
[47]Wolfram S.,Theory and Application of Cellular Automata,World Scientific,Singapore,1986
[48]Nagel K.,Schreckenberg M.,A cellular automaton model for freeway traffic,J.Phys.I(France),1992,2:2221-2233
[49]Nagel K.,Paczuski M.,Emergent traffic jams,Phys.Rev.E,1995,51:2909-2918
[50]Takayasu M.,Takayasu H.,1/f noise in a traffic model,Fractals,1993,1:860-866
[51]Benjamin S.C.,Johnson N.F.,Hui P.M.,Cellular automaton models of traffic flow along a highway containing a junction,J.Phys.A,1996,29:3119-3127
[52]Barlovic R.,Santen L.,Schreckenburg A.,Metastable states in cellular automata for traffic flow,Eur.Phys.J.B,1998,5:793-800
[53]Kemer B.S.,et al.,Cellular automata approach to three-phase traffic theory,J.Phys.A,2002,35:9971-10013
[54]Knospe W.,et al.,Towards a realistic microscopic description of highway traffic,J.Phys.A,2000,33:L477-L485
[55]胡永涛,改进的元胞自动机模型及其应用,硕士学位论文,上海:上海大学,1999
[56]薛郁,董力耘,戴世强,一种改进的一维元胞自动机交通流模型及减速概率的影响,物理学报,2001,50(3):445-449
[57]Li X.B.,Wu Q.S.,Jiang R.,Cellular automaton model considering the velocity effect of a car on the successive car,Phy.Rev.E,2001,64:066128
[58]董力耘,薛郁,戴世强,基于跟驰思想的一维元胞自动机交通流模型,应用数学和力学,2002,23(4):331-337
[59]雷丽,薛郁,戴世强,交通流的一维元胞自动机敏感驾驶模型,物理学报,2003,52(9):2121-2126
[60]Ge H.X.,Dong L.Y.,Lei L.,Dai S.Q.,A modified cellular automaton model for traffic flow,J.Shahghai Univ.,2004,8(1):1-3
[61]谭惠丽,刘慕仁,孔令江,开放边界条件下改进的Nagel-Schreckenberg交通流模型的研究,物理学报,2002,51(12):2713-2718
[62]Fukui M.,Ishibashi Y.,Traffic flow in 1D cellular automaton model including cars moving with high speed,J.Phys.Soc.Japan,1996,65(6):1868-1870
[63]Wang B.H.,et al.,Analytical results for the steady state of traffic flow models with stochastic delay,Phy.Rev.E,1998,58:2876-2882
[64]王雷,一维交通流元胞自动机模型中自组织临界性及相变行为研究,博士学位论文,合肥:中国科学技术大学,2000
[65]Wang L.,Wang B.H.,Hu B.,Cellular automaton traffic flow model between the Fukui-Ishibashi and Nagel-Schreckenberg models,Phys.Rev.E,2001,63:056117
[66]Schadschneider A.,Schreckenberg M.,Cellular-automaton models and traffic flow,J.Phys.A,1993,26:L679-L683
[67]Schadschneider A.,Schreckenberg M.,Car-oriented mean-field theory for traffic flow models,J.Phys.A,1997,30:L69-L75
[68]Rickert M.,Nagel K.,Schreckenberg M.,Latour A.,Two lane traffic simulations using cellular automata,Physica A,1996,231:534-550
[69]Chowdhury D.,Wolf D.E.,Schreckenberg M.,Particle hopping models for two-lane traffic with two kinds of vehicles:effects of lane changing rules,Physica A,1997,235:417-439
[70]Nagel K.,et al.,Two-lane traffic rules for cellular automata:A systematic approach,Phy.Rev.E,1998,58:1425-1437
[71]Wagner P.,Nagel K.,Wolf D.E.,Realistic multi-lane traffic rules for cellular automata,Physica A,1997,234:687-698
[72]Chowdhury D.,Wolf D.E.and Schreckenberg M.,Particle hopping models for two-lane traffic with two kinds of vehicles:effects of lane changing rules,Physica A,1997,235:417-439
[73]Knospe W.,Santen L.,Schadschneider A.,Schreckenberg M.,Disorder effects in cellular automata for two-lane traffic,Physica A,1999,265:614-633
[74]Knospe W.,Santen L.,Schadschneider A.,Schreckenberg M.,A realistic two-lane traffic model for highway traffic,J.Phys.A,2002,35:3369-3388
[75]贾斌,交通瓶颈处车流复杂动态特性的元胞自动机模拟,博士学位论文,合肥:中国科学技术大学,2003
[76]Meng J.P.,Dai S.Q.,Dong L.Y.,Zhang J.F.,Cellular automaton model for mixed traffic flow with motorcycles.Physica A,2007,380:470-480
[77]Kerner B.S.,Klenov S.L.,Spatial-temporal patterns in heterogeneous traffic flow with a variety of driver behavioral characteristics and vehicle parameters,J.Phys.A,2004,37:8753-8788
[78]Jia B.,Jiang R.,Gao Z.Y.and Zhao X.M.,The effect of mixed vehicles on traffic flow in two lane cellular automata model,Int.J.Mod.Phys.C,2005,16(10):1617-1626
[79]Wahle J.,et al,A cellular automaton traffic flow model for online simulation of traffic,Parallel Comput.,2001,27:719-735
[80]Rickert M.,Nagal K.,Experiences with a simplified microsimulation for the Dallas/Fort-Worth area,Int.J.Mod.Phys.,1997,C8:483-503
[81]Kauman O.,et al,On-line simulation of the freeway network of North Rhine Westphatia,Helbing D.,Herrmann M.,Schreckenberg M.,Wolf D.E.(Eds.),In:Traffic and Granular Flow 99,Springer,Berlin,2000:351-356
[82]Biham O.,Middleton A.A.,Levine D.A.,Self-organization and a dynamical transition in traffic flow models,Phys.Rev.A,1992,46:R6124-R6127
[83]Nagatani T.,Effect of traffic accident on jamming transition in traffic flow model,J.Phys.A,1993,26:1015-1020
[84]Gu G.Q.,Chung K.H.,Hui P.M.,Two-dimensional traffic flow problems in inhomogeneous lattice,Physica A,1995,217:339-347
[85]Chung K.H.,Hui P.M.,Gu G.Q.,Two-dimensional traffic problems with faulty traffic lights,Phys.Rev.E,1995,56(1):772-774
[86]冯苏苇,戴世强,交通灯的数学建模与数值模拟,现代数学和力学(MMM-Ⅶ),上海大学出版社,1997:390-392
[87]Feng S.W.,Gu G.Q.,Dai S.Q.,Effects of traffic lights on CA traffic model,Comm.in Nonli.Sci.and Numer.Simul.,1997,2(2):70-74
[88]Chowdhury D.,Schadschneider A.,Self-organization of traffic jams in cities:Effects of stochastic dynamics and signal periods,Phys.Rev.E,1999,59:R131 l-R1314
[89]薛郁,戴世强,顾国庆,元胞自动机的交通立体模型与相变,第14届全国水动力学研讨会,周连第主编,海洋出版社,2000:1-7
[90]Xue Y.,Dai S.Q.,Gu G.Q.,Analysis of phase transition of traffic flow in a two-layer network via cellular automaton model,ICNM-IV(ed.by WZ Chien et al),Shanghai University Press,2002:913-918
[91]Emmerich H.,Rank E.,Investigating traffic flow in the presence of hindrances by cellular automata,Physica A,1995,216:435-444
[92]Pottmeier A.,et al.,Localized defects in a cellular automaton model for traffic flow with phase separation,Physica A,2002,308:471-482
[93]Campari E.G.,Levi G.,A cellular automata model for highway traffic,Eur.Phys.J.B,2000,17:159-166
[94]Pederson M.M.,Ruhoff P.T.,Entry ramps in the Nagel-Schreckenberg model,Phys.Rev.E,2002,65:056705
[95]Jiang R.,Wu Q.S.,Wang B.H.,Cellular automata model simulating traffic interactions between on-ramp and main road,Phys.Rev.E,2002,66:036104
[96]高自友,李克平,城市平面交叉路口辅助信号灯控制系统,专利授权号:200410006109.2,授权日期:2005.11.23
[97]Jia B.,Jiang R.,Wu Q.S.,The traffic bottleneck effects caused by the lane closing in the cellular automata model,Int.J.Mod.Phys.C,2003,14(10):1295-1303
[98] Huang D. W., Huang W. N., The influence of tollbooths on highway traffic, Physica A, 2002, 312:597-608
[99] Lighthill M.J., Whitham J.B., On Kinematic Waves. I: Flow movement in long rivers; II: A theory of traffic flow on long crowded roads, Proc. Royal Soc. A, 1955, 229: 281-345
[100] Richards P.I., Shockwaves on the highway, Oper. Res., 1956,4: 42-51
[101] Daganzo C.F., Requiem for second-order fluid approximations of traffic flow, Trans. Res., 1995, 29B: 277-286
[102] Bick J.H., Newell G.F., A continuum model for two-directional traffic flow, Q. App. Math., 1960, 18(2): 191-204
[103] Rorbech R., Determining the length of the approach lanes required at signal-controlled intersections on through highways—An application of the shock wave theory of Lighthill and Whitham, Trans. Res., 1968, 2: 283-291
[104] Michalopoulos P.G., Stephanopoulos G, Pisharody V.B., Modeling of traffic flow at signalized links, Trans. Sci., 1980, 14: 9-41
[105] Michalopoulos P.G., Beskos D.E., Lin J.K., Analysis of interrupted traffic flow by finite difference methods, Trans. Res., 1984, 18B: 409-421
[106] Ansorge R., What does the entropy condition mean in traffic flow theory? Trans. Res., 1990, 24B: 133-143
[107] Leo C.J., Pretty R., Numerical simulation of macroscopic continuum traffic models, Trans. Res., 1992,26B: 207-220
[108] Edie L.C., Bavarez E., Generation and propagation of stop-start traffic waves, In: Edie L.C., Herman R., Roghery R.(Eds.), Vehicular Traffic Science, Elsevier, Amsterdam, 1967: 26-37
[109] Payne H.J., Models of freeway traffic and control, In: Bekey GA.(ed.), Mathematical Methods of Public Systems, 1971, 1(1): 51-61
[110] Whitham G.B., Linear and nonlinear waves, John Wiley and Sons, 1974
[111] Payne H.J., FREFLO: A macroscopic simulation model of freeway traffic, Trans. Res. Rec, 1979,772:68-75
[112] Payne H.J., A critical review of a macroscopic freeway model, Proc. Research Directions in Computer Control of Urban Traffic Systems,ASCE,New York,1979:251-265
[113]Rathi A.K.,Lieberman E.B.,Yedlin M.,Enhanced FREFLO program:Simulation of congested environments,TRR,1987,1112:67-71
[114]Ross P.,Traffic dynamics,Trans.Res.,1988,22B:421-435
[115]Papageorgiou M.,Blosseville J.,Hadj-Salem H.,Macroscopic modeling of traffic flow on the Boulevard Peripherique in Paris,Trans.Res.,1989,23B:29-47
[116]Hauer E.,Hurdle V.E,Discussions in Payne H.J.,"FREFLO:a macroscopic simulation model of freeway traffic",TRR,1979:722
[117]Leo C.H.,Pretty R.L.,Numerical simulation of macroscopic continuum traffic models,Trans.Res.,1992,26B:207-220
[118]Papageorgiou M.,A hierarchical control system for freeway traffic,Trans.Res.,1983,17B:251-261
[119]Kerner B.S.,Konhauser P.,Cluster effect in initially homogeneous traffic flow,Phys.Rev.E,1993,48:R2335-2338
[120]Kemer B.S.,Konhauser P.,Structure and parameters of clusters in traffic flow,Phys.Rev.E,1994,50(1):54-83
[121]冯苏苇,低速混合型城市交通流的建模、实测与模拟,博士学位论文,上海:上海大学,1997
[122]Zhang H.M.,A nonequilibrium traffic model devoid of gas-like behavior,Trans.Res.,2002,36B:275-290
[123]Jiang R.,Wu Q.S.,Zhu Z.J.,A new continuum model for traffic flow and numerical tests,Trans.Res.,2002,36B:405-419
[124]Xue Y.,Dai S.Q.,Continuum traffic model with the consideration of two delay time scales,Phy.Rev.E,2003,68:066123
[125]薛郁,交通流的建模、数值模拟及其临界相变行为的研究,博士学位论文,上海:上海大学,2002
[126]Nagatani T.,Modified KdV equation for jamming transition in the continuum models of traffic,Physica A,1998,261:599-607
[127]Nagatani T.,TDGL and MKdV equations for jamming transition in the lattice models for traffic,Physica A,1999,264:581-592
[128]Nagatani T.,Jamming transitions and the modified Korteweg-de Vries equation in a two-lane traffic flow,Physica A,1999,265:297-310
[129]Nagatani T.,Jamming transition in a two-dimensional traffic flow model,Phys.Rev.E,1999,59(5):4857-4921
[130]薛郁,优化车流的交通流格子模型,物理学报,2004,53:25-30
[131]Ge H.X.,Dai S.Q.,Xue Y.and Dong L.Y.,Phase transition and modified KdV equation in a cooperative driving system,Phys.Rev.E,2005,71:066119
[132]Ge H.X.,Dai S.Q.,Dong L.Y.and Xue Y.,Two novel lattice traffic models with ITS consideration,MMM-Ⅸ,2004:475
[133]Prigogine I.,In:Herman R.(Eds.),Theory of Traffic Flow,Elsevier,Amsterdam,1961:158
[134]Prigogine I.,Herman R.,Kinetic Theory of Vehicular Traffic,American Elsevier,New York,1971:17-54
[135]Phillips W.F.,A new continuum traffic model obtained from kinetic theory,IEEE Trans.Autom.Control.,1978,AC-23:1032-1036
[136]Paveri-Fontana S.L.,On Boltzmann-like treatments for traffic flow:a critical review of the basic model and an alternative proposal for dilute traffic analysis.Trans.Res.,1975,9B:225-235
[137]Helbing D.,Greiner A.,Modeling and simulation of multilane traffic flow,Phys.Rev.E,1997,55:5498-5508
[138]Nagatani T.,Kinetic segregation in a multilane highway traffic flow,Physica A,1997,237:67-74
[139]Hoogendoorn S.P.,Bovy P.H.L.,Continuum modeling ofmulticlass traffic flow,Trans.Res.,2000,34B:123-146
[140]Hoogendoorn S.P.,Bovy P.H.L.,Genetic gas-kinetic traffic systems modeling with applications to vehicular traffic flow,Trans.Res.,2001,35B:317-336
[141]Helbing D.,Treiber M.,Gas-kinetic-based traffic model explaining observed hysteretic phase transition, Phys. Rev. Letters, 1998, 81(14): 3042-3045
[142] Treiber M., Hennecke A., Helbing D., Derivation, properties, and simulation of a gas-kinetic-based, nonlocal traffic model, Phys. Rev. E, 1999, 59(1): 239-253
[143] Zhu H.B., Ge H.X., Dong L.Y., Dai S.Q., A modified NaSch model with density-dependent randomization for traffic flow, Eur. Phys. J. B, 2007, 57: 103-108
[144] Zhu H.B., Dai S.Q., New cellular automaton traffic model with density-dependent randomization, Proceedings of the 5th International Conference on Nonlinear Mechanics (ICNM-V), Shanghai, June 2007: 1210-1214
[145] Zhu H.B., Ge H.X., Dai S.Q., A new cellular automaton model for traffic flow with different probability for drivers, International Journal of Modern Physics C, 2007, 18(5): 773-782
[146] Zhu H.B., Dai S.Q., Numerical simulation of soliton and kink density waves in traffic flow with periodic boundaries, Physica A, 2008, 387: 4367-4375
[147] Zhu H.B., Dai S.Q., Analysis of car-following model considering driver's physical delay in sensing headway, Physica A, 2008, 387: 3290-3298
[148] Whitham G.B., Exact solutions for a discrete system arising in traffic flow, Proc. R. Soc. London, Ser. A, 1990,428: 49
[149] Nagatani T., Nakanishi K.., Emmerich H., Phase transition in a difference equation model of traffic flow, J. Phys. A, 1998,31: 5431
[150] Treiterer J., Investigation of traffic dynamics by aerial photogrammetry techniques, Techn. Rep. B, 1975, 246094, Columbus, OH
[151] Wagner P., in Traffic and Granular Flow, edited by Wolf D.E., Schreckenberg M. and Bachem A., 1996, World Scientific, Singapore, 139
[152] Nagatani T., Self-organization and phase-transition in traffic-flow model of a 2-lane roadway, J. Phys. A, 1993, 26: L781-L787
[153] Nagatani T., Dynamical jamming transition induced by a car accident in traffic-flow model of a 2-lane roadway, Physica A, 1994, 202: 449-458
[154] Nagei K., Stretz P., Pieck M., et al. Los Alamos National Laboratory Report No. LA-UR 97～3530, 1997 (unpublished). See http:// transims. Tsasa.lanl.gov/research-team/
[155]Yang X.Q.,Ma Y.Q.,Zhao Y.M.,Effects of quenched randomness induced by car accidents on traffic flow in a cellular automata model,Phys.Rev.E,2004,70:046121
[156]Ge H.X.,Cheng R.J.,Dai S.Q.,KdV and kink-antikink solitons in car-following models,Physica A,2005,357:466-476
[157]Muramatsu M.,Nagatani T.,Soliton and kink jams in traffic flow with open boundaries,Phys.Rev.E,1999,60:180-187
[158]Liu MR,Lattics Boltzmann Method for one dimensional traffic flow,In:Meng QG eds.Proceedings of the Conference of Yong Scholars on New Directions of Fliud Mechanics,Hangzhou,1998,113-118(in Chinese)
[159]吕晓阳,孔令江,刘幕仁,一维元胞自动机随机交通流模型的宏观方程的分析,物理学报,2001,50(7):1255
[160]Kurtze D.A.,Hong D.C.,Traffic jams,granular flow,and soliton selection,Phys.Rev.E,1995,52:218-221
[161]戴世强,科学引路 畅通有日,科学时报,2004