【作者】 祝会兵；

【导师】 戴世强；

【作者基本信息】 上海大学 ， 流体力学， 2008， 博士

【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。更多还原

【Abstract】 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.更多还原