从基本图方法到三相交通流理论

【作者】 高坤；

【导师】 汪秉宏；

【作者基本信息】 中国科学技术大学 ， 理论物理， 2008， 博士

【摘要】 本文中,我们分别在传统的基本图方法和新兴的三相交通流理论这两种不同的交通流理论体系下对交通流元胞自动机模型进行了研究。我们的研究对象,交通运输系统,正在社会经济中正扮演着重要的角色,其发展水平已经成为评价一个国家现代化程度的重要标准之一。然而,交通系统建设上的相对滞后和社会经济的飞速发展之间的矛盾,却已经成为全世界范围内的一个突出的难题。一方面,交通拥塞引起了严重的环境污染和巨额的经济损失,并大有愈演愈烈之势;另一方面,缺乏科学理论指导的交通系统建设,不仅耗资巨大,往往还收效甚微。因此,世界各发达国家都相继投入大量的人力、物理和财力用于交通工程学和交通流理论的研究,以期揭示交通流动的基本规律,掌握适合各自国情的交通控制方法,进而对其进行科学的控制和优化。另一方面,从科学研究的角度来看,交通流系统作为一种典型的自驱动远离平衡态系统,表现出了人类社会中常见的一类伴有复杂相互作用的多体系统在远离平衡态时的典型演化规律。交通流理论研究将对统计物理、流体力学、非线性动力学、应用数学、交通工程学等诸多学科的交叉和发展都有很大的促进作用。因此开展交通流理论研究,不仅具有重要的工程应用价值,还具有及其深远的科学意义。而作为交通流理论研究重要组成部分的交通流建模工作,则是人们通过理论方法复现和解释交通现象时首先就要面对的重要研究内容。在诸多的模型方法中,元胞自动机模型(Cellular Automata,简称CA模型)由于其结构简单,使用离散的时间和空间变量,使得它相对易于模拟由大量车辆组成的复杂系统的行为,因而特别受到了研究者的青睐和关注。当前的交通流理论研究领域,存在两大主导性的交通流理论体系,即基本图方法和三相交通流理论。在这两个理论体系中,研究者们都建立了逻辑上符合真实交通行为的交通流模型,并借此模拟出了许多与实测结果相符合的交通现象。其中,作为当前交通流理论研究的前沿之一,三相交通流理论把所有的交通流状态划分成三个交通相,即自由流相、同步流相和宽运动堵塞相。这一新的对于交通相的认识方式使得三相交通流理论在模拟交通瓶颈诱发的交通拥塞模式图谱方面,得到了比基本图方法更符合实际观测的模拟结果,因此逐渐得到了世界各国学者的认同。本文中,在对交通流理论研究的背景,包括基本图方法和三相交通流理论各自的要点做了简要的介绍之后,我们着重介绍了在自己的研究工作中已经取得的进展,其要点概括如下:(1)利用交通流元胞自动机建模的方法,我们实现了Kaupu(?)s等人提到的一种交通机制,即车辆的慢起动行为依赖于包含该车辆的堵塞集团的长度这一改进了的车辆慢起动机制。由此得到的改进模型同以往的车辆慢起动模型一样,模拟出了交通迟滞现象、交通亚稳态及交通中的相分离现象等。另一方面,这一改进模型又同时具有如下的新性质。首先,改进了的慢起动规则产生了自适应效应,这使得新模型中初始堵塞集团的疏散过程相比于以往的慢起动模型中相同的过程变得更为迅速和流畅。新模型有效地减少了系统中小堵塞集团不断的形成—溶解—再形成这一过程带来的系统振荡,明显的提高了交通系统的运行效率。其次,新模型特征性的区分了初始堵塞集团疏散过程中的三个典型时期,即堵塞集团长度随时间线性衰减的头部、指数衰减的中段以及近似幂律衰减的尾部,充分揭示了交通疏散过程的动态微观统计特性。最后,该模型中的堵塞集团长度在低密度和高密度下分别表现出单峰值和双峰值的分布规律,且分布中数据点的散布相比以往模型较小。这种分布特性一方面表明该模型具有更为鲜明的相分离性质,另一方面则揭示了低密度和高密度下对应于两个不同峰值的相分离现象具有不同的成因。这一工作的主要结果发表于Chinese Physics Vol.16,No.11,2007。(2)将NS元胞自动机模型与经典跟驰模型相结合,我们得到了一个考虑连续车辆间速度差效应的CA模型。该模型正数值模拟过程中表现出了一些特别的性质。首先,模型模拟的基本图中存在一种反常的迟滞现象,即与以往模型的结果相比,其中均匀态和非均匀态交通的流量关系被倒置了。其次,模型的基本图中存在两个流量的极大值,表现为一双峰现象。通过对模型的时空演化过程和相关函数的研究,我们发现上述两点都与一种“均匀拥挤交通流”的出现有关,这种交通流状态的宏观特性和微观特性都与同步流态极为相似。于是,该模型一方面说明了在某些特殊情况下,非均匀态交通反而可能更好的利用道路的通行能力。另一方面,虽然该模型本质上仍旧属于基本图方法体系,却也可以理解为介于基本图方法和三相交通流理论中间的一个过渡模型。它对于这两种不同的交通流理论体系的研究与对比具有一定的意义。这一工作发表于Physica A 386(2007):397—406。(3)紧接着上一个工作的基础上,我们对速度差效应模型进行了进一步的改进与发展。一方面,我们在模型规则中引进车辆慢起动效应,以诱发从同步流到宽运动堵塞的自发一阶相变。另一方面,我们进一步修改了速度差效应在模型规则中的作用方式,即直接将经典跟驰模型的方程离散化后引入到模型的相关部分。于是,我们便建立起了一个真正隶属于三相交通流理论体系的交通流元胞自动机模型。该模型能够正确的模拟自由流相、同步流相和宽运动堵塞相三个交通相,以及从同步流相到宽运动堵塞堵塞相的自发一阶相变。在带有孤立上匝道瓶颈的开边界道路上,该模型在瓶颈上游模拟出了包括全面模式(GP)、扩张的同步流模式(WSP)、消退的全面模式(DGP)、局部同步流模式(LSP)和交替同步流模式(ASP)在内的五种交通拥塞模式,以及它们在匝道系统的二维流量平面上的分布图谱。所有这些模拟结果与Kerner的实际观测结果和三相交通流理论的推论完全一致。这一工作最重要的意义在于它成功模拟出了各种不同类型的同步流,因而使速度差效应系列模型迈出了从基本图方法到三相交通流理论决定性的一步。相关工作发表于Phys.Rev.E76,026105(2007)。(4)继上一个研究工作成功建立了三相交通流理论框架下的模型之后,我们进一步研究了上一个模型中的一些遗留问题,主要是它尚未能正确模拟从自由流到同步流的一阶相变过程和与此相关的运动同步流(MSP)交通模式。我们在上一个模型的基础上引进了相邻车辆间发生相互作用的有效距离的概念,即规定相邻车辆也只有在近距离相隔的情况下才能够发生相互作用。由此,我们成功地模拟出了从自由流到同步流的自发一阶相变和运动同步流模式。这一改良后的模型,其基本图已经具有三相交通理论中典型的双Z结构特征,与Kerner的理论预言完全吻合。我们还进一步利用该模型分别研究了自由流态和同步流态的时间序列的相关性问题,揭示了这两种不同的交通状态内部结构的不同,并印证了三相交通流理论关于自由流态非平凡特性的预言。此外,我们还研究了该模型的时间车头距分布与优化速度函数的性质。相比三相交通流理论框架下的的前人的模型,我们的模型在模拟的时间车头距分布方面与前人模型的效果相当,都还存在一些关键性的不足之处;但优化速度函数的模拟结果则有了很大的改善,基本上完全复现了实测结果的各个主要特征。至此,我们已经完成了三相交通流理论框架下一次较为完满的建模工作,所建立的模型不但在宏观统计特性上完全复现了交通实测和前人的理论结果,而且在微观特性的模拟上有了重要的进步。这一工作现正处于Physical Review E审稿过程中。更多还原

【Abstract】 In this dissertation,we investigate the Cellular Automaton(CA)models for traffic flow in the theoretical frameworks of both the traditional Fundamental Diagram Approach and the newly-developed Three-phase Traffic Theory.Traffic and transportation systems,whose level of advancement has become one of the most important criterions in evaluating the modernization of a country,are playing important roles in social economy. However,the relatively weaker traffic system constructions versus the high-speed development of social economy,has become a prominent contradictions throughout the whole world.Traffic congestions have caused serious pollution and huge economic ex penses,which with time are even becoming more and more serious.On the other hand, transportation constructions which lack of scientific directions,are not only extremely expensive but also ineffective at all.Therefore,one after another,the developed countries in the world are all devoted into the research programs of traffic engineering and traffic flow theory,in order to discover the basic rules of traffic flow,take hold of proper strategies in traffic managements,and furthermore,to have their transportation systems managed and optimized scientifically.On the other hand,in the viewpoint of academic research,as a classical type of selfdriven systems which are far from equilibrium,traffic flow systems exhibit typical laws of non-equilibrium many body systems evolution with complex interactions,which are ubiquitous in human society.Traffic flow research may help promoting the interdisciplinary developments among statistical physics,fluid mechanics,nonlinear dynamics,application mathematics,traffic engineering,and so on.Therefore,the theoretical research on traffic flow is significant not only in engineering applications,but also in scientific discoveries. And traffic flow modeling,as a important part of theoretical research,provides us available approaches to have the traffic phenomena reproduced and interpreted.Among the modeling approaches,cellular automaton models(CA)is especially popular because of its simple structure and discrete spatial and temporal variables,which makes it easy to simulate the dynamical processes of a huge number of interacting vehicles.Currently,there are two different theoretical frameworks of traffic flow which dominate this area,i.e.,the fundamental diagram approach and the three-phase traffic theory. In both frameworks,researchers have established realistic and logical traffic flow models, and reproduced many traffic phenomena consistent with empirical findings.As the current frontier of theoretical research of traffic flow,three-phase traffic theory distinguished all the traffic states into three traffic phases,i.e.,the free flow phase,the synchronized flow phase and the wide moving jams phase.Three-phase traffic approach can reproduce more realistic results comparing to the fundamental diagram approach when dealing with the bottleneck-induced congestion patterns.As a results,it is gradually recognized by researchers all over the world.In this dissertation,on top of a brief introduction to the research background of traffic flow theory,including the outlines of both the fundamental diagram approach and the three-phase traffic theory,we introduce our own research accomplishments,summarized as following:(1)With cellular automaton modeling approach,we made realizations of the traffic mechanism proposed by Kaupu(z)s et.al.,in which the slow-to-start(s2s)action of each vehicle depends on the length of the cluster which contains the corresponding vehicle.As a result,we established an improved s2s traffic model,which as well as the previous s2s models,can reproduce the hysteresis effect,the metastable states, and the phase-separated phenomenon of traffic.On the other hand,the improved model has the following improved characteristics.First,the improved s2s rules produce self-adaptation effect,which makes the dissolving process of initial jams more rapid and fluent comparing to the same process in previous s2s models.Furthermore, the improved model effectively reduces the systematic perturbations in which little jams continuously form,dissolve and then reform.As a result,it promoted the traffic efficiency remarkably.Second,the improved model characteristically exhibits three distinguishable periods during the dissolving process of initial jams,i.e.,the linearly declining head part,the exponentially declining middle part, and the approximately power-law declining tail,which dynamically reflects the microscopic statistical characters in great details.Third,the improved model exhibits the cluster-size distributions having a single peak at low densities,or double peaks at high densities,which discovers the different origins of the phase-separations corresponding to the two different peaks.Furthermore,the diffusion of data points in the distribution is much less than in previous models,which reflects more explicit characters of phase-separation.This work has been published on Chinese Physics Vol.16,No.11,2007。(2)Combining the NS CA model with the classical car-following model,we got an improved CA model which considers the velocity-difference effect between successive vehicles.This model shows some particular characteristics in numerical simulations.First,it simulates an abnormal hysteresis effect in which the flux relations between homogeneous and inhomogeneous traffic are reversed.Second,the fundamental diagram of this model has two maximums in flux,showing as a doublepeak structure.Through investigations on the spatial-temporal evolutions and the correlation functions,we find both the two points listed above are related to the emergence of one kind of "homogeneous congested traffic",which is quite similar to the synchronized flow in both macroscopic characters and microscopic characters. This model discovers that in some particular cases,inhomogeneous traffic flow may take better utilizations of the traffic capacity of the system comparing to homogeneous flow.On the other hand,although it is essentially a model in the framework of fundamental diagram approach,however,it could also be understood as an intermediate model between the fundamental diagram approach and the three-phase traffic theory,which has shed some light on the research and comparison between the two theoretical frameworks of traffic.This work has been published on Physica A 386(2007):397-406.(3)On top of the previous work mentioned above,we have the model further developed. We introduced the slow-to-start effect into the model,in order to induce the spontaneously phase transition from synchronized flow to wide moving jams.On the other hand,we directly dispersed the equation of the classical car-following model,and incorporates the velocity-difference effect into our model.As a result, we have established a traffic flow model in the framework of three-phase traffic theory. This model can simulate the three traffic phases and the spontaneous first-order phase transition from synchronized flow to wide moving jams rightly.On an open road with isolated on-ramp bottleneck,this model simulates five traffic congested patterns,including General Pattern(GP),Widening Synchronized Pattern(WSP), Dissolving General Pattern(DGP),Localized Synchronized Flow Pattern(LSP)and Synchronized Pattern Alternation of Free and Synchronized Flow(ASP).All these congested patterns are consistent with empirical findings and theoretical deductions of the three-phase traffic theory.This work has accomplished the most important step from the fundamental diagram approach to the three-phase traffic theory.It has been published on Phys.Rev.E 76,026105(2007)。(4)Based on the previous two works,in which we have established a three-phase traffic model,we further studied some unresolved problems previously.In order to reproduce the spontaneous first-order phase transition from free flow to synchronized flow,and the related "moving synchronized pattern"(MSP),which are absent in the previous model,we proposed a limitation of the interaction range between successive vehicles.In the improved model,only vehicles being close enough to each other can have interactions.As a result,the improved model successfully reproduced the expected items mentioned above.The fundamental diagram of the improved model exhibits typical double-Z characteristics of three-phase traffic models, which is well consistent with Kerner’s theory.Furthermore,we studied the correlation functions for free flow and synchronized flow respectively.The analysis results are not only well consistent with empirical findings,but also good illustrations to the nontrivial characteristics of free flow especially.Besides,we also studied the time headway distributions and the optimal velocity(OV)functions of the model.Comparing to previous models in the framework of three-phase traffic theory, this model simulates similar time-headway distributions,which are only partly consistent with empirical results.But the simulation results of the OV functions are greatly improved in this model.The simulations results are in great accordance with empirical findings.Therefore,we have accomplished a successful modeling work in the framework of three-phase traffic theory,in which we have established a CA model whose simulation results are not only consistent with empirical resuits in macroscopic features,but also a great improvement in microscopic features comparing to previous models.This work is currently under the review of Physical Review E.更多还原