【作者】 孟剑平；

【导师】 戴世强；

【作者基本信息】 上海大学 ， 流体力学， 2008， 博士

【摘要】 本文从介观和微观角度研究交通流的建模和模拟。面对我国交通平面、混合与低速的实际特征以及交通规划、管理实践中的信息化与智能化的趋势,基于Nagel-Schreckenberg(NaSch)元胞自动机模型,建立了适用于汽车-摩托车混合交通的改进型模型,并针对一类较为实际的双路径交通情境研究了实时信息反馈对交通系统的影响;为了克服传统的介观模型中包含复杂的积分微分项所导致的困难,建立了道路交通流的格子玻尔兹曼模型,并将其推广到城市网络交通流的建模研究中。相关的模拟表明,所建立的模型可以再现交通流的复杂非线性动力学特性。全文主要内容如下:一.汽车与摩托车混合交通建模研究基于划分“虚拟子车道”的思想,推广了描述单车道汽车流的NaSch模型,首次尝试建立了汽车-摩托车混合交通流模型。通过在周期性边界条件下进行的数值模拟,详细考察了这种混合交通流的流量-密度关系以及摩托车的“换道”行为。模拟发现,在摩托车“换道”行为的影响下,最大汽车流量明显降低,而最大总体车流量则随着摩托车密度的增加而先增后减,且模型中总体车流由自由流向拥挤交通的相变是平滑的。摩托车“换道”率随汽车密度演化的趋势相当复杂,但最终将随着汽车密度的增加而趋于零。所发现的另一个令人感兴趣的事实是:随着摩托车密度增加,摩托车“换道”率先增后减,与前人在多车道纯汽车流中发现的现象十分相似。当摩托车密度较小时,“换道”行为几乎无助于提高摩托车流量。但是,当摩托车密度足够大时,“换道”行为可显著提高摩托车流量,而且这时随汽车密度增加,摩托车流量逐渐降低并趋于与摩托车NaSch模型一致。数值模拟结果表明,除非摩托车密度甚大而汽车密度甚小,实施摩托车与汽车分道行驶确有必要。二.双路径交通流决策动力学研究针对一类包含长短不同路径的双路径交通情境,基于NaSch元胞自动机模型,讨论了各种信息反馈策略对交通系统的影响。分析了现有策略的不足之处,提出了一类预测策略与无预测策略联合使用的新途径。在适当的开放边界条件下进行的数值模拟显示,与无信息反馈相比,信息反馈策略可在一定程度上提高交通效率,但各种信息反馈策略的效果并不相同。一般而言,双路径策略优于单路径策略,有预测策略优于无预测策略。除了一些有预测策略以外,其它策略都会引起平均密度和平均速度的振荡。此外,还考察了各种信息反馈策略对双路径系统中长路径的影响。模拟结果还表明,各种信息反馈策略都或多或少地对两条路径中长路径上的交通产生影响,不过,有预测策略产生的影响通常小于无预测策略。但在长路径上的交通负载过重的情况下,即使是有预测策略在提高交通效率等方面也无明显效果。本项研究证实:控制交通的正确诱导策略极其重要。三.道路交通流的格子玻尔兹曼模型建模研究由于存在复杂的积分微分项,直接应用传统的介观交通流模型通常非常困难。因此,本文基于类Bhatnagar-Gross-Krook(BGK)近似与时间和相空间的离散化,建立了道路交通流的格子玻尔兹曼模型(lattice Boltzmann model,LBM)。该模型属于离散模型,具有形式简洁、参数物理意义明确的特点。因此,利用该模型可以方便地实现交通流模拟。随后,文中利用Taylor展开与Chapman-Enskog展开考察了模型的宏观动力学特性。为检验模型的有效性,在周期性边界条件下进行了数值模拟。结果显示:模型能够合理地再现基本图,且能够捕捉一些基本的非线性物理现象,如亚稳态和时停时走交通等。结果表明,格子玻尔兹曼模型是一种行之有效的交通模型。四.基于格子玻尔兹曼模型的城市网络交通流建模研究揭示道路交通网络的动力学特性具有重要意义,目前在介观层次上研究交通网络的工作尚不多见。基于将Biham-Middleton-Levine(BML)元胞自动机模型与路段格子玻尔兹曼模型相耦合的思想,我们建立了一个适用于城市网络交通流的格子玻尔兹曼模型。该模型通过将具有红绿灯的交叉口视为随时间演变的边界条件来实现对城市网络交通流的介观描述。通过数值模拟,详细考察了平均速度随时间的演化行为,得到了与Chowdbury-Schadschneider(ChSch)元胞自动机模型相符的结果,而且由于我们的离散模型具有统计噪声较小的特征,因而具有较高的计算效率。研究表明,只要引用合理的假设和技巧,介观模型在交通流研究中大有用武之地。更多还原

【Abstract】 This thesis is concerned with the modeling and simulation of traffic flows from mesoscopic and microscopic viewpoints. In view of the realistic characteristics of plane, low-velocity and mixed transportation systems in China and the trend of widely applying real-time information in traffic planning and management, based on the Nagel-Schreckenberg (NaSch) cellular automaton (CA) model, an improved CA model is proposed for mixed traffic flow with motorcycles, and the decision dynamics in a realistic two-route scenario is investigated. Then in order to overcome the difficulties in applying the traditional mesoscopic models with the appearance of integro-differential terms in the models, a lattice Boltzmann model for road traffic flows is established and then extended to modeling and simulating urban network traffic flows. The related simulations show that the presented models can be employed to reproduce the complicated nonlinear dynamic characteristics in traffic flows.The main contents of the dissertation are as follows.I. Cellular automaton model for the mixed traffic flow with motorcyclesA single-lane cellular automaton model is firstly proposed to simulate the traffic flow of cars mixed with motorcycles by dividing a single lane into three virtual sub-lanes and extending the NaSch model for single-lane car flows. Through performing numerical simulations under the periodic boundary conditions, some flow-density relations and the "lane-changing"behavior of motorcycles are investigated in detail. It is found that the maximum car flow remarkably decreases due to the "lane-changing "behavior of motorcycles, while the maximum total flow increases first and then decreases with increasing motorcycle density. Moreover, the phase transition of the total flow from the free flow to the congested flow is smooth in this model. The "lane-changing" rate of motorcycles will finally decrease to zero with the increase of the car density. But its evolutionary trend is considerably complex. Another interesting fact found in the simulation is that, with the increase of the motorcycle density, the "lane-changing" rate increases first and decreases later. This phenomenon is very similar to the findings in previous work on multi-lane pure car flows. The "lane-changing" is almost of no use in increasing the flow of motorcycles as the motorcycle density is small. But it distinctly causes the increase in the flow of motorcycles as the motorcycle density is sufficiently high, and in this density regime, the flow of motorcycles gradually decreases to the one given with the NaSch model for motorcycles with the increase of the car density. The simulation results indicate that it is necessary to set a barrier or a partition lane for separating the motorcycle flow from the car flow except for the situation of higher motocycle density and lower car density.II. Decision dynamics in a realistic two-route scenarioThe optimal information feedback is of great importance in making full use of the existing transportation resources and improving the performance of traffic systems. Thus, several information feedback strategies were proposed in literature and their effects on the traffic systems were also investigated. However, there is still a paradox remaining in some research reports that no information feedback strategy seems to be the best ones. For examining this paradox, a further study is conducted with a realistic two-route traffic scenario containing a longer route and a shorter route and appropriate open boundary conditions. The effects of several previous strategies on traffic systems are reconsidered in detail. Meanwhile, through analyzing the shortcomings of the existing strategies, a new approach of combing a prediction strategy with various prediction-free strategies is proposed in this work. By conducting numerical simulations, it is found that all the strategies can more or less improve the efficiency compared with the situation with no information feedback. However, various information feedback strategies might have different consequences. Generally speaking, two-route strategies are superior to single-route ones, and strategies based on prediction are better than prediction-free ones. Except for several strategies with prediction, most of the strategies will cause the oscillations of average density and velocity. In addition, the influence of various strategies on the traffic on the longer route is studied, which proves to exist in general, but less remarkable for the strategies with prediction. Especially, the appropriate strategy with prediction is helpful for improving the traffic efficiency and stabilizing the traffic flow. Nevertheless, further simulations show that the information feedback is not very helpful for improving the efficiency if the traffic load on the longer route is too heavy. This study shows that it is essential to correctly choose information feedback strategies.III. Lattice Boltzmann model for road traffic flowTraditional mesoscopic models for traffic flows are usually difficult to be directly employed because of the appearance of integro-differential terms in the models. Thus, a more applicable lattice Boltzmann model (LBM) for road traffic flows is constructed on the basis of the Bhatnagar-Gross-Krook (BGK)-like approximation for the Boltzmann equation and its discretization in time and phase-space. The so-obtained model is a simpler discrete version of the gas kinetics model with the physically meaningful distinct parameters, which can be easily used to investigate numerically the behavior of traffic flows. In consequence, the macroscopic dynamics of the model is derived through the Taylor expansion and Chapman-Enskog expansion. For validating the model, numerical simulations are conducted under the periodic boundary conditions. It is found that the presented model could reasonably reproduce the fundamental diagram. Moreover, certain interesting physical phenomena can be captured, such as the metastability and stop-and-go phenomena, etc. The results imply that the presented model is one of the effective and efficient traffic models.IV. Modeling of urban network traffic flows with lattice Boltzmann modelIt is of great importance to uncover the characteristics of traffic networks. However, there have appeared few researches concerning kinetics models for traffic networks. Thus, an LBM for road traffic networks is proposed by incorporating the ideas of the Biham-Middleton-Levine (BML) CA model into the LBM for road traffic. In the present model, situations at intersections with the traffic signals are treated as a kind of boundary conditions varying with time. Thus, the network traffic flow could be described in the mesoscopic level. By performing numerical simulations under the periodic boundary conditions, the evolution of average velocity is investigated in detail. The numerical results agree quite well with those given by the Chowdhury-Schadschneider (ChSch) CA model. Furthermore, the statistical noise is reduced in this discrete kinetics model, and thus the present model has considerably higher computational efficiency. This study shows that the meso-scopic traffic model could find its extensive applications, provided that reasonable assumptions and techniques are introduced.更多还原