ASEP模型在交通流中的应用

发布时间：2018-06-20 03:46

  本文选题：交通流 + ASEP模型　； 参考：《昆明理工大学》2017年硕士论文

【摘要】：交通拥堵所引发的经济损失、环境污染、交通事故等问题已经引起了广大学者们的关注。如何缓解交通压力,避免道路发生交通堵塞已经成为人们急需解决的难题。为了能更好的对交通系统进行规划调整,交通流理论作为一种研究交通拥堵机制的基础理论应运而生,并在短短几十年间迅速发展起来。迄今为止,已有上百个交通流模型被提出,经过几代人不断的改进与完善,非对称简单排它过程因其简单易懂、计算精度高及易于拓展等特点从众多微观交通模型中脱颖而出。另外,该模型可对非平衡系统中发生的一些复杂现象(如自发对称性破缺、边界条件及非平衡导致的相变等)进行模拟,这一性质使其成为了研究交通流理论的重要模型,同时也成为了一种研究非平衡现象的重要手段而被广泛应用于物理、化学、生物等领域。本文分别采用平均场理论的解析方法和蒙特卡洛计算机模拟对三种以实际道路为原型的ASEP模型进行了研究。第三章以粒子入口概率不同的耦合双通道道路为原型,考虑通道中的粒子仅能进行单方向变道,在建立ASEP模型的过程中同时引入粒子跳跃率这一变量,并采用随机更新的规则,分析其对耦合双通道系统的影响。结果发现,系统相图与两格子链的粒子跳跃率有关,与变道概率无关。当两格子链的粒子跳跃率相同时,相图包含六种稳态相,粒子跳跃率不同时,系统相图中会出现第七种稳态相(MC,MC)。对该模型进行计算机模拟得出的结果与理论解析的结果吻合。第四章以出入口限速道路为原型,采用随机更新规则,分别对左边界和右边界处粒子跳跃率不同的ASEP模型进行研究,分析边界处粒子跳跃率不同对系统的影响。发现:两个模型的相图均以2p=q2作为MC相是否存在的界限。当2p≤q2时,系统中不存在MC相,而当2pq2时,两模型与一般ASEP模型的相图类似。两个模型的相图中均存在三种稳态相时,减小p/q的值,入口限速模型中的HD相缩小,出口限速模型中的HD相扩大。模拟结果与计算结果一致。第五章以环状交叉路口为原型建立了 ASEP模型,采用全局并行更新的更新规则,设定粒子可在两个远离边界的特殊格子处分别以概率p和q进入或离开系统。通过对该模型的研究发现,系统相图中共包含七个稳态相,且改变p或q的值,相图中稳态相的面积会扩大或缩小,但不会发生消失的情况。采用平均场理论解析得到的结果与计算机模拟的结果基本相同。
[Abstract]:The economic loss, environmental pollution and traffic accidents caused by traffic congestion have attracted the attention of scholars. How to relieve traffic pressure and avoid traffic jam has become an urgent problem. In order to better plan and adjust the traffic system, traffic flow theory, as a basic theory to study traffic congestion mechanism, emerged as the times require, and developed rapidly in just a few decades. Up to now, hundreds of traffic flow models have been proposed. After several generations of continuous improvement and improvement, asymmetric simple exclusion process is distinguished from many microscopic traffic models because of its simplicity, high calculation accuracy and easy to expand. In addition, the model can simulate some complex phenomena (such as spontaneous symmetry breaking, boundary conditions and phase transitions caused by non-equilibrium) in non-equilibrium systems, which makes it an important model for the study of traffic flow theory. At the same time, it is widely used in physics, chemistry, biology and so on. In this paper, three ASEP models based on actual road are studied by using the analytical method of mean field theory and Monte Carlo computer simulation. In chapter 3, the coupling two-channel path with different particle entry probability is taken as the prototype, considering that the particle in the channel can only be changed in one direction, the variable of particle hopping rate is introduced in the course of establishing the ASEP model, and the rule of random update is adopted. The influence of the system on the coupled two-channel system is analyzed. It is found that the phase diagram of the system is related to the particle hopping rate of the two lattice chains and independent of the probability of changing the trace. When the particle hopping rate of the two lattice chains is the same, the phase diagram contains six stable phases. The results obtained by computer simulation are in agreement with those obtained by theoretical analysis. In chapter 4, the ASEP models with different particle hopping rates at left and right boundaries are studied by using random update rules, and the effects of different particle hopping rates on the system are analyzed. It is found that the phase diagrams of the two models take 2p=q2 as the boundary of the existence of MC phase. When 2p 鈮，

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