本文選題：交通流 + ASEP模型�。� 參考：《昆明理工大學(xué)》2017年碩士論文

【摘要】：交通擁堵所引發(fā)的經(jīng)濟(jì)損失、環(huán)境污染、交通事故等問題已經(jīng)引起了廣大學(xué)者們的關(guān)注。如何緩解交通壓力,避免道路發(fā)生交通堵塞已經(jīng)成為人們急需解決的難題。為了能更好的對交通系統(tǒng)進(jìn)行規(guī)劃調(diào)整,交通流理論作為一種研究交通擁堵機(jī)制的基礎(chǔ)理論應(yīng)運而生,并在短短幾十年間迅速發(fā)展起來。迄今為止,已有上百個交通流模型被提出,經(jīng)過幾代人不斷的改進(jìn)與完善,非對稱簡單排它過程因其簡單易懂、計算精度高及易于拓展等特點從眾多微觀交通模型中脫穎而出。另外,該模型可對非平衡系統(tǒng)中發(fā)生的一些復(fù)雜現(xiàn)象(如自發(fā)對稱性破缺、邊界條件及非平衡導(dǎo)致的相變等)進(jìn)行模擬,這一性質(zhì)使其成為了研究交通流理論的重要模型,同時也成為了一種研究非平衡現(xiàn)象的重要手段而被廣泛應(yīng)用于物理、化學(xué)、生物等領(lǐng)域。本文分別采用平均場理論的解析方法和蒙特卡洛計算機(jī)模擬對三種以實際道路為原型的ASEP模型進(jìn)行了研究。第三章以粒子入口概率不同的耦合雙通道道路為原型,考慮通道中的粒子僅能進(jìn)行單方向變道,在建立ASEP模型的過程中同時引入粒子跳躍率這一變量,并采用隨機(jī)更新的規(guī)則,分析其對耦合雙通道系統(tǒng)的影響。結(jié)果發(fā)現(xiàn),系統(tǒng)相圖與兩格子鏈的粒子跳躍率有關(guān),與變道概率無關(guān)。當(dāng)兩格子鏈的粒子跳躍率相同時,相圖包含六種穩(wěn)態(tài)相,粒子跳躍率不同時,系統(tǒng)相圖中會出現(xiàn)第七種穩(wěn)態(tài)相(MC,MC)。對該模型進(jìn)行計算機(jī)模擬得出的結(jié)果與理論解析的結(jié)果吻合。第四章以出入口限速道路為原型,采用隨機(jī)更新規(guī)則,分別對左邊界和右邊界處粒子跳躍率不同的ASEP模型進(jìn)行研究,分析邊界處粒子跳躍率不同對系統(tǒng)的影響。發(fā)現(xiàn):兩個模型的相圖均以2p=q2作為MC相是否存在的界限。當(dāng)2p≤q2時,系統(tǒng)中不存在MC相,而當(dāng)2pq2時,兩模型與一般ASEP模型的相圖類似。兩個模型的相圖中均存在三種穩(wěn)態(tài)相時,減小p/q的值,入口限速模型中的HD相縮小,出口限速模型中的HD相擴(kuò)大。模擬結(jié)果與計算結(jié)果一致。第五章以環(huán)狀交叉路口為原型建立了 ASEP模型,采用全局并行更新的更新規(guī)則,設(shè)定粒子可在兩個遠(yuǎn)離邊界的特殊格子處分別以概率p和q進(jìn)入或離開系統(tǒng)。通過對該模型的研究發(fā)現(xiàn),系統(tǒng)相圖中共包含七個穩(wěn)態(tài)相,且改變p或q的值,相圖中穩(wěn)態(tài)相的面積會擴(kuò)大或縮小,但不會發(fā)生消失的情況。采用平均場理論解析得到的結(jié)果與計算機(jī)模擬的結(jié)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，

本文編號：2042797