運用位勢理論構建車流模式之基礎研究

Abstract

近年來由於經濟的快速成長、人口及國民所得的提高，使得車輛的擁有數及道路的使用率大幅增加。而台灣地區地狹人稠，道路容量在短期內無法大幅擴充，面對不斷升高的車輛數目，早已超出道路設計時的最大容量，造成了各地區交通壅塞的嚴重情況。交通壅塞除了用路者的時間損失外，更會發生能源損失、空氣污染及噪音的問題，所造成的社會成本十分龐大。因此，建立一良好的車流模擬模式，輔助交通工程師規劃運輸系統管理與設計相關的控制措施，以解決交通壅塞情況便顯得重要。 本研究提出一與空間及容量有關之車流模式，此模式允許當車流密度發生變化時，車流模式仍就受空間與容量之影響。並根據向量場理論，說明此模式為一保守場，運用位勢理論構建含容量變化之車流模式，並利用格林(Green)定理證明此模式在不同邊界條件下解之存在及唯一性，且對此模式討論在不同狀況下之一般解。 接著利用電子計算機來模擬車流模式之有限差分演算法數值解，並將結果透過電腦繪圖描繪出車流模式隨著空間及容量的變動情形。本趼究比較不同條件下的車流模式之數值解與解析解，研究的結果可以發現，數值解與解析解的結果近似，因此，可以利用數值解求解更複雜之車流模式。 最後，本研究以一簡單的道路狀況來探討在不同容量下之車流量變化情形，以作為此車流模式於實際上的應用情形。

A new traffic flow model based on spatial and capacity has been proposed. By field theory, we have claimed the flow is conservation field. Furthermore an existence and uniqueness of the solution for the model has been also proved by Green's identity. Some general analytical solution formula has discussed for proposed model. In order to analyze for physical based model problem, numerical solutions are also given and compared with the analytical results. Congestion is defined to be the breakdown of fluent traffic flow due to the inefficiency of the transport link to handle the volume of traffic. This is precipitated by a multitude of disruptive phenomena within the dynamics of traffic flow. Congestion and traffic flow will be dealt within a framework of three dimensions composed of geographic space (x, y), capacity(c) under steady state assumption. Capacity is measured as a third dimension orthogonal to the plane and is defined to be the ability to transfer traffic in space. Conventional traffic flow model is widely used for studying some macroscopic traffic flow phenomena. The main property of that approach is based on mass, energy or momentum conservation law. In this thesis, a new traffic flow model so called traffic dispersion model is presented. And the main concept of this new model is that it takes the potential approach for the flow, density, and capacity relationships. We also proposed implantation solution approaches and algorithms for the proposed model and method in detail.