跟車現象及穩定性之微觀分析

Abstract

隨著對運輸品質的要求增加，近年來大力發展智慧型運輸系統。而智慧型運輸系統中的先進旅行者資訊系統及先進交通管理系統，則各需車流模式提供交通資訊預估及車流分析。因此本研究發展一簡單的車流模式，以期其能描述車流現象，且不需複雜的計算以節省模擬時間，並能據以分析車流性質，最終並可延伸至巨觀車流模式。 本研究所提出的跟車模式引入外生變數－個人最大速度，以描述駕駛人的差異性，及不同外在環境所造成的影響。而模擬結果及數學分析顯示，本模式確能反應並且解釋在相同的車流狀況下，為何不同的駕駛人採取不同的行為反應。 為瞭解本模式是否確能反應車流現象，本研究探討均衡及非均衡狀態下的各種車流現象，並且探討系統收斂到均衡狀態的條件（穩定性分析）及時間。在穩定性分析方面，本模式發現若個人最大速度與車流均衡速度差異不大，則車流會收斂到均衡狀態；反之，則車流會一直處於非均衡狀態。此一分析可解釋為何在擁擠的狀況下，車流常呈現不穩定的狀態。此外，在車流由非均衡狀態收斂到均衡狀態所需的鬆弛時間方面，模擬結果顯示，個人最大速度與車流均衡速度差異越大，其鬆弛時間越長。在均衡狀態的探討方面，均衡時的車間距只取決於均衡速度與個人最大速度，與起始狀態無關。個人最大速度愈大者，其駕駛行為越激進，所保持的車間距也愈短。另外假設駕駛人為均質，將微觀均衡狀態延伸到巨觀均衡狀態，則自由流速率越高者其容量愈高。不同的參數值，其車流基礎構圖所呈現出來的形態也不同。而在非均衡狀態方面，本研究探討走走停停、closing-in、shying-away、及車流磁滯現象，並分別進行數學分析及提供數值範例。數學分析顯示，在相同的車流狀況下，激進的駕駛人可能選擇加速，而保守的駕駛人可能選擇減速。而單一駕駛人，其在加速及減速上的速度與車間距之間的關係並不相同；不同的起始條件及邊界條件，將可模擬出不同的車流磁滯現象形態。

The increment of vehicle number and life quality request lead to develop ITS in the recent years. ATIS needs traffic flow model to provide real time prediction. ATMS needs traffic flow models to analyze traffic flow properties so that they can provide better traffic control strategies. Thus, this dissertation aims to develop a simple car-following model which can analyze traffic properties, represent traffic flow phenomena, save execution time, and have potential for extending to macroscopic models. The proposed model employs driver’s individual maximum speed as an exogenous variable to reflect the external environment and driver’s characteristics. The proposed model can explain why speeds and spacing differ among drivers even when the driving conditions are identical. This dissertation discusses the equilibrium and disequilibrium states of the proposed model, local stability between two moving cars, and relaxation time of different equilibrium states. The stability analysis indicates that traffic is stable if driver’s individual maximum speed is close to the equilibrium speed. Otherwise, if the difference between the individual maximum speed and the equilibrium speed is large, traffic may be unstable. It can explain why heavy traffic is unstable. Furthermore, numerical examples show that relaxation time increases if the difference between the individual maximum speed and the equilibrium speed increases. This dissertation derives the equilibrium state of the proposed model, and it indicates that equilibrium state is only dependent on the individual maximum speed and the equilibrium speed, not on initial conditions. A driver with higher individual maximum speed is more aggressive and keeps shorter equilibrium spacing under identical equilibrium speed. Fundamental diagrams based on microscopic equilibrium state and homogeneous drivers are also discussed. The capacity increases with free flow speed, and different parameter values result in different fundamental diagram patterns. Some traffic phenomena of disequilibrium states are discussed, such as closing-in, shying-away, stop-and-go, and traffic hysteresis. The mathematical analysis indicates that aggressive drivers may decide to accelerate while conservative drivers may decide to decelerate under identical driving condition. The speed-spacing relationships for acceleration and deceleration traffic are different. Different initial conditions and boundary conditions result in various traffic hysteresis patterns.