車流動力學之連續減速模式

Abstract

欲發展良好的交通控制解決交通問題需要有充足的資訊，在相關資訊中最重要且不易估算的就是車流量的預測，車流模式的發展就是朝此方向之研究，關於介觀車流的相關研究國內相關研究仍未完整，尚有許多介觀車流議題需要被討論與研究，所以本研究欲藉由回顧較具重要性的介觀的車流動力學模式，將其重要貢獻與特性整理，並且建構一可較真確描述道路車流情形之介觀車流模式。 本研究引入具有物理意義之減速度考慮項目，放鬆交互影響項中瞬時速度變化與未考慮有限空間因素影響，藉由將這些特性納入並建構一新的介觀車流之動力學方程之中；並且利用動差函數方式將本研究所建構的介觀模式積分，可以獲得以巨觀參數─密度 、平均速度 與變異數 為主的巨觀方程式；而後再以特徵速度、均衡解與數值模擬加以分析該模式的特性，並獲得因本研究引入等減速度可比以往研究的模式可多加解釋的特性，比較不同超車機率下不同的加速度值，在低的超車機率下，等減速度會比較有差別，在高的超車機率下，等減速度看不出差別，因為可很自由的超車情況下，使用到等減速度的車輛相形較少，所以對整體較看不出差別。由此可知本研究所建構的介觀車流動力學模式可較真確描地述更多車流情形。另外在撰寫論文時，將本研究的想法與行為意義清楚傳達，並將過程中的數學推導詳細記錄，希冀能對於介觀車流有興趣者有所幫助，以期許將來能有利於實際應用的發展。

In order to develop traffic control to solve traffic problem, we need sufficient information. The related and the most important information is to estimate quantity of traffic flow. Developing traffic flow model is one of ways to research. However, the research about mesoscopic traffic flow, gas-kinetic traffic flow, is not yet complete so we want to review some important researches and arrange the focus. And we construct a gas-kinetic traffic flow model in order to describe real traffic more. In this research, we introduce uniform deceleration with physical meaning to relax instant velocity-changing and not consider finite space in interaction term and construct a new model. Then we use momentum function to obtain three macroscopic models with density , average velocity and variance . We use characteristic velocity, equilibrium and numerical simulation to analysis the accent of our model, and we know our model could describe more phenomenon than others. Compared with different uniform decelerations in different passing probability conditions, we could observe that different uniform decelerations make difference in smaller passing probability. Different uniform decelerations make no difference in bigger passing probability, because cars use few uniform decelerations in dilute traffic. Therefore, our research could describe more traffic phenomenon. Besides, we explain our thought and the meaning of our model clear, and record mathematic processes explicitly. We hope this research could help those who are interested in mesoscopic traffic flow and help the development of real application.