具有自我規律性的匝道交通系統之特性探討

Abstract

我們的工作是建立在由Bando等人在八零年代所提出所謂的最適速度跟車交通模型上。我們在原本的單線道系統上加上了了一個匝道，並且在空間上採用週期條件。車輛採取一些策略來進入或離開匝道。數值模擬的方式顯現系統的一些特性：系統似乎有一個極為強烈的穩定解，在某些車輛數目的區間，以及不同的起始條件或是系統幾何（主支線道的長度），系統都會保有固定的型態以及流量。分析之後的結果我們認為應該要引入所謂延遲微分方程式(delay differential equation, or retarded functional differential equation, RFDE)來描述這個系統。我們提出一個可能的近似變分原理來解釋固定流量的現象。我們也將在最後提出近似的物理詮釋。

This work was based on the so-called optimal velocity car-following model proposed by Bando et al. One more route in some region was added for the spatially periodic traffic system. Cars adopt several strategies to enter and leave the branching region. Numerical simulations were done to verify the evolution of the system. The system seems to have a robust stable solution: Within certain range, it appears to have a fixed flux, irrespective of the car number, the initial condtions and the geometry (length of the main and the branch). We tried to analyze such phenomenum and verify the essentiality of introducing delay di¤erential equations. An approximate variational principle with a delay argument is constructed and used to interpret the…fixed-flux phenomenon. The meaning of the approximate scheme is also discussed.