快速路交通流时间序列分形维数研究

Research on Fractal Dimensions of Traffic Flow Time Series on Expressway

对取自于北京、沈阳和上海3座城市的4组快速路交通流数据进行分析,判别出交通状态为同步流或自由流。通过改变时间尺度观察时间序列的自相似特性和利用功率谱法判别,发现在两种状态下,系统都具有分形和混沌特性,可以应用相关理论进行研究。应用G-P算法计算了流率和速度序列在不同统计间隔下的关联维,计算了流率、速度的Hausdorff维数,并对计算结果进行了讨论。在此基础上,指出了分维在交通流理论研究中的应用方向。

Four sets of traffic flow data obtained from expressway in Beijing, Shenyang and Shanghai are analyzed , and the traffic states are distinguished as synchronized flow, or free flow state.In both states, the system is fractal and chaotic, which is judged by two means： One is observing the fluctuating of the time series with different intervals （which takes on a characteristic of self-similarity）, and the other is the power spectrum discrirninance, thus the fractal and chaos theories could be applied. G-P arithmetic is adopted to estimate correlation dimensions of flow rate and speed time series drawn from original data by different intervals, and Hausdorff dimension is also estimated. A discussion of the results and the application prospects of fractal dimensions in the research of traffic flow theories are also included in this paper.