Abstract: In order to simulate the traffic flow speed-density relationship accurately, stochastic fundamental diagram model of traffic flow speed-density relationship was established based on quantile regression. The quantile regression was used to fit the speed-density curve to obtain clusters of speed-density curves at different quantile levels. The hypothesis test and confidence interval calculation were carried out for the parameter values, and the fitting results were numerically analyzed. The calculation results show that the proposed model can reflect the relationship between traffic flow speed and density at different quantile levels. Compared with Greenshields quantile model and Newell quantile model, the error of Northwestern quantile model decreases by 54.1% and 33.6% respectively. The proposed method provides a methodology for the construction of traffic flow stochastic fundamental graph model, which can be extended to other future traffic flow models and has a very important application in traffic flow theory.

Key words: traffic engineering; fundamental diagram of traffic flow; speed-density relationship; quantile regression; parameter fitting

摘要： 为了准确模拟仿真交通流速度-密度关系，基于分位数回归建立交通流速度-密度关系随机基本图模型。利用分位数回归对速度-密度曲线进行参数拟合，获得不同分位数水平的速度-密度曲线簇，对参数值进行了假设检验和置信区间的计算，并对拟合结果进行数值分析。计算结果表明：提出的模型可以反映不同分位数水平下交通流速度和密度的关系，其中Northwestern分位数模型相较于Greenshields分位数模型和Newell分位数模型误差值分别降低了54.1%和33.6%；所提出的方法为交通流随机基本图模型构建提供了一个方法论，可以推广到其他未来交通流模型,在交通流理论中有非常重要的应用。

关键词: 交通工程；交通流基本图；速度-密度关系；分位数回归；参数拟合