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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2022, Vol. 56 Issue (8): 1553-1559    DOI: 10.3785/j.issn.1008-973X.2022.08.009
    
Stochastic optimal velocity car-following model based on quantile regression
Yi-yong PAN(),Xing-yu GUAN
College of Automobile and Traffic Engineering, Nanjing Forestry University, Nanjing 210037, China
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Abstract  

The optimized velocity function was improved based on quantile-regression method, in order to study the influence of traffic flow heterogeneity on car-following behavior. The parameters of the improved optimized velocity function were calibrated according to the actual traffic flow data, and the hypothesis test of the parameter results was carried out. Combined with the improved optimized velocity function and the full speed difference car-following model, a stochastic optimized velocity car-following model was established, and the stability conditions of the car-following model were deduced by using Fourier transform theory. A loop lane simulation platform was built to carry out numerical experiments on the car-following model. Results show that the improved optimized velocity function can better reflect the impact of traffic flow heterogeneity on traffic flow. There was a positive correlation between the time when the single quantile team reached the stable state and the quantile. The time to reach steady state was decreased with the increase of the number of vehicles at 0.5 quantile in the multi quantile fleet. Compared with the single quantile fleet, the proposed multi quantile fleet can truly reflect the complex operation of traffic flow.

Key words： traffic engineering      car-following model      nonlinear quantile-regression calibration      optimal velocity model      traffic flow theory     
Received: 17 August 2021      Published: 30 August 2022
CLC:  U 491  
Fund:  国家自然科学基金资助项目（51508280）；南京林业大学高学历人才基金资助项目（GXL2014031）
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Yi-yong PAN
Xing-yu GUAN
Cite this article:

Yi-yong PAN,Xing-yu GUAN. Stochastic optimal velocity car-following model based on quantile regression. Journal of ZheJiang University (Engineering Science), 2022, 56(8): 1553-1559.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2022.08.009     OR     https://www.zjujournals.com/eng/Y2022/V56/I8/1553


基于分位数回归的随机优化速度跟驰模型

为了研究交通流异质性对车辆跟驰行为的影响，基于分位数回归方法改进优化速度函数. 根据实际交通流数据对改进的优化速度函数进行参数标定，并对参数结果进行假设检验，结合改进的优化速度函数和全速度差跟驰模型建立随机优化速度跟驰模型，利用傅里叶变换理论推导跟驰模型的稳定性条件，并搭建环形车道仿真平台对跟驰模型进行数值实验. 结果表明：改进的优化速度函数能更好地反映交通流异质性对交通流的影响；单一分位点车队达到稳定状态的时间与分位点呈正相关；多分位点组合车队随着0.5分位点车辆数的增加，达到稳定状态的时间减少. 提出的多分位点车队相比于单一分位点车队可以更真实地反映交通流复杂的运行状况.


关键词： 交通工程,  跟驰模型,  非线性分位数回归,  优化速度函数,  交通流理论 
Fig.1 Speed distribution under different traffic flow densities
$\tau $ $V_1^\tau $ $V_2^\tau $ $C_1^\tau $ $C_2^\tau $ $\tau $ $V_1^\tau $ $V_2^\tau $ $C_1^\tau $ $C_2^\tau $
0.1 10.028 6.396 0.081 2.071 0.6 11.040 6.737 0.121 2.304
0.2 10.423 6.476 0.095 2.226 0.7 10.990 7.051 0.115 2.059
0.3 10.608 6.615 0.101 2.230 0.8 11.195 7.139 0.120 2.085
0.4 10.840 6.408 0.125 2.619 0.9 11.512 7.327 0.129 2.071
0.5 10.908 6.608 0.119 2.358 ? ? ? ? ?
Tab.1 Fitting results of quantile regression models
Fig.2 Fitting curves of speed-density relationship
Fig.3 Speed distribution under different densities based on quantile regression
k
（辆/km） 		原始数据速度分布 分位数回归速度拟合值分布
SK N/
（km·h?1） 		M/
（km·h?1） 		SK N/
（km·h?1） 		M/
（km·h?1）
5.03 0.003 17.780 17.963(0.352) ?0.086 17.230 17.564(0.447)
35.20 ?1.098 12.500 16.381(0.224) ?0.480 12.694 15.068(0.140)
47.77 1.049 11.250 7.510(0.191) 1.435 11.775 7.581(0.164)
Tab.2 Speed distribution of raw data and quantile-regression fitting value
Fig.4 Stability critical curve of FVD model（ $\lambda $=0.4）
Fig.5 Circular lane car following simulation scenario
Fig.6 Speed distribution at different quantiles
Fig.7 Speed distribution of mixed driving at multiple quantiles
Fig.8 Displacement range of different quantiles
Fig.9 Speed change of different quantiles
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