速度梯度模型在限速条件下的小扰动传播分析

Analysis of small disturbance propagation under speed limit based on velocity gradient model

针对以往相关速度梯度模型中初始密度、E值、限速均取定值的现象,在LWR(Lighthill-WhithamRichards)模型中施加限速,不断模拟找到最佳的符合实际交通情况的三个定值,在此基础上分别改变上述三个参数值,得到相关的密度和速度的变化趋势,从而进一步研究此三个参数对交通流的影响。结果表明初始密度为0.035,E值为100,限速为22 km/h时比较符合交通实际情况。由密度结果表明:随着初始密度的增大,小扰动发展成为单个、多个集簇,但其并不是随着初始密度的增加而增加而是先减小再增加;随着E值增大,集簇的数目和小扰动的波动幅度也随之增加;随着限速的增大,集簇的数目和小扰动的波动幅度先减小再增大。同时,通过对每一位置的速度在稳定时刻取标准差得到以下结果:改变这三个参数在限速区间内速度的标准差均有减小的现象,且对速度标准差的影响大小依次为:初始密度、E值、限速。结论表明合理地选择初始密度、限速能够有效缓解交通堵塞现象。

In view of the phenomenon that initial density,E value and the speed limit in previous article related velocity gradient model are fixed,the speed limit was applied in the LWR（ Lighthill-Whitham-Richards） model,simulation was made to find the best values of initial density,E value and speed limit to conform to actual traffic conditions. The change trend of relative density and speed is got,to explores the influence of the three parameters on the traffic flow. It turns out that the best values of initial density,E value and speed limit is 0. 035,100,and 22 km / h. The density results show that with the increase of initial density,small disturbance developed into a single cluster,then multiple clusters,and the number of clusters does not increase with the increase of initial density but decreases and then increases; As the E value increases,the number of clusters and small disturbance volatility also will increase; with the increase of speed limit,the number of clusters and small disturbance volatility decrease first and then increase. At the same time,based on the standard deviation from each position of the speed in a stable moment,it is concluded that with the changing of the three parameters the standard deviation of speed is reduced in the range limit,and their influence on standard deviation of speed from big to small is initial density,E value and speed limit,which shows that reasonable choice of initial density,E value and speed limit can alleviate traffic jam phenomenon.