This paper analyzes the car following behavioral stochasticity based on two sets of field experimental trajectory data by measuring the wave travel time series ${\tilde{\tau }}_n\left(t\right)$ of vehicle n. The analysis shows that (i) No matter the speed of leading vehicle oscillates significantly or slightly, ${\tilde{\tau }}_n\left(t\right)$ might change significantly; (ii) A follower's ${\tilde{\tau }}_n\left(t\right)$ can vary from run to run even if the leader travels at the same stable speed; (iii) Sometimes, even if the leader's speed fluctuates significantly, the follower can keep a nearly constant value of ${\tilde{\tau }}_n\left(t\right)$. The Augmented Dickey-Fuller test indicates that the time series ${\xi }_n\left(t\right)=d{\tilde{\tau }}_n\left(t\right)/dt$ follows a mean reversion process, no matter the oscillations fully developed or not. Based on the finding, a simple stochastic Newell model is proposed. The concave growth pattern of traffic oscillations has been derived analytically. Furthermore, simulation results demonstrate that the new model well captures both macroscopic characteristic of traffic flow evolution and microscopic characteristic of car following.

本文通过测量波动时间序列，基于两组现场实验轨迹数据，分析了汽车跟随行为的随机性。 ${\stackrel{〜}{\tau }}_{ñ}（Ť）$车辆n。分析表明：（i）领先车辆的速度无论是明显波动还是轻微波动，${\stackrel{〜}{\tau }}_{ñ}（Ť）$可能会发生重大变化；（ii）追随者的${\stackrel{〜}{\tau }}_{ñ}（Ť）$即使领导者以相同的稳定速度行驶，奔跑之间也可能有所不同；（iii）有时，即使领导者的速度波动很大，跟随者也可以保持几乎恒定的${\stackrel{〜}{\tau }}_{ñ}（Ť）$。增强Dickey-Fuller测试表明时间序列${\xi }_{ñ}（Ť）=d{\stackrel{〜}{\tau }}_{ñ}（Ť）/dŤ$无论振荡是否完全发展，都遵循平均回归过程。基于这一发现，提出了一种简单的随机Newell模型。通过分析得出了交通振荡的凹形增长模式。此外，仿真结果表明，新模型很好地捕捉了交通流演变的宏观特征和跟车者的微观特征。