This paper analyzes the car following behavioral stochasticity based on two sets of field experimental trajectory data by measuring the wave travel time series of vehicle n. The analysis shows that (i) No matter the speed of leading vehicle oscillates significantly or slightly, wave travel time might change significantly; (ii) A followers wave travel time can vary from run to run even the leader travels at the same stable speed; (iii) Sometimes, even if the leader speed fluctuates significantly, the follower can keep a nearly constant value of wave travel time. The Augmented Dickey-Fuller test indicates that the time series the changing rate of wave travel time 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.
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