  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 follower's 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.
