  The emergence dynamics of traffic instability has always attracted particular
attention. For several decades, researchers have studied the stability of
traffic flow using deterministic traffic models, with less emphasis on the
presence of stochastic factors. However, recent empirical and theoretical
findings have demonstrated that the stochastic factors tend to destabilize
traffic flow and stimulate the concave growth pattern of traffic oscillations.
In this paper, we derive a string stability condition of a general stochastic
continuous car-following model by the mean of the generalized Lyapunov
equation. We have found, indeed, that the presence of stochasticity
destabilizes the traffic flow. The impact of stochasticity depends on both the
sensitivity to the gap and the sensitivity to the velocity difference.
Numerical simulations of three typical car-following models have been carried
out to validate our theoretical analysis. Finally, we have calibrated and
validated the stochastic car-following models against empirical data. It is
found that the stochastic car-following models reproduce the observed traffic
instability and capture the concave growth pattern of traffic oscillations. Our
results further highlight theoretically and numerically that the stochastic
factors have a significant impact on traffic dynamics.
