Stochastic factors and string stability of traffic flow: Analytical investigation and numerical study based on car-following models

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.