A dynamic and stochastic perspective on time headway in traffic oscillations and its implications for traffic safety

Traffic oscillations refer to the alternating patterns of vehicle deceleration and acceleration in congested conditions, which usually create significant safety concerns on freeways. Thus, it is imperative to understand the mechanisms of traffic oscillations and their underlying safety implications. This paper presents a novel approach to exploring the combined effects of dynamic time headway (DTH) and stochasticity on traffic oscillations during car-following. Using high-precision trajectory data, we demonstrate a strong correlation between DTH and stochasticity strength with the power functions of speed. We then extend the car-following model framework that considers both the dynamic characteristics and stochasticity of time headway to investigate the mechanisms of traffic oscillation. The model calibration and validation results demonstrate that our extended model outperforms the original model in terms of trajectory fitting accuracy, successfully replicating the asymmetric driving behavior and the concave growth pattern of speed standard deviation. Building upon this novel perspective, linear stability and safety evaluation are systematically conducted to understand the comprehensive influence of DTH and stochasticity. Our theoretical and numerical experiments show that DTH significantly increases the range of string instability in traffic flow, particularly at low-speed regimes. The influence of the stochasticity on the marginal stability of traffic flow shows a pattern of increasing followed by decreasing tendencies. Also, the combined effect of drivers' DTH characteristics and stochasticity could expand the rear-end collision risks at low-speed regimes, showing a backward diffusion effect. Our findings further establish the interconnection of traffic oscillations with traffic stability and safety concerns.