Analysis of secondary risks induced by defensive braking in autonomous vehicles: a study based on stochastic distribution of drivers

Abstract

Defensive braking measures in autonomous vehicles effectively enhance driving safety but also raise concerns about the secondary risks they may pose, particularly the potential for rear-end collisions caused by following vehicles. Indeed, being rear-ended by human driven vehicles is already the most common type of accident involving autonomous vehicles. However, the uncertainty in driver following behavior makes it challenging to assess this risk directly. In response, this paper characterizes the stochastic distribution of drivers to simulate and evaluate the impact of defensive braking behavior on the likelihood of rear-end collisions. First, based on Risk Homeostasis Theory and the central limit theorem, we propose the hypothesis that the risk tolerance levels (RTL) of driver populations follow a normal distribution. This hypothesis is validated using the Waymo dataset, leading to the development of a Stochastic Following Model (SFM) that effectively represents the stochastic distribution of drivers. Subsequently, a comparison with the Intelligent Driver Model (IDM) reveals that the SFM not only accurately reflects the stochastic distribution of drivers in mixed traffic flow but also demonstrates its effectiveness in capturing the diversity of driving behaviors. Finally, through the design of simulation experiments across various scenarios using Monte Carlo methods, the results indicate that while brief defensive braking by autonomous vehicles does not significantly affect the collision probability of following vehicles compared to manually driven vehicles, continuous defensive braking behavior substantially increases the likelihood of being rear-ended. The proposed SFM captures the extensive diversity of drivers and the stochasticity of the following process, illustrating the uncertainties inherent in mixed traffic flow. This model may serve as a valuable reference for future studies on the safety characteristics of mixed traffic flows.