On the Local and String Stability Analysis of Traffic Collision Risk

Conventional traffic stability studies primarily concentrate on the evolution of disturbances in vehicle motion but seldom consider how collision risk changes spatially and temporally. This study bridges the gap by extending the principles of traffic stability analysis to the field of traffic safety, focusing specifically on the temporal and spatial dynamics of collision risk. Leveraging the concepts of local and string stability, we formulate conditions under which collision risk behaves in a stable manner over time and space through the transfer function approach. A comparative analysis between conventional traffic stability and the newly introduced concept of collision risk stability reveals that while conditions for local stability are largely aligned in both domains, the criteria for string stability differ. These theoretical insights are substantiated through microscopic simulations using a variety of car-following models. The simulations also indicate that the consistency between theoretical and simulation outcomes diminishes as the disturbance magnitude increases, which is attributed to the linearization errors inherent in applying the transfer function in the theoretical derivations.