Analysis of the transition condition of rear-end collisions using time-to-collision index and vehicle trajectory data

Time-to-collision (TTC) index has been extensively utilized to evaluate rear-end collision risks, but few studies have focused on the special transition process that vehicles change from a safe to a dangerous situation. This study conducts an in-depth analysis of the transition condition of rear-end collisions. Realistic vehicle trajectory data were extracted from the Federal Highway Administration's Next Generation Simulation (NGSIM) datasets. The TTC index was utilized to pinpoint dangerous and transition conditions. A total of 13 types of transition conditions were categorized and a novel indicator, the derivative of TTC (TTCD), is proposed to evaluate changing rate of TTCs. Three types of TTCDs, corresponding to different time point or interval, were further analyzed based on developed regression models. The results indicate that: (1) although theoretically there are a total of 13 types of transition conditions, three types are dominant in practice; (2) the TTCD(t₀) values at transition start points are significantly smaller than the TTCD(t₁) at end points and the average TTCD(t₀,t₁), which indicates the quickest change of TTC values, while the TTCD(t₁) has the slowest changes of TTC values; and (3) the following vehicle's speed and acceleration rate, and speed difference and acceleration difference between two vehicles have significant effects on TTCDs. The influences are more remarkable of TTCD(t₀) than those of TTCD(t₁), and the TTCD(t₀,t₁) always shows the average characteristic. Lastly, corresponding countermeasures are discussed based on findings above.