An extended dynamic probabilistic risk approach based on a surrogate safety measure for rear-end collisions on two-lane roads

The rear-end collisions have significantly increased on two-lane roads because of drivers’ overtaking behaviors, and the time to collision (TTC) plays an effective role in these collisions. To prevent this type of collision, investigating the effect of overtaking behaviors on the TTC and predicting the risk probability of collisions are essential issues in road safety. To this end, the present study evaluated overtaking behaviors to find the effect of these behaviors on the TTC to determine a TTC threshold as a surrogate safety measure. Moreover, a dynamic probabilistic risk approach was developed based on binomial logistic regression and higher-order ordinary differential equations to examine the risk probability of the TTC threshold, which is then numerically solved by relying on Euler’s method. Accordingly, the importance weights of overtaking variables on the TTC were studied by multilayer perceptron to determine the importance weights in the risk value. The obtained data indicated that the TTC threshold was 2.4 s under the influence of overtaking behavior. Further, the results from dynamic risk probabilistic models revealed that space headway, time headway, and overtaking speed could raise the probability risk of the TTC threshold by 97, 95, and 93%, respectively. Finally, data related to the risk of the TTC for the proposed models indicated that the highest and lowest risks belong to space headway (1.3 times higher than other variables) and decision time (0.6 times less than other variables), respectively. •The effect of overtaking behaviors on surrogate safety measure (TTC) is investigated on two-lane roads.•The dynamic probabilistic risk models are proposed based on higher-order ordinary differential equations.•Under the influence of overtaking behaviors, the TTC threshold is estimated as 2.4 s.•Space headway, time headway, and overtaking speed raise the probability risk of the TTC threshold, respectively.•The maximum risk belongs to the space headway while the minimum risk is related to decision time.