Abstarct: To prevent Rear-end collision on Two-lane roads, the effect of Overtaking behavioral and platoon characteristics on the time-to-collision (TTC) index and reducing the probability of collisions is one of the important road safety issues. Therefore, the present study first examines the characteristics of overtaking behavior of drivers in two-lane roads, and then to impact these parameters on the collision probability, a dynamic risk probability model baxsed on Higher Ordinary Differential Equation and Binomial Logistic Regression has presented and a numerical solution using Euler's numerical method is presented. Then the effect of variables on the time index to the collision with the artificial neural network multilxayer perceptron (ANN-MLP) determine. The results of this study showed that the surrogate safety measure to collision is affected by overtaking behaviors of drivers and queuing is 2.4 seconds. Also, the probabilistic dynamic model of risk and its solution by Euler numerical method to investigate the effect of overtaking and driver behavior characteristics of drivers on the time-to-collision index showed that the variables of speed, lateral distance, and decision time increase the critical time risk index The time-to- collision is 0.95, 0.92, and 0.91, respectively. While factors such as time headway, overtaking time in both directions, and overtaking distance have an inverse effect on the probability of critical time of time-to- collision index, by reducing these variables, the probability of risk of the time-to-collision index, respectively, with values Increases to 0.92, and0.87. The results of the effect of the variables affecting the risk of the time-to-collision index showed that the highest effect is related to the Time headway factor of 1.70 and the lowest effect is related to the lateral placement factor with a value of 0.70 times the other variables affecting the risk of the time-to-collision index.