A unified risk metric for freeway vehicles based on the spatio-temporal overlap probability of predicted positions

Surrogate Safety Measures (SSMs) are widely used to quantify driving risks and support proactive traffic safety management. However, the existing metrics primarily focus on single scenarios, such as rear-end collisions in car-following situations. These metrics assume that the vehicles comply with specific motion equations, overlooking the uncertainties intrinsic to vehicle operation. To address these limitations, this study proposes a novel metric, the Risk Metric based on Predicted Position (RMPP), which evaluates the probability of collision. RMPP is designed to comprehensively capture all risk within a unified framework by incorporating the future positional distributions of vehicles. Firstly, the target vehicle and surrounding vehicles are constructed as a graph structure. The Generalized Dynamic Graph Convolutional Network (GDGCN) is used to predict the position distribution of vehicles. Then, spatial proximity risk and temporal proximity risk are computed based on the predicted positions. Spatial proximity risk is the sum of probabilities of predicted position overlap at the same time, while temporal proximity risk is the sum of probabilities of predicted position overlap at different times. RMPP is obtained through a weighted summation of these two risks. To validate the effectiveness of RMPP, we conducted experimental analyses using the Freeway B of CitySim dataset, which is collected in an Asian region using drones. We compared the prediction results of our GDGCN model with several baseline models. The experimental results demonstrated that our GDGCN model achieved good prediction accuracy. Additionally, using vehicle trajectories from CitySim, we compared RMPP with traditional metrics such as Time-to-Collision (TTC), Deceleration Rate to Avoid Collision (DRAC), and Safety Margin (SM) across both basic and high-risk driving scenarios. The results indicate that RMPP more accurately captures risk characteristics that align with real-world driving conditions. Furthermore, we evaluated the impact of prediction accuracy on RMPP by analyzing risk variations under different RMSE values. When the position prediction accuracy of both vehicles reaches a certain level, its impact on risk is small, confirming the reliability and stability of RMPP. With the advancement of technology and the improvement of prediction accuracy, the precision of RMPP will be further enhanced, making it a robust and powerful tool for traffic safety management.