The Butterfly Effect in Vehicular Digital Twin Systems: Complexity and Risk Analysis for Mixed-Traffic Scenarios

Digital twin (DT) is a promising technology for mixed-traffic scenarios with connected automated vehicles (CAVs) and human vehicles (HVs). Utilizing the DT's virtualization capability gets the virtual vehicle state and risk analysis for mixed-traffic scenarios to accurately predict vehicle trajectory and driving safety. However, even if a vehicular DT system is perfectly derived, the vehicular DT system might still fail to accurately predict the trajectory and assess driving risk due to its complexity. Under the complexity of the vehicular DT system, small initial state deviations lead to trajectories diverging increasingly from the true trajectory and unpredictably over time. Meanwhile, performing crash risk evaluation services of the vehicular DT system leads to false alarms. This impact is called the butterfly effect of complexity on the trajectory in the vehicular DT system. In this paper, we focus on the effect of complexity on trajectory and risk assessment in the vehicular DT system for mixed-traffic scenarios. Firstly, we consider the communication delay of CAVs and HVs to implement the vehicle model in the vehicular DT system. Then, we verify the existence of complexity in the vehicular DT system. Finally, we evaluate the effect of the complexity on trajectory and risk assessment under initial state deviation in the vehicular DT system. Theoretical and experimental results indicate that the control gain of the CAV's controller is less than (0.075,0.1) by analyzing the butterfly effect of complexity on trajectory prediction and risk assessment in the vehicular DT system. This control gain range avoids the butterfly effect's impact on vehicle trajectories and risks. This provides an effective decision range to realize the trajectory prediction of high fidelity and driving safety in the vehicular DT system.