A speed optimization model for connected and autonomous vehicles at expressway tunnel entrance under mixed traffic environment

Rear-end collisions frequently occurred in the entrance zone of expressway tunnel, necessitating enhanced traffic safety through speed guidance. However, existing speed optimization models mainly focus on urban signal-controlled intersections or expressway weaving zones, neglecting research on speed optimization in expressway tunnel entrances. This paper addresses this gap by proposing a framework for a speed guidance model in the entrance zone of expressway tunnels under a mixed traffic environment, comprising both Connected and Autonomous Vehicles (CAVs) and Human-driven Vehicles (HVs). Firstly, a CAV speed optimization model is established based on a shooting heuristic algorithm. The model targets the minimization of the weighted sum of the speed difference between adjacent vehicles and the time taken to reach the tunnel entrance. The model's constraints incorporate safe following distances, speed, and acceleration limits. For HVs, speed trajectories are determined using the Intelligent Driver Model (IDM). The CAV speed optimization model, represented as a mixed-integer nonlinear optimization problem, is solved using A Mathematical Programming Language (AMPL) and the BONMIN solver. Safety performance is evaluated using Time-to-Collision (TTC) and speed standard deviation (SD) metrics. Case study results show a significant decrease in SD as the CAV penetration rate increases, with a 58.38% reduction from 0% to 100%. The impact on SD and mean TTC is most pronounced when the CAV penetration rate is between 0% and 40%, compared to rates above 40%. The minimum TTC values at different CAV penetration rates consistently exceed the safety threshold TTC*, confirming the effectiveness of the proposed control method in enhanced safety. Sensitivity analysis further supports these findings.