Spring-based hierarchical eco-driving control for connected automated vehicles at consecutive signalized intersections in mixed traffic considering backward shockwave propagation

Eco-driving strategies for connected automated vehicles (CAVs) at signalized intersections can reduce energy consumption and improve traffic efficiency by enabling CAVs to decelerate in advance, cruise at a low speed, and re-accelerate to pass the next green phase smoothly without coming to a full stop. However, a low-speed CAV can act as a moving bottleneck, generating shockwaves that propagate upstream. This may impede vehicles from upstream intersections, even when there is substantial empty space ahead of the CAV. Furthermore, existing strategies often optimize CAV trajectories for isolated intersections—either by fixing terminal states or leaving them unconstrained—which frequently results in sub-optimality across consecutive intersections. To address these challenges, this paper develops a spring-based hierarchical eco-driving control framework that incorporates downstream Signal Phase and Timing (SPaT) information across consecutive intersections and explicitly addresses backward shockwave propagation. The upper layer performs long-horizon terminal-state planning using explicit analytical energy-optimal trajectories. To account for SPaT uncertainty and the stochastic start-up lost time of human-driven vehicles, this layer formulates the passing time window as chance constraints governed by a risk coefficient α . The lower layer employs a spatial-domain Model Predictive Control (MPC) to optimize the acceleration profile approaching the current intersection. This layer tracks the upper-layer terminal states while incorporating a spring-based backward-pressure indicator to adaptively tune eco-driving weights, thereby mitigating shockwaves during heavy traffic and prioritizing energy efficiency during light traffic. The proposed method was evaluated via microscopic simulation on a three-intersection corridor and a realistic urban network. Results indicate that the strategy reduces average energy consumption by 3.2%, 7.7%, and 4.8% for risk coefficients α = 0.1 , 0.5 , and 0.9, respectively, compared to the baseline. Besides, on the urban network with a demand of 8000 veh/h and 5% CAV penetration rate, the proposed method increases the maximum throughput by 3.4% (from 674.25 to 696.87 veh/h) and decreases the average energy consumption by 13.8% (from 509.68 to 439.35 mL).