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Emerging connected autonomous vehicles (CAV) technologies provide an opportunity to the detailed vehicle trajectory control to reduce adverse impacts of stop-and-go traffic imposed by freeway bottlenecks. This study proposes a CAV-based trajectory-smoothing concept to harmonize traffic, improve fuel-efficiency and reduce environmental impacts. The presented algorithm is applicable to mixed-traffic environments with human-driven vehicles (HVs), connected vehicles (CVs), and CAVs. This algorithm controls CAVs so that they smoothly hedge against the backward deceleration waves and gradually merge into the downstream traffic with a reasonable speed. This model addresses the full spectrum of CV and CAV market penetration rates and various traffic conditions. Numerical experiments are performed to assess the algorithm performance with different traffic conditions and CV and CAV market penetration …