This paper aims to optimize on-ramp merging processes for connected automated vehicles by utilizing an existing hierarchical control architecture including a decision-maker and an operational controller. The decision-maker employs surrogate linear models to predict future vehicular acceleration analytically and computes a merging sequence to minimize merging times of on-ramp vehicles. The operational controller is formulated as a model predictive control problem, which utilizes a second-order vehicle dynamics model, and regulates vehicles' accelerations and time instants to execute lateral movements of on-ramp vehicles for the merging processes respectively. Constraints on vehicular acceleration, speed, and inter-vehicle distance are considered by the decision-maker and the operational controller for practical usage. The proposed method to minimize the merging times of on-ramp vehicles and a first-in-first-out method are tested under different initial settings, including initial vehicular speeds, distributions of vehicular positions, and desired time gaps. The simulation results show that the proposed method is superior to the first-in-first-out method widely used in literature in improving merging traffic efficiency. We find that cooperation among vehicles makes the on-ramp vehicles join mainline traffic faster, and the acceptable time gap for merging affect choices of optimal merging sequences.