•Conduct theoretical analysis of intersection capacity and vehicle delay under reservation-based control.•Propose a mixed integer linear programming (MILP) model that can dynamically form batches with the optimal sizes and determine service sequence of vehicles under varying traffic condition.•Simulation results show that:○The proposed optimization-based control performs best compared with reservation-based control and vehicle-actuated control.○Reservation-based control outperforms actuated control under low demand or under-saturated demand.○FCFS-based control is incapable of handling high demand and multiple conflicting streams. Reservation-based methods with simple policies such as first-come-first-service (FCFS) have been proposed in the literature to manage connected and automated vehicles (CAVs) at isolated intersections. However, a comprehensive analysis of intersection capacity and vehicle delay under FCFS-based control is missing, especially under high traffic demand. To address this problem, this study adopts queueing theory and analytically shows that such method is incapable of handling high demand with multiple conflicting traffic streams. Furthermore, an optimization model is proposed to optimally serve CAVs arriving at an intersection for delay minimization. This study then compares the performance of the proposed optimization-based control with reservation-based control as well as conventional vehicle-actuated control at different demand levels. Simulation results show that the proposed optimization-based control performs best and it has noticeable advantages over the other two control methods. The advantages of reservation-based control are insignificant compared with vehicle-actuated control under high demand.