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This paper investigates the effect of real-time control system computational delay on the performance of a hybrid adaptive cruise control (ACC) system during braking/coasting scenarios. A hierarchical hybrid ACC system with a finite state machine (FSM) at the high-rank and a nonlinear sliding mode controller (SMC) at the low-rank is designed based on a vehicle dynamics model with a brake-by-wire platform. From simulations, parametric studies are used to evaluate the effect of the bounded random computational delay on the system performance in terms of tracking errors and control effort. The effect of the computational delay location within the control system hierarchy is also evaluated. The system performance generally becomes worse as the upper boundary of the computational delay increases while the effect of the computational delay located at the high-rank controller is more pronounced.