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With the emergence of vehicle-communication technologies, many researchers have strongly focused their interest in vehicle energy-efficiency control using this connectivity. For instance, the exploitation of preview traffic enables the vehicle to plan its speed and position trajectories given a prediction horizon so that energy consumption is minimized. To handle the strong uncertainties in the traffic model in the future, a constrained controller is generally employed in the existing researches. However, its expensive computational feature largely prevents its commercialization. This paper addresses computational burden of the constrained controller by proposing a computationally tractable model prediction control (MPC) for real-time implementation in autonomous electric vehicles. We present several remedies to achieve a computationally manageable constrained control, and analyze its real-time computation feasibility and effectiveness in various driving conditions. In particular, both warmstarting and move-blocking methods could relax the computations significantly. Through the validations, we confirm the effectiveness of the proposed approach while maintaining good performance compared to other alternative schemes.