Traffic anticipation enhances driving intelligence and strengthens the ability to take early vehicle control action, e.g., lane change and speed adjustment, in a dynamically varying traffic environment. This paper presents an efficient vehicle driving system, based on detailed anticipation of surrounding traffic, that aims at optimizing the driving performance of individual vehicles and smoothening traffic flows on multilane roads. More elaborately, under a connected vehicle environment, the system receives the states of all vehicles that exist within its communication range. Based on their predicted states in a look forward horizon, the system generates the optimal acceleration and makes lane change decision simultaneously in the model predictive control framework. A fast hierarchical optimization scheme is used in the framework for its onboard implementation. The proposed efficient driving system is applied to a fraction of traffic, and both the individual and overall traffic performances are evaluated using a microscopic traffic simulator. It is revealed that the vehicles under the proposed efficient driving system improve their fuel economy and travel efficiency, significantly. In the mixed traffic, by the influence of the vehicle with the proposed driving system, the other traditionally driven vehicles also improve their performance.