This paper proposes a mathematical model to regulate the acceleration (deceleration) applied by self-driving vehicles in car-following situations. A virtual environment is designed to test the model in different circumstances: (1) the followers decelerate in time if the leader decelerates, considering a time delay of up to 5 s to refresh data (vehicles position coordinates) required by the model, (2) with the intention of optimizing space, the vehicles are grouped in platoons, where 3 s of time delay (to update data) is supported if the vehicles have a centre-to-centre spacing of 20 m and a time delay of 1 s is supported at a spacing of 6 m (considering a maximum speed of 20 m/s in both cases), and (3) an algorithm is presented to manage the vehicles’ priority at a traffic intersection, where the model regulates the vehicles’ acceleration (deceleration) and a balance in the number of vehicles passing from each side is achieved.