The increased traffic flow on both existing highways and city roads leads to the appearance of stop-and-go waves which have many disadvantages, e.g., increased risk of accidents, higher fuel consumption, increased pollution, increased wear of vehicle mechanical parts, driving stress and passenger discomfort. The platooning of vehicles could be the solution to this problem by enforcing them to follow each other and to maintain a safe distance between them. The advantages brought by this solution depend on ensuring the string stability of the vehicle platoon. In this paper the leader-follower system is employed to illustrate the stop-and-go waves mitigation. Several controllers (P, PI) were designed based on the conditions that have to be met in order to ensure the string stability of the vehicle platoon and comparisons were made with a controller based on the driver behavior.