Vehicle following and its effects on traffic flow has been an active area of research. Human Driving involves reaction, delays, and human errors that has adverse effects on traffic flow . We can eliminate human errors by introducing a computer control system. The purpose of this research was to develop and evaluate a control law and a simulation tool for the study of automatic vehicle headway control. This research considers longitudinal control of a platoon of vehicles on automated highways. A new way of designing control law for vehicle following is presented by introducing safe boundary concept - the trail vehicle should never exceed the maximum safe velocity and at the same time keeps the passengers comfort when accelerating or decelerating except under emergency circumstances. After finding the safe boundary, we design the automatic control law and then using our simulation tool to simulate its performance, adjust parameters until we reach a satisfactory result. System dynamics concept and basic individual vehicle motion laws are used through the research. System dynamics provides a common foundation that can be applied wherever we want to understand and influence how things change through time. We look at the platoon system as a whole and study all the objects, such as vehicle dynamics, road condition, motor dynamics, in this system interact with one another. A third-order nonlinear, Car-following, PID control law is designed using System Dynamics concept. System dynamics' simulation language DYNAMO and Spreadsheet are have been used for our development of a simulation tooL A Satisfactory result is found after the extensive simulation which indicates that the platoon assumptions are achievable using the advanced technologies, like automatic vehicle control, radar, and sensors. / Master of Science