Conditions for Safe Deceleration of Strings of Vehicles

A simple model for a string of vehicles is constructed. The model explicitly accounts for the possibility of repeated collisions between the vehicles in the string. Based on the model a notion of safety is formulated for the string. Necessary and sufficient conditions are presented that specify when a string of vehicles is safe while performing a simple emergency deceleration maneuver where all vehicles start decelerating at a fixed rate after some delay. The conditions are interpreted in terms of their implications for the safety of platoons of vehicles.