This Demonstration solves a Gazis–Herman–Rothery (GHR) car-following model. In this model a vehicle accelerates in response to the velocity and distance of the vehicle in front. The model in its most general form is:
, in which , is time; and are the positions of the leading and following vehicles, respectively; is the velocity; is the acceleration; , , and are constants; and is the driver reaction (delay) time .
The GHR model is solved for nine cars traveling in a single lane with . For , the lead vehicle has a velocity of 70 mph and this velocity changes at time . The results are presented in the velocity time plane and in the delay phase plane. You can vary the velocity of the leading vehicle and the delay time to see the evolution of the GHR equation.