A Safety Index for Traffic with Linear Spacings

Abstract

The authors have tried to improve the traffic dynamic theory of Prof. Pipes and have found the fundamental equation of traffic dynamics for a case in which the velocity of the following vehicle is determined not only by the space between following and lead cars but also by the velocity of the lead car. The safety of the following car with respect to rear end collision when the lead car is in sinusoidal motion is quantified by introducing a safety index. At the same time, the authors describe the stability of the indicial response of the following car, and the stability of the propagation of a sinusoidal disturbance down a line of cars.