The Laplace Transform of the Linear Car-following Model

Abstract

Laplace transform is used to analyze the differential-difference equation for the linear car-following model. The car-following model has been developed to describe the dynamics of a platoon of vehicles initially traveling at uniform speed and spacing when the lead vehicle introduces a perturbation by decelerating or accelerating. Shifting theorem and the convolution theorem for Laplace transforms are used to model fluctuations in velocities and spacing of following vehicles as a function of the deceleration or acceleration of the lead car when the initial velocity and spacing are given.