Stochastic Analysis Of Microscopic Car Follow The Leader Model And Traffic Management

Abstract

We consider follow -the leader tra_c model describing the dynamics of N cars on a single lane road, where each car driver chooses his acceleration according to a certain law.Tra_c ow is a many-car system with complex and stochastic movement. It is di_cult to describe the system dynamics solely using deterministic models which describe average system be- havior. Therefore, a stochastic headway distribution is presented as further step forward to over come the well known a drawbacks of deterministic models. Modeling results will show that by taking car of second order statistics (that is mean and variance) a stochastic speed-density model is measure of the uctuation of velocity and headway of the vehicle on single lane. Finally,we consider the uctuation of velocity by calculating probability density from Fokker-Plank equation.