A review of mathematical models for the flow of traffic and some recent results

After reviewing a variety of macroscopic models based on the continuum approach, cellular automata models, models based on the kinetic theory of gases as well as microscopic models, and delineating their usefulness and deficiencies, we present a model based on a discrete system of dynamical systems. We evaluate the efficacy of the model by comparing the predictions of the model with real time data from monitoring facilities on a highway in Austin, Texas.