A Lagrange representation of cellular automaton traffic-flow models

A new cellular automaton (CA) model of traffic flow in the Lagrange form is proposed in this paper. We study the algebraic relationship between models with the Lagrange form and the Euler form of Burger's CA, which is constructed from Burger's equation using the ultradiscrete method. It is found that the Lagrange form has made the description of traffic flow in one lane simpler. Thus we have extended a simple Lagrange model to include the effects of inertia of cars and drivers' perspective. The extended model shows metastable states and complex phase transition from a free to congested state, which is similar to the observed data for expressways.