Dynamical Evolution of Highway Traffic Flow: from Microscopic to Macroscopic

In this paper, a derivation of the macroscopic mean field theory of the cellular automaton (CA) model of highway traffic flow starting from the microscopic dynamical point of view is presented. Starting from an equation describing the time evolution of the Boolean state variable at each site of the basic CA model, and using a two-site approximation for the multi-site correlation functions, a dynamical mapping between the macroscopic average speeds v(t + 1) and v ( t ) at different time can be derived. Mean field results consistent with the simulation data are obtained by considering the attractors of the mapping and their corresponding basins.