Coarse-grained cellular automaton for traffic systems

A coarse-grained cellular automaton is proposed to simulate traffic systems. There, cells represent road sections. A cell can be in two states: jammed or passable. Numerical calculations are performed for a piece of square lattice with open boundary conditions, for the same piece with some cells removed and for a map of a small city. The results indicate the presence of a phase transition in the parameter space, between two macroscopic phases: passable and jammed. The results are supplemented by exact calculations of the stationary probabilities of states for the related Kripke structure constructed for the traffic system. There, the symmetry-based reduction of the state space allows to partially reduce the computational limitations of the numerical method.