Evolution of Traffic Jam in Traffic Flow Model

Abstract

Traffic flow is simulated in a three-state cellular automaton model. In a two-dimensional cell without a crashed car, the ensemble average of the velocity of the cars is enhanced by the self-organization in the low-density phase of cars. In the high-density phase above p =0.5 of car density, the velocity is decreased and the system then degenerates into a global jamming phase in which all cars are stopped. A crashed car provides the seed of a jamming cluster, which grows into a global traffic jam even in the low-density phase. The growth of the jamming cluster is studied, and the time dependence of the number of jamming cars and the scaling law for the cell sizes are discussed.