Resonance, criticality, and emergence in city traffic investigated in cellular automaton models

The complex behavior that occurs when traffic lights are synchronized is studied for a row of interacting cars. The system is modeled through a cellular automaton. Two strategies are considered: all lights in phase and a "green wave" with a propagating green signal. It is found that the mean velocity near the resonant condition follows a critical scaling law. For the green wave, it is shown that the mean velocity scaling law holds even for random separation between traffic lights and is not dependent on the density. This independence on car density is broken when random perturbations are considered in the car velocity. Random velocity perturbations also have the effect of leading the system to an emergent state, where cars move in clusters, but with an average velocity which is independent of traffic light switching for large injection rates.