Green-light paths in city traffic controlled by signals

When a vehicle moves through a series of green lights with avoiding red signals in the traffic network, the travel time has a minimal value and the vehicle draws a characteristic trajectory. We study the trajectories (green-light paths) of a vehicle for various values of both cycle time and split at the synchronized and random-phase strategies. The trajectory depends highly on both signal's characteristics and control strategy. We clarify the dependence of green-light paths on both cycle time and split. At the random phase strategy, the vehicle draws a trajectory of the random walk. It is shown where the vehicle arrives if a driver selects the green-light path.