Transition and saturation of traffic flow controlled by traffic lights

We study the traffic flow controlled by traffic lights on a single-lane roadway by using the optimal velocity model. The characteristic of traffic flow is clarified for the three different strategies of traffic light control: the simple synchronized, green wave, and random switching strategies. The current–density diagrams are calculated for the three different strategies. It is found that the saturation of current occurs at the critical density. The critical density of the dynamical transition depends on the cycle time of the traffic light and strategy. The value of the saturated current does not depend on the cycle time and the strategies. The density wave propagating backward appears when the current saturates. It is shown that the density wave is consistent with the spontaneous jam. A theoretical analysis is also presented for the dynamical transition.