Traffic-light boundary in the deterministic Nagel-Schreckenberg model.

The characteristics of the deterministic Nagel-Schreckenberg model with traffic-light boundary conditions are investigated and elucidated in a mostly theoretically way. First, precise analytical results of the outflow are obtained for cases in which the duration of the red phase is longer than one step. Then, some results are found and studied for cases in which the red phase equals one step. The main findings include the following. The maximum outflow is "road-length related" if the inflow is saturated; otherwise, if the inbound cars are generated stochastically, multiple theoretical outflow volumes may exist. The findings indicate that although the traffic-light boundary can be implemented in a simple and deterministic manner, the deterministic Nagel-Schreckenberg model with such a boundary has some unique and interesting behaviors.