Clustering and maximal flow in vehicular traffic through a sequence of traffic lights

We study the maximal current (maximum traffic capacity) of vehicular traffic through a sequence of traffic lights on a highway, where all signals turn on and off synchronously. The dynamical model of vehicular traffic controlled by signals is expressed in terms of a nonlinear map, where the excluded-volume effect is taken into account. The dynamical behaviors of vehicles are clarified by analyzing traffic patterns. The clustering of vehicles varies with the cycle time of signals. The maximum current is closely connected to vehicular clustering. Clustering of vehicles is controlled by varying both split and cycle time of signals. The dependence of the maximal current on both split and cycle time is derived.