Nonlinear-map model for split effect on vehicular traffic through periodic signals

We study the effects of both split and cycle time on dynamical behavior of vehicles moving through a sequence of traffic lights on a highway, where the traffic lights turn on and off periodically. The dynamical model of vehicular traffic controlled by signals is expressed in terms of a nonlinear map. The vehicle exhibits complex behavior with varying split and cycle time. The tour time between signals shows a self-similar behavior. When split sp is lower than 0.5, vehicular traffic shows a similar behavior as that of sp=0.5, while vehicular traffic of sp>0.5 is definitely different from that of sp⩽0.5. The algebraic expression among the tour time, cycle time, and split is derived.