Effect of irregularity on vehicular traffic through a sequence of traffic lights

We present the stochastic nonlinear-map model of vehicular traffic controlled by irregular signals. The signal's interval, the split of signal, and the offset time changes irregularly from signal to signal on a roadway. We study the effect of irregularity on dynamical behavior of vehicular traffic through a sequence of traffic lights. The vehicle exhibits the very complex behavior with varying cycle time. When the strength of irregularity is small, the arrival time does not change with irregularity for some values of cycle time, while it changes for other values of cycle time. The region in which the arrival time changes is expanding with increasing irregularity's strength. The region map (phase diagram) is shown in the cycle time-irregularity's strength space.