Traffic dispersion through a series of signals with irregular split

We study the traffic behavior of a group of vehicles moving through a sequence of signals with irregular splits on a roadway. We present the stochastic model of vehicular traffic controlled by signals. The dynamic behavior of vehicular traffic is clarified by analyzing traffic pattern and travel time numerically. The group of vehicles breaks up more and more by the irregularity of signal's split. The traffic dispersion is induced by the irregular split. We show that the traffic dispersion depends highly on the cycle time and the strength of split's irregularity. Also, we study the traffic behavior through the series of signals at the green-wave strategy. The dependence of the travel time on offset time is derived for various values of cycle time. The region map of the traffic dispersion is shown in (cycle time, offset time)-space.