Dispersion and scaling of fluctuating vehicles through a sequence of traffic lights

We study the dynamical behavior of vehicles moving with fluctuating speed through a sequence of traffic lights which are controlled by the synchronized strategy. The dynamics of fluctuating vehicular traffic controlled by traffic lights is described in terms of the stochastic nonlinear map. We study two kinds of traffic: case (A) in which vehicles are allowed to pass other vehicles freely and case (B) in which vehicles are inhibited to pass other vehicles. Vehicles move together (without dispersion) for specific values of cycle time, while vehicles extend over the road for other values of cycle time. Then, vehicular traffic exhibits the dispersion. When the dispersion of vehicles occurs, the variance of arrival time shows the scaling behavior. The scaling properties are derived. The scaling form and exponents are discussed by comparing with those of dynamic scaling of rough surface.