Vehicular traffic through a self-similar sequence of traffic lights

We study the dynamical behavior of vehicular traffic through a sequence of traffic lights positioned self-similarly on a highway, where all traffic lights turn on and off simultaneously with cycle time T-s. The signals are positioned self-similarly by Cantor set. The nonlinear-map model of vehicular traffic controlled by self-similar signals is presented. The vehicle exhibits the complex behavior with varying cycle time. The tour time is much lower such that signals are positioned periodically with the same interval. The arrival time T(x) at position x scales as (T(x) - x) alpha x(df), where d(f) is the fractal dimension of Cantor set. The landscape in the plot of T(x)-x against cycle time T-s shows a self-affine fractal with roughness exponent alpha = 1-d(f). (c) 2007 Elsevier B.V. All rights reserved.