Fractal behavior in the headway fluctuation simulated by the NaSch model

• The fractal behavior of traffic flow is studied by the adaptive fractal analysis method.
• The power-law fluctuation of 1/fα1/fα type behavior exists in the free flow phase.
• The sharp spectral peaks are found in the power spectral density with increasing of vehicle density.
• The spectral peaks correspond to stop-and-go waves.
• A fractal behavior with long-range correlations appears in the high density regime.

The fractal behavior of traffic flow is studied by the adaptive fractal analysis method on the basis of the vehicle headway time series, which are obtained from the numerical simulation of the NaSch model. We find that the vehicle headway time series has a fractal behavior that is similar to the standard Brownian motion (BM) over a wide range of scales when the density is low. As the density increases well-defined sharp spectral peaks, corresponding to the stop-and-go waves, appear while the scale range showing BM-like behavior rapidly shrinks. In the high density regime, a new type of fractal behavior with long-range correlations appears, accompanying the worsening of traffic congestions. The underlying dynamics of traffic flow is analyzed, and some meaningful results are obtained.