Long-range correlations in vehicular traffic flow studied in the framework of Kerner's three-phase theory based on rescaled range analysis

In this paper, a study on the characteristics of synchronized traffic flow in a two-lane case with partial reduced lane based on the Kerner-Klenov-Wolf (KKW) cellular automaton model in the framework of Kerner' three-phase theory is reported by using the rescaled range analysis. The local fundamental diagram and the cross correlation near the entry of the reduced lane have been analyzed. The typical two-dimensional scatter diagram in the local fundamental diagram and the non-correlation of the cross correlation between the local density and the flow reveal the characteristics of synchronized traffic flow near the entry of the reduced lane. By using the rescaled range analysis (R/S) method to calculate the Hurst exponent, we can obtain the long-range correlated characteristics of the synchronized flow at a traffic bottleneck. We have found that the larger the length of bottleneck, the higher the Hurst's exponent does as well as the stronger the correlations of the system. Applying our correlation analysis to traffic flow simulations with the NaSch model, which cannot reproduce synchronized flow of the three-phase theory, we have indeed found that the NaSch model does not exhibit long-range correlation characteristics found for synchronized flow.