Detrended fluctuation analysis (DFA) is a useful tool to measure the long-range power-law correlations in 1f noise. In this paper, we investigate the power-law dynamics behavior of the density fluctuation time series generated by the famous Kerner-Klenov-Wolf cellular automata model in road traffic. Then the complexities of spatiotemporal, average speed, and the average density have been analyzed in detail. By introducing the DFA method, our main observation is that the free flow and wide moving jam phases correspond to the long-range anticorrelations. On the contrary, at the synchronized flow phase, the long-range correlated property is observed.
In this paper, we investigate the complexity behind the mixed traffic flow time series generated by multi-lane cellular automaton model. Throughout the paper, the cross-correlation coefficient is introduced to characterize the time series. It is found that there exists a critical vehicle density S, when S < S1 and the ratio of slow vehicle R > 0.01, the cross-correlation coefficient r is larger than 0.5, which indicates a significant linear correlation. Otherwise, the cross-correlation coefficient r < 0.5 which corresponds to a weak linear correlation. That is to say, the vehicle density plays an important role in the cross-correlation coefficient. Additionally, we also found that the asymmetric lane-change probability has no great influence on the cross-correlation coefficient.
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