Traffic Flow Volume Fluctuation Analysis using MF-DFA

Abundant observations have shown that road traffic flow contains complex fluctuations. One frequently mentioned question is: Whether traffic flow belongs to 1/f fluctuation and in which time-scale region the 1/f fluctuation appears? The answer of this problem is useful, since it may help to distinguish the implicit short-range/long-range correlation and self-similarity of traffic flow time series. Notice that traffic flow yields different behaviors at different time scale, some previous studies applies Detrended Fluctuation Analysis (DFA) method to filter out the polynomial trends. In this paper, the urban traffic flow data collected from Beijing China and the freeway traffic flow data collected from Washington State, USA are analyzed using Multi-Fractal Detrended Fluctuation Analysis (MF-DFA). The Hurst exponents of these two kinds of traffic flow are larger than that of 1/f noises and smaller than Brownian noises, which indicates the existence of the long-range correlation in urban traffic flow time series. The multi-fractal spectra of these two flows are carefully studied and the differences are highlighted. Results indicate that a multi-fractal description is required for traffic flow, since multi-fractal behaviors are found. This result also partly answers another attractive question: What difference can we observe between freeway and urban transportation network traffic flow?