Multi-fractal detrended fluctuation analysis algorithm based identification method of scale-less range for multi-fractal charateristics of traffic flow

Scale-less range is an interval of measurement of time series in which fractional self-similarity exists statistically. In order to solve the problem of the lack of necessary steps to calculate fractal range in multi-fractal detrended fluctuation analysis algorithm (MF-DFA) in traffic flow, a new scale-less identification method based on MF-DFA is proposed through analyzing the characteristics of the mutation point in logistic curve of traffic flow wave function in steps of MF-DFA and the principles of the traditional fractal scale-less range identification method. Beijing's road network is taken for example to investigate the fractal scale-less range. Analysis results show that the identification method based on MF-DFA algorithm is valid, automatic and steady in identifying the fractal scale-less range in Beijing's traffic flow. Further, the reason why the scale-less range in traffic is limited is that small traffic flow waves account for a bigger percentage in scale-less range while big wave is bigger so that it is out of the scale-less range.