Multi-fractal analysis for vehicle distribution based on cellular automation model

Abstract

It is well known that traffic flow presents multi-fractal characteristics at time scales. The aim of this study is to test its multi-fractality at spacial scales. The vehicular cellular automation (CA) model is chosen as a tool to get vehicle positions on a single lane road. First, multi-fractal of vehicle distribution is checked, and multi-fractal spectrums are plotted. Second, analysis results show that the width of a multi-fractal spectrum expresses the ratio of the maximum to minimum densities, and the height difference between the left and right vertexes represents the relative size between the numbers of sections with the maximum and minimum densities. Finally, the effects of the random deceleration probability and the average density on homogeneity of vehicle distribution are analyzed. The results show that random deceleration increases the ratio of the maximum to minimum densities, and deceases the relative size between the numbers of sections with the maximum and minimum densities, when the global density is limited to a specific range. Therefore, the multi-fractal spectrum can be used to quantify the homogeneity of spacial distribution of traffic flow.