The Fractal and Multifractal Nature of Traffic

Traffic flow has traditionally been viewed either as a stochastic process, or as a kinematic fluid. In the case of the former usually only the equilibria and mean results have been of interest. In the latter situation traffic has been viewed as having a continuous differentiable density (perhaps with occasional shocks). Neither of these properly address the nature of traffic if the inherent traffic structure is fractal. The purpose of this paper is to provide evidence for the fractal and multifractal structure of traffic, outline implications this has on the how traffic can be modelled, provide alternative models of traffic based on fractal geometry, and venture possible reasons for the fractal nature of traffic. In order to examine traffic data for fractals, fractal dimensions and multifractal dimensions are calculated. One of the characteristics of fractals is self-similarity, and so Fourier power spectra are examined for 1/f functions which indicate self-similar behaviour. Lastly, so called variance-time graphs are plotted to check for long-run dependence, another feature of stochastic fractals. This paper provides evidence for fractal structure from each of the methods of analysis. It lists circumstances when this view of traffic is more appropriate than the traditional views. It provides models of traffic based upon fractal methods, and outlines how these methods could be utilised for providing simulation data, filling missing traffic data, and traffic prediction. Lastly it gives reasons why this fractal structure could occur, using renewal models of travel behaviour and models of traffic flow. This paper is produced and circulated privately and does not constitute publication. It may be subject to revision before publication.