Fractal nature of highway traffic data. (English) Zbl 1122.62111

Summary: We applied a fractal approach to analyze the traffic data collected from the Beijing Yuquanying. The power spectrum, the empirical probability distribution function, the statistical moment scaling function and the autocorrelation function are used as indicators to investigate the presence of the fractal. The results from the fractal identification methods indicate that these data exhibit fractal behavior. A fractal framework seemed well suited for description of the data observed here, but its suitability for general traffic systems was not clear.


62P99 Applications of statistics
90B20 Traffic problems in operations research
28A80 Fractals
Full Text: DOI


[1] A.S. Nair, J.-C. Liu, L. Rilett, S. Gupta, Non-Linear Analysis of Traffic Flow. http://translink.tamu.edu/docs/Research/Linear Analysis Traffic Flow/ chaos1. PDF, 2001. Accessed May 27, 2003
[2] Park, D.; Rilett, L.R., Forecasting freeway link travel times with a multilayer feedforward neural network (advanced computer technologies in transportation engineering, blackwell publishers, malden, MA and Oxford, UK), International journal of computer-aided civil and infrastructure engineering, 14, 357-367, (1999), (special issue)
[3] Peitgen, H.-O.; Jürgens, H.; Saupe, D., Chaos and fractals: new frontiers of science, (1992), Springer-Verlag · Zbl 0779.58004
[4] Shang, P.; Li, X.; Kamae, S., Chaotic analysis of traffic time series, Chaos, solitons and fractals, 25, 1, 121-128, (2005) · Zbl 1075.37543
[5] May, A.D., Traffic flow fundamentals, (1990), Prentice Hall Englewood Cliffs
[6] van Zuylen, H.J.; van Geenhuizen, M.S.; Nijkamp, P., (un)predictability in traffic and transport decision making, (), 21-28
[7] Prigogine, I.; Herman, R., Kinetic theory of vehicular traffic, (1971), Elsevier New York · Zbl 0226.90011
[8] Disbro, J.E.; Frame, M., (), 109-115
[9] Gazis, D.C.; Herman, R.; Rothery, R.W., Nonlinear follow-the-leader models for traffic flow, Operations research, 9, 545-567, (1961) · Zbl 0096.14205
[10] Safanov, L.A.; Tomer, E.; Strygin, V.V.; Ashkenazy, Y.; Havlin, S., Delay-induced chaos with multi-fractal attractor in a traffic flow model, Europhysics letters, 57, 151-157, (2002)
[11] Weidlich, W., Sociodynamics: A systematic approach to mathematical modeling in the social sciences, (2000), Harwood Academic Amsterdam · Zbl 0978.91074
[12] Hilborn, R.C., Chaos and nonlinear dynamics: an introduction for scientists and engineers, (2001), Oxford University Press Oxford · Zbl 1015.37001
[13] Kantz, H.; Schreiber, T., Nonlinear time series analysis, (1996), Cambridge University Press Cambridge
[14] Falconer, K., Fractal geometry, (1990), Wiley New York
[15] Takens, F., Detecting strange attractors in turbulence, (), 366-381
[16] Tessier, Y.; Lovejoy, S.; Schertzer, D., Universal multifractals: theory and observations for rain and clouds, Journal of applied meteorology, 32, 223-250, (1993)
[17] Lovejoy, S.; Mandelbrot, B., Fractal properties of rain and a fractal model, Tellus, 37A, 209-232, (1985)
[18] R. Macfadyen, Self-Similarity: Complication or Distraction? From the COST-257 project. http:// www.info3.informatik.uni-wuerzburg.de /cost/html/temp.htm
[19] Menabde, M.; Harris, D.; Seed, A.; Austin, G.; Stow, D., Multiscaling properties of rainfall and bounded random cascades, Water resources research, 33, 12, 2823-2830, (1997)
[20] Olsson, J.; Niemczynowicz, J.; Berndtsson, R., Fractal analysis of high-resolution rainfall time series, Journal of geophysical research, 98, D12, 23 265-23 274, (1993)
[21] Svensson, C.; Olsson, J.; Berndtsson, R., Multifractal properties of daily rainfall in two different climates, Water resources research, 32, 8, 2463-2472, (1996)
[22] Fraedrich, K.; Larnder, C., Scaling regimes of composite rainfall time series, Tellus, 45A, 289-298, (1993)
[23] Ladoy, P.; Lovejoy, S.; Schertzer, D., Extreme variability of climatological data: scaling and intermittency, (), 241-250
[24] Tessier, Y.; Lovejoy, S.; Hubert, P.; Schertzer, D.; Pecknold, S., Multifractal analysis and modeling of rainfall and river flows and scaling, causal transfer functions, Journal of geophysical research, 101, D21, 26 427-26 440, (1996)
[25] Kumar, P.P.G.; Foufoula-Georgiou, E., A probability-weighted moment test to assess simple scaling, Stochastic hydrology and hydraulics, 8, 173-183, (1994)
[26] Over, T.M.; Gupta, V.K., Statistical analysis of mesoscale rainfall: dependence of a random cascade generator on large-scaling forcing, Journal of applied meteorology, 33, 1526-1542, (1994)
[27] Frisch, U.; Parisi, G., On the singularity structure of fully developed turbulence, (), 84-88
[28] Schertzer, D.; Lovejoy, S., Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes, Journal of geophysical research, 92, D8, 9693-9714, (1987)
[29] Rodriguez-Iturbe, I.; De Power, F.B.; Sharifi, M.B.; Georgakakos, K.P., Chaos in rainfall, Water resources research, 25, 7, 1667-1675, (1989)
[30] Willinger, W.; Taqqu, M.S.; Sherman, W.; Wilson, D., Self-similarity through high variability: statistical analysis of Ethernet LAN traffic at the source level, IEEE/ACM transactions on networking, 5, 1, 71-86, (1997)
[31] Taqqu, M.S.; Levy, J.B., Using renewal processes to generate long-range dependence and high variability, (), 73-89
[32] Mandelbrot, B.B., Long-run linearity, locally Gaussian processes, H-spectra and infinite variances, International economic review, 10, 82-113, (1969) · Zbl 0191.51002
[33] Hill, B.M., A simple general approach to inference about the tail of a distribution, The annals of statistics, 3, 1163-1174, (1975) · Zbl 0323.62033
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.