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Exploratory analysis of Zipf’s universal power law in activity schedules

Author

Listed:
  • Wim Ectors

    (UHasselt – Universiteit Hasselt)

  • Bruno Kochan

    (UHasselt – Universiteit Hasselt)

  • Davy Janssens

    (UHasselt – Universiteit Hasselt)

  • Tom Bellemans

    (UHasselt – Universiteit Hasselt)

  • Geert Wets

    (UHasselt – Universiteit Hasselt)

Abstract

People’s behavior is governed by extremely complex, multidimensional processes. This fact is well-established in the transportation research community, which has been working on travel behavior (travel demand) models for many years. The number of degrees of freedom in a person’s activity schedule is enormous. However, the frequency of occurrence of day-long activity schedules obeys a remarkably simple, scale-free distribution. This particular distribution has been observed in many natural and social processes and is commonly referred to as Zipf’s law, a power law distribution. This research provides evidence that activity schedules from various study areas exhibit a universal power law distribution. To this end, an elaborate analysis using 13 household travel surveys from diverse study areas discusses the effect of proportional outlier removal on the power law’s exponent value. Statistical evidence is provided for the hypothesis that activity schedules in all these datasets exhibit a power law distribution with a common exponent value. The study proposes that a Zipf power law could be used as an additional dimension within a travel demand model’s validation process. Contrary to other validation methods, no new data is required. The observation of a Zipf power law distribution in the generated schedules appears to be a necessary condition. Additionally, the universal activity schedule distribution might enable the full integration of activity schedules in models based on universal mobility patterns.

Suggested Citation

  • Wim Ectors & Bruno Kochan & Davy Janssens & Tom Bellemans & Geert Wets, 2019. "Exploratory analysis of Zipf’s universal power law in activity schedules," Transportation, Springer, vol. 46(5), pages 1689-1712, October.
    • Handle: RePEc:kap:transp:v:46:y:2019:i:5:d:10.1007_s11116-018-9864-9
    DOI: 10.1007/s11116-018-9864-9
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    1. Anastasios Noulas & Salvatore Scellato & Renaud Lambiotte & Massimiliano Pontil & Cecilia Mascolo, 2012. "A Tale of Many Cities: Universal Patterns in Human Urban Mobility," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-10, May.
    2. Fujiwara, Yoshi, 2004. "Zipf law in firms bankruptcy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(1), pages 219-230.
    3. Reed, William J., 2001. "The Pareto, Zipf and other power laws," Economics Letters, Elsevier, vol. 74(1), pages 15-19, December.
    4. Paleari, Stefano & Redondi, Renato & Malighetti, Paolo, 2010. "A comparative study of airport connectivity in China, Europe and US: Which network provides the best service to passengers?," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 46(2), pages 198-210, March.
    5. Michael Batty, 2005. "Agents, Cells, and Cities: New Representational Models for Simulating Multiscale Urban Dynamics," Environment and Planning A, , vol. 37(8), pages 1373-1394, August.
    6. Siyu Li & Der-Horng Lee, 2017. "Learning daily activity patterns with probabilistic grammars," Transportation, Springer, vol. 44(1), pages 49-68, January.
    7. Soo, Kwok Tong, 2005. "Zipf's Law for cities: a cross-country investigation," Regional Science and Urban Economics, Elsevier, vol. 35(3), pages 239-263, May.
    8. Yang, Xu-Hua & Chen, Guang & Chen, Sheng-Yong & Wang, Wan-Liang & Wang, Lei, 2014. "Study on some bus transport networks in China with considering spatial characteristics," Transportation Research Part A: Policy and Practice, Elsevier, vol. 69(C), pages 1-10.
    9. D. Brockmann & L. Hufnagel & T. Geisel, 2006. "The scaling laws of human travel," Nature, Nature, vol. 439(7075), pages 462-465, January.
    10. David Boyce & Hillel Bar–Gera, 2003. "Validation of Multiclass Urban Travel Forecasting Models Combining Origin–Destination, Mode, and Route Choices," Journal of Regional Science, Wiley Blackwell, vol. 43(3), pages 517-540, August.
    11. Meead Saberi & Hani S. Mahmassani & Dirk Brockmann & Amir Hosseini, 2017. "A complex network perspective for characterizing urban travel demand patterns: graph theoretical analysis of large-scale origin–destination demand networks," Transportation, Springer, vol. 44(6), pages 1383-1402, November.
    12. Rudolf Hanel & Bernat Corominas-Murtra & Bo Liu & Stefan Thurner, 2017. "Fitting power-laws in empirical data with estimators that work for all exponents," PLOS ONE, Public Library of Science, vol. 12(2), pages 1-15, February.
    13. Gillespie, Colin S., 2015. "Fitting Heavy Tailed Distributions: The poweRlaw Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(i02).
    14. Filippo Simini & Marta C. González & Amos Maritan & Albert-László Barabási, 2012. "A universal model for mobility and migration patterns," Nature, Nature, vol. 484(7392), pages 96-100, April.
    15. Okuyama, K & Takayasu, M & Takayasu, H, 1999. "Zipf's law in income distribution of companies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 125-131.
    16. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
    17. Volchenkov, D. & Blanchard, Ph., 2008. "Scaling and universality in city space syntax: Between Zipf and Matthew," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(10), pages 2353-2364.
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