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Transportation

, Volume 46, Issue 5, pp 1689–1712 | Cite as

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

  • Wim EctorsEmail author
  • Bruno Kochan
  • Davy Janssens
  • Tom Bellemans
  • Geert Wets
Article

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.

Keywords

Zipf’s law Power law Activity schedules Universal distributions 

Notes

Acknowledgements

The authors are deeply grateful to the original data creators, depositors and/or copyright holders for making the microdata available for this research. The copyright and all other intellectual property rights in the data and associated documentation are vested in the original data creators or depositors. The original data creators and analyzers bear no responsibility for the further analysis or interpretation of the data in this research. The authors would like to acknowledge the researches, works, individuals and institutions supporting the following data collections for making this research possible: US NHTS 2009 (US Department of Transportation and Federal Highway Administration 2009), NLD OViN 2013 (Centraal Bureau voor de Statistiek (CBS) and Rijkswaterstaat (RWS) 2014), BEL OVG 3.0--4.5 (Janssens et al. 2014), SVN Ljubljana 2013 (Klemenčič et al. 2014) [Acknowledgements go out to the City Municipality of Ljubljana], GBR NTS 2009--2014 (Department for Transport 2015), KOR Seoul HTS 2010 (Korea Transportation Institute 2011; Metropolitan Transport Authority 2012), DEU Mobidrive 1999 (Chalasani and Axhausen 2004), CHE Thurgau 2003 (Loechl 2005), FRA ENTD 2008 (Armoogum et al. 2011), BEL Beldam 2010 (Cornelis et al. 2012) [financed by BELSPO, FOD Mobiliteit & Vervoer and others. Coordinated by GRT (Université de Namur) in cooperation with IMOB (Universiteit Hasselt) and CES (FUSL)], IRL NTS 2009 (Central Statistics Office 2011) [Accessed via the Irish Social Science Data Archive - www.ucd.ie/issda], FIN HLT 2010--2011 (Liikennevirasto - Finnish Transport Agency) [Finnish National Travel Survey 2010--2011/Finnish Transport Agency and Wim Ectors], SWE RVU 2011--2014 (Trafik Analys 2015), AUS VISTA 2007 & 2009 (Department of Economic Development; Jobs; Transport and Resources (DEDJTR) 2009; Department of Economic Development; Jobs; Transport and Resources (DEDJTR) 2007). Part of this work was presented at the hEART 2016 conference in Delft, The Netherlands, offering valuable reflections during the preparation of this work. (Ectors et al. 2016a)

Author's contributions

WE: literature Search and Review, manuscript writing and editing; BK: meta-analysis, content planning and detailed manuscript review; DJ: meta-analysis and content planning; TB: meta-analysis and content planning; GW: meta-analysis and content planning.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no competing interests.

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Authors and Affiliations

  1. 1.Transportation Research Institute (IMOB)UHasselt – Universiteit HasseltDiepenbeekBelgium

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