Monday, December 16, 2013

Human Mobility Patterns: Power Law or Exponential?

Brockmann, D., Hufnagel, L. & Geisel, T.
The scaling laws of human travel.
Nature 439,462–465 (2006).
Several studies in the literature have suggested that human mobility patterns follow a power law (scaling law):
Brockmann, D., Hufnagel, L. & Geisel, T. The scaling laws of human travel. Nature 439,462–465 (2006).
González, M.C., Hidalgo, C.A., Barabási, A.L., 2008. Understanding individual human mobility patterns. Nature 453, 779-782
Woolley-Meza, O., Thiemann, C., Grady, D., Lee, J.J., Seebens, H., Blasius, B., Brockmann, D., 2011. Complexity in human transportation networks: A comparative analysis of worldwide air transportation and global cargo ship movements. European Physical Journal B 84. 589-600.
Song, C., Koren, T., Wang, P. & Barabási, A.-L. Modelling the scaling properties of human mobility. Nat. Phys. 6, 818–823 (2010).
Jiang, B., Yin, J. & Zhao, S. Characterizing the human mobility pattern in a large street network. Phys. Rev. E 80, 1–11 (2009).
Noulas, A., Scellato, S., Lambiotte, R., Pontil, M. & Mascolo, C.
A tale of many cities: universal patterns in human urban mobility.
PLoS ONE 7, e37027 (2012).
Other studies proposed that an exponential function provides a better fit:
Liang, X., Zheng, X., Lv, W., Zhu, T. & Xu, K. The scaling of human mobility by taxis is exponential. Physica A 391, 2135–2144 (2012).
Peng, C., Jin, X., Wong, K.-C., Shi, M. & Liò, P. Collective Human Mobility Pattern from Taxi Trips in Urban Area. PLoS ONE 7, e34487 (2012).
Bazzani, A., Giorgini, B., Rambaldi, S., Gallotti, R. & Giovannini, L. Statistical laws in urban mobility from microscopic GPS data in the area of Florence. J. Stat. Mech. 2010, P05001(2010).
Roth, C., Kang, S. M., Batty, M. & Barthélemy, M. Structure of urban movements: polycentric activity and entangled hierarchical flows. PLoS ONE 6, e15923 (2011).
Kang, C., Ma, X., Tong, D. & Liu, Y. Intra-urban human mobility patterns: An urban morphology perspective. Physica A 391, 1702–1717 (2012).
Noulas, A., Scellato, S., Lambiotte, R., Pontil, M. & Mascolo, C. A tale of many cities: universal patterns in human urban mobility. PLoS ONE 7, e37027 (2012).
The difference comes from the scale of the study and perhaps the data . The mobility patterns in the global scale (e.g. air transportation and cargo ship movements) or national scale (using bank notes and mobile data calls) tend to follow the power law. However, at the city scale, human mobility tends to follow an exponential law. Source of data could also affect the results. Use of mobile phone calls and taxi data do not completely represent individuals daily mobility patterns. Overall, the exponential law of human mobility in cities could be partly explained by the economies of agglomeration and thus, following a "natural decay". While at the global scale where the economies of agglomeration does not play a significant role, the power law seems to better describe the mobility patterns.

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