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The origin of bursts and heavy tails in human dynamics

Nature volume 435, pages 207–211 (2005)Cite this article

Abstract

The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behaviour into a central question of modern science. Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes1,2,3. In contrast, there is increasing evidence that the timing of many human activities, ranging from communication to entertainment and work patterns, follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity4,5,6,7,8. Here I show that the bursty nature of human behaviour is a consequence of a decision-based queuing process9,10: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, with most tasks being rapidly executed, whereas a few experience very long waiting times. In contrast, random or priority blind execution is well approximated by uniform inter-event statistics. These finding have important implications, ranging from resource management to service allocation, in both communications and retail.

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Figure 1: The difference between the activity patterns predicted by a Poisson process and the heavy-tailed distributions observed in human dynamics.
Figure 2: Heavy-tailed activity patterns in e-mail communications.
Figure 3: The waiting time distribution predicted by the investigated queuing model.

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Acknowledgements

I have benefited from discussions with A. Vazquez on the mathematical aspects of the model. I also thank L. A. N. Amaral, Z. Dezsö, P. Ivanov, J. Kelley, J. Kertész, A. Motter, M. Paczuski, K. Sneppen, T. Vicsek, W. Whitt and E. Zambrano for useful discussions and comments on the manuscript; J.-P. Eckmann for providing the e-mail database; and S. Aleva for assisting me with manuscript preparation. This research was supported by NSF grants.

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Authors and Affiliations

  1. Center for Complex Networks Research and Department of Physics, University of Notre, Dame, Indiana, 46556, USA

    Albert-László Barabási

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  1. Albert-László Barabási
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Correspondence to Albert-László Barabási.

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The author declares that he has no competing financial interests.

Supplementary information

Supplementary Notes

This file contains additional notes and discussions relating to the study, including information on: queuing theory, calculating P(τ) for the priority list model, random removal limit of the priority list model, power law generating processes and mapping to evolutionary models. This file also contains additional references. (PDF 179 kb)

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Barabási, AL. The origin of bursts and heavy tails in human dynamics. Nature 435, 207–211 (2005). https://doi.org/10.1038/nature03459

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