Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

The origin of bursts and heavy tails in human dynamics


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.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it


Prices may be subject to local taxes which are calculated during checkout

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.


  1. Haight, F. A. Handbook of the Poisson Distribution (Wiley, New York, 1967)

    MATH  Google Scholar 

  2. Reynolds, P. Call Center Staffing (The Call Center School Press, Lebanon, Tennessee, 2003)

    Google Scholar 

  3. Greene, J. H. Production and Inventory Control Handbook 3rd edn (McGraw-Hill, New York, 1997)

    Google Scholar 

  4. Anderson, H. R. Fixed Broadband Wireless System Design (Wiley, New York, 2003)

    Book  Google Scholar 

  5. Dewes, C., Wichmann, A. & Feldman, A. in Proc. 2003 ACM SIGCOMM Conf. Internet Measurement (IMC-03) (ACM Press, New York, 2003)

    Google Scholar 

  6. Kleban, S. D. & Clearwater, S. H. Hierarchical Dynamics, Interarrival Times and Performance. Proc. SC2003 (2003).

  7. Paxson, V. & Floyd, S. Wide-area traffic: The failure of Poisson modeling. IEEE/ACM Trans. Netw. 3, 226 (1996)

    Article  Google Scholar 

  8. Masoliver, J., Montero, M. & Weiss, G. H. Continuous-time random-walk model for financial distributions. Phys. Rev. E 67, 021112 (2003)

    Article  ADS  Google Scholar 

  9. Cobham, A. Priority assignment in waiting line problems. J. Oper. Res. Sec. Am. 2, 70–76 (1954)

    Google Scholar 

  10. Cohen, J. W. The Single Server Queue (North Holland, Amsterdam, 1969)

    MATH  Google Scholar 

  11. Eckmann, J.-P., Moses, E. & Sergi, D. Entropy of dialogues creates coherent structure in e-mail traffic. Proc. Natl Acd. Sci. USA 101, 14333–14337 (2004)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  12. Ebel, H., Mielsch, L. I. & Bornholdt, S. Scale-free topology of e-mail network. Phys. Rev. E 66, R35103 (2002)

    Article  ADS  Google Scholar 

  13. Harder, U. & Paczuski, M. Correlated dynamics in human printing behavior. Preprint at (2004).

  14. Henderson, T. & Nhatti, S. Modelling user behavior in networked games. Proc. 9th ACM Int. Conf. on Multimetia 212–220 (ACM Press, New York, 2001).

  15. Crovella, M. & Bestravros, A. Self-similarity in World Wide Web traffic: evidence and possible causes. IEEE/ACM Trans. Netw. 5, 835–846 (1997)

    Article  Google Scholar 

  16. Mitzenmacher, M. A brief history of generative models for power law and lognormal distributions. Internet Math. 1, 226–251 (2004)

    Article  MathSciNet  Google Scholar 

  17. Miller, G. A. The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychol. Rev. 63, 8197 (1956)

    Article  Google Scholar 

  18. Bak, P. & Sneppen, K. Punctuated equilibrium and criticality in a simple model of evolution. Phys. Rev. Lett. 71, 4083–4086 (1993)

    Article  ADS  CAS  PubMed  Google Scholar 

  19. Jensen, H. J. Self Organised Criticality (Cambridge Univ. Press, Cambridge, 1998)

    Book  Google Scholar 

  20. Park, K. & Willinger, W. Self-Similar Networks Traffic and Performance Evaluation (Wiley, New York, 2000)

    Book  Google Scholar 

  21. Leighton, F. T., Maggs, B. M. & Rao, S. B. Packet routing and job-shop scheduling in O(congestion + dilation) steps. Combinatorica 14, 167–186 (1994)

    Article  MathSciNet  Google Scholar 

  22. Harris, C. M., Brill, P. H. & Fischer, M. J. Internet-type queues with power-tailed interarrival times and computational methods for their analysis. INFORMS J. Comp. 12, 261–271 (2000)

    Article  Google Scholar 

  23. Eubank, H. et al. Controlling epidemics in realistic urban social networks. Nature 429, 180–184 (2004)

    Article  ADS  CAS  PubMed  Google Scholar 

  24. Manrubia, S. C., Zanette, D. & Sole, R. V. Transient dynamics and scaling phenomena in urban growth. Fractals 7, 1–8 (1999)

    Article  Google Scholar 

  25. Helbing, D., Farkas, I. & Vicsek, T. Simulating dynamic features of escape panic. Nature 407, 487–490 (2000)

    Article  ADS  CAS  PubMed  Google Scholar 

  26. Caldarelli, G., Marsili, M. & Zhang, Y.-C. A prototype model of stock exchange. Europhys. Lett. 40, 479–484 (1997)

    Article  ADS  CAS  Google Scholar 

  27. Kleinberg, J. in Proc. 8th ACM SIGKDD Intl Conf. Knowledge Discov. Data Mining, 91–101 (2002)

    Google Scholar 

  28. Viswanathan, G. M. et al. Optimizing the success of random searches. Nature 401, 911–914 (1999)

    Article  ADS  CAS  Google Scholar 

Download references


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.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Albert-László Barabási.

Ethics declarations

Competing interests

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)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Barabási, AL. The origin of bursts and heavy tails in human dynamics. Nature 435, 207–211 (2005).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing