A Poissonian explanation for heavy tails in e-mail communication

R. Dean Malmgren, Daniel B. Stouffer, Adilson E. Motter, Luís A.N. Amaral

Research output: Contribution to journalArticlepeer-review

324 Scopus citations


Patterns of deliberate human activity and behavior are of utmost importance in areas as diverse as disease spread, resource allocation, and emergency response. Because of its widespread availability and use, e-mail correspondence provides an attractive proxy for studying human activity. Recently, it was reported that the probability density for the inter-event time τ between consecutively sent e-mails decays asymptotically as τ, with α ≈ 1. The slower-than-exponential decay of the inter-event time distribution suggests that deliberate human activity is inherently non-Poissonian. Here, we demonstrate that the approximate power-law scaling of the inter-event time distribution is a consequence of circadian and weekly cycles of human activity. We propose a cascading nonhomogeneous Poisson process that explicitly integrates these periodic patterns in activity with an individual's tendency to continue participating in an activity. Using standard statistical techniques, we show that our model is consistent with the empirical data. Our findings may also provide insight into the origins of heavy-tailed distributions in other complex systems.

Original languageEnglish (US)
Pages (from-to)18153-18158
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number47
StatePublished - Nov 25 2008


  • Complex systems
  • Human activity
  • Hypothesis testing
  • Point process

ASJC Scopus subject areas

  • General


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