The origin of bursts and heavy tails in human dynamics

Notes on Barabási, A.-L. (2005). The origin of bursts and heavy tails in human dynamics. https://doi.org/10.1038/nature03459

Many forms of human behaviour (both individual and aggregate) show bursts of activity interspersed with periods of relative quiet. This is a result of decision-making based on perceived priority. In such cases most tasks are executed rapidly, but a few tasks will be delayed significantly.

In any queue, wait times are influenced by the method used to choose the next task:

• strict FIFO typically leads to a waiting time distribution with an exponential tail, most tasks have approximately the same wait time
• random selection also leads to a waiting time distribution with an exponential tail
• priority-based selecting leads to high-priority tasks being serviced quickly, whilst low-priority tasks wait until all higher priority tasks have been cleared, typically causing an extended wait time
  • with strict priority-based selection simulations the probability that a task will spend $\tau$ in the queue, $\text{Rho}(\tau )\sim {\tau }^{-}1$
  • the study compared this with measurements of the time to respond to emails^[1] which also exhibited $\text{Rho}(\tau )\sim {\tau }^{-}1$
  • even a queue of only 2 items exhibits this form of dynamics where priority-based selection is used

See also

• Zotero link
• Barabasi's detailed analysis
• Komjathy2012

References

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1. Harder, U., & Paczuski, M., Correlated dynamics in human printing behavior, http://xxx.lanl.gov/abs/cs.PF/0412027 .] ↩︎