A Poissonian explanation for heavy-tails in e-mail communication

TL;DR

This paper explains the heavy-tailed distribution of inter-email times as a result of circadian and weekly human activity cycles modeled through a cascading non-homogeneous Poisson process, aligning well with empirical data.

Contribution

It introduces a novel cascading non-homogeneous Poisson process model that accounts for periodic activity patterns to explain heavy-tailed inter-event times in email communication.

Findings

Model fits empirical email data well

Periodic activity cycles produce power-law inter-event times

Provides a potential explanation for heavy tails in complex systems

Abstract

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 $\tau$ between consecutively sent e-mails decays asymptotically as $\tau^{-\alpha}$, with $\alpha \approx 1$. 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 non-homogeneous Poisson process which 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.