Poissonian bursts in e-mail correspondence

TL;DR

This paper demonstrates that e-mail communication burstiness and correlations can be explained by a non-homogeneous Poisson process, showing no additional complex correlations beyond what a cascading Poisson model predicts.

Contribution

The study extends analysis of e-mail communication to higher-order statistics, revealing that observed burstiness is consistent with a non-homogeneous Poisson process, challenging previous notions of complex correlations.

Findings

Higher-order statistics match those of randomized data

Synthetic cascading Poisson models replicate empirical burstiness

Correlations arise from non-homogeneous Poisson process

Abstract

Recent work has shown that the distribution of inter-event times for e-mail communication exhibits a heavy tail which is statistically consistent with a cascading Poisson process. In this work we extend the analysis to higher-order statistics, using the Fano and Allan factors to quantify the extent to which the empirical data depart from the known correlations of Poissonian statistics. The analysis shows that the higher-order statistics from the empirical data is indistinguishable from that of randomly reordered time series, thus demonstrating that e-mail correspondence is no more bursty or correlated than a Poisson process. Furthermore synthetic data sets generated by a cascading Poisson process replicate the burstiness and correlations observed in the empirical data. Finally, a simple rescaling analysis using the best-estimate rate of activity, confirms that the empirically observed correlations arise from a non-homogeneus Poisson process.