Eur. Phys. J. B 75, 389-394 (2010)
https://doi.org/10.1140/epjb/e2010-00139-9

Poissonian bursts in e-mail correspondence

¹ Departamento de Física, PUC-Rio and National Institute of Science and Technology for Complex Systems, Rua Marquês de São Vicente 225, CEP 22453-900, RJ, Rio de Janeiro, Brazil
² Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL, 60208, USA
³ Datascope Analytics, Evanston, IL, 60201, USA
⁴ Department of Physiology, Feinberg Medical School, Northwestern University, 303, East Chicago Ave. Chicago, IL, 60611, USA

Corresponding author: ^a celia@fis.puc-rio.br

Received: 8 July 2009
Revised: 22 November 2009
Published online: 6 May 2010

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 this analysis to higher-order statistics, using the Fano and Allan factors to quantify the extent to which the empirical data are more correlated – bursty – than a Poisson process. Our analysis demonstrates that the correlations in the empirical data are indistinguishable from those of randomly reordered time series, illustrating that any correlations in the data are not due to the precise ordering of events. We further find that correlations in synthetic time series generated from a cascading Poisson process agree quite well with the correlations observed in the empirical data. Finally, we rescale the empirical time series to confirm that e-mail correspondence is no more correlated than expected from a suitably chosen Poisson process.