Study of the Power-Law Fluctuations in the Email Size

TL;DR

This study investigates power-law fluctuations in email sizes across different user groups and time periods, confirming consistent distribution patterns and proposing a model that accurately predicts email size distributions.

Contribution

The paper introduces a model that explains email size distributions as a sum of subdistributions, validated with high correlation, extending previous findings over multiple years and user groups.

Findings

Power-law distribution of email sizes confirmed across datasets.

Model predicts email size distribution with a correlation coefficient of 0.8408.

Disaggregated data analysis supports the model's validity.

Abstract

In a previous study, we investigated the frequency distribution of the email size in the system log data of the main email server for the staff on a campus network. We found that the frequencies of email sizes followed a power-law distribution and discovered two inflection points in the distribution. After analyzing these results, we collected new system log data for both staff and students for the period from April 1, 2009 to March 31, 2015 and analyzed the frequency distributions per academic year. The results of the earlier investigation were replicated for each of these distributions. Then, we disaggregated the system log data for the staff for the period from May 1, 2015 to July 31, 2015 using the email header "Content-Type" and created four subdistributions. Frequency distributions were calculated for the disaggregated data. We then proposed and evaluated a model to explain the overall frequency distribution as a sum of the four subdistributions. The correlation coefficient between the observed frequency distribution and the distribution predicted by our model was 0.8408 for the staff. This coefficient confirmed that our approach can successfully model and predict the size distribution of emails.