Dynamic Models for File Sizes and Double Pareto Distributions

Abstract

In this paper, we introduce and analyze a new generative user model to explain the behavior of file size distributions. Our Recursive Forest File model combines ideas from recent work by Downey with ideas from recent work on random graph models for the Web. Unlike similar previous work, our Recursive Forest File model allows new files to be created and old files to be deleted over time, and our analysis covers problematic issues such as correlation among file sizes. Moreover, our model allows natural variations where files that are copied or modified are more likely to be copied or modified subsequently. Previous empirical work suggests that file sizes tend to have a lognormal body but a Pareto tail. The Recursive Forest File model explains this behavior, yielding a double Pareto distribution, which has a Pareto tail but close to a lognormal body. We believe the Recursive Forest model may be useful for describing other power law phenomena in computer systems as well as other fields.