File Size Distributions and Caching for Offloading

We consider order statistics of products of random variables to understand the relationship between traffic offloading and storage space consumption in an edge caching network. Given a statistical model for the popularities and sizes of data objects in a caching network, we derive the order statistics describing the probability density function of the size of the object that accounts for, e.g., the largest amount of data traffic. We further study the asymptotic behavior of these distributions, and give analytical results for both the general case and the asymptotic case. The derived results can be used to estimate an upper bound on the cache size needed when one is interested in offloading a certain fraction of all traffic for file catalogues with changing content but known distributions of popularities and object sizes.