Universal rank-size statistics in network traffic: Modeling collective access patterns by Zipf's law with long-term correlations

Abstract

We analyze network traffic rank-size statistics at different levels and organization. Our results support the emergence of Zipf's law in the rank-size traffic distributions by time, source and destination. The corresponding empirical laws considering typical discreteness and finite-size effects can be well approximated by q-exponential distributions for external IPs as well as by β- and Γ-distributions for internal LAN IPs and time fragments, respectively. Once appropriately normalized, the observed rank-size statistics exhibit rather universal shapes that are well reproduced by nonextensive entropy maximization algorithm for finite system sizes and can be used to model typical network activity patterns for a given community with a given number of active nodes as a sole free parameter.