The Fundamentals of Heavy-tails: Properties, Emergence, and Identification

Heavy-tails are a continual source of excitement and confusion across disciplines as they are repeatedly "discovered" in new contexts. This is especially true within computer systems, where heavy-tails seemingly pop up everywhere -- from degree distributions in the internet and social networks to file sizes and interarrival times of workloads. However, despite nearly a decade of work on heavy-tails they are still treated as mysterious, surprising, and even controversial. The goal of this tutorial is to show that heavy-tailed distributions need not be mysterious and should not be surprising or controversial. In particular, we will demystify heavy-tailed distributions by showing how to reason formally about their counter-intuitive properties; we will highlight that their emergence should be expected (not surprising) by showing that a wide variety of general processes lead to heavy-tailed distributions; and we will highlight that most of the controversy surrounding heavy-tails is the result of bad statistics, and can be avoided by using the proper tools.