A tale of the tails: Power-laws in internet measurements

Power-laws are ubiquitous in the Internet and its applications. This tutorial presents a review of power-laws with emphasis on observations from Internet measurements. First, we introduce power-laws and describe two commonly observed power-law distributions, the Pareto and Zipf distributions. Two frequently occurring terms associated with these distributions, specifically heavy tails and long tails, are also discussed. Second, the preferential attachment model, which is a widely used model for generating power-law graph structures, is reviewed. Subsequently, we present several examples of Internet workload properties that exhibit power-law behavior. Finally, we explore several implications of power-laws in computer networks. Using examples from past and present, we review how researchers have studied and exploited power-law properties. We observe that despite the challenges posed, power-laws have been effectively leveraged by researchers to improve the design and performance of Internet-based systems.