A pragmatic approach to dealing with high-variability in network measurements

The Internet is teeming with high variability phenomena, from mea-sured IP flow sizes to aspects of inferred router-level connectivity, but there still exists considerable debate about how best to deal with this encountered high variability and model it. While one popular approach favors modeling highly variable event sizes with conven-tional, finite variance distributions such as lognormal or Weibull distributions, Mandelbrot has argued for the last 40 years that there are compelling mathematical, statistical, and practical reasons for why infinite variance distributions are natural candidates for captur-ing the essence behind high variability phenomena. In this paper, we elaborate on Mandelbrot’s arguments and present a methodol-ogy that often allows for a clear distinction between the two ap-proaches. In particular, by requiring the resulting models to be resilient to ambiguities (i.e., robust to real-world deficiencies in the underlying network measurements) and internally self-consistent (i.e., insensitive with respect the duration, location, or time of the data collection), we provide a rigorous framework for a qualitative assessment of the observed high variability. We apply the proposed framework to assess previously reported findings about measured Internet traffic and inferred router- and AS-level connectivity. In the process, we also discuss what our approach has to say about re-cent discussions concerning network traffic being Poisson or self-similar and router-level or AS-level connectivity graphs of the In-ternet being scale-free or not