Discussion of “ Heavy Tail Modeling and Teletraffic Data ” by S . R . Resnick

As network researchers who have spent many long days in the past few years poring over Gigabytes of networkrelated measurements to try to get some basic understanding of network traffic, we are very pleased to see this article and to be able to comment on it. Historically, the field of networking and communications research has suffered from a severe and constant shortage of traffic measurements [11]; however, during the past 5-10 years, an abundance of enormoussized data sets of high-quality network traffic measurements have become available and keep on being collected in ever-increasing quantities and from ever-faster networks. Unfortunately, the development of statistical techniques and methods for efficiently dealing with this “flood” and for effectively handling phenomena such as heavy tails and longrange dependence, hitherto unknown in the networking arena, has not kept up with the rate at which newer and larger data sets of traffic measurements are being captured, nor with the pace at which the networks themselves change. Prof. Resnick's paper is therefore extremely timely and highly welcome by traffic analysts who are stymied by the many unfamiliar features that appear in networking-related data sets, and typically lack even the most basic tools to sensibly deal with them. At the same time, Prof. Resnick's paper also serves as useful reminder that collected data often determine the utility and relevance of one data analysis ormodeling approach over another. To illustrate this, we first point out to the interested statisticians and data analysts some of the features that make data sets of traffic measurements from today's networks unique and challenging, especially when compared to available data sets from other areas of science and engineering (e.g., hydrology, medicine, biophysics, economics, finance). Given the special nature of the data at hand, we then argue – in contrast to Resnick – for abandoning the black box modeling approach from traditional time series analysis and focusing instead on structural models that take into account the context in which the data arose in the first place, namely the highly intertwined hierarchies of networking functions that form the basis of modern computer communication. While we readily admit that black box models can be and are useful in other contexts, we strongly believe that they are essentially of no use for our main purposes of trying to understand the dynamic and complex nature of traffic in today's packet networks and, subsequently, of exploiting this understanding to design, manage and control these networks. The Annals of Statistics, 25(5), pp. 1805–1869, 1997. Includes this and other discussion articles, and rejoinder.