There's a new article on up at Notices of the AMS entitled Mathematics and the Internet: A Source of Enormous Confusion and Great Potential, by Willinger, Alderson, and Doyle.
It's an interesting read, although I've heard some of the main points in talking with them before. In terms of specific examples of how problems in the modeling of the Internet arose, my take on their take of the history is that the trouble started with the well-known Faloutsos^3 paper (On Power-Law Relationships on the Internet Topology), which first appeared in SIGCOMM 1999, and which claimed that the degree distribution of the Internet's router-level topology followed a power law. It has been argued that there are a number of flaws with this paper, most notably in the underlying data, as described in this article, making their conclusions on the power-law relationship unreliable. (Given my recent posts and corresponding discussions on the SIGCOMM PC meeting, it's interesting to reflect on the importance this paper has played after being published in SIGCOMM.) The second part of this troublesome history is the subsequent work of Barabasi and Albert, who leveraged this result to help proclaim that the underlying mechanism of the Internet topology is preferential attachment, explaining this power law behavior. The authors discuss how this claim was made without sufficient validation, and argue that there are other optimization-based models that much better explain the guiding mechanisms behind the Internet topology, based on actual Internet engineering.
To start, I should admit not-so-humbly that I think the authors could have mentioned my very-relevant survey and editorial on these issues (the editorial, in particular, discusses the validation issue in this context). But leaving that aside, it's an interesting read with many possible lessons to draw or questions to think about. Are we insufficiently critical at early stages (e.g., conference publications), so that once a result is accepted, it becomes difficult to point out where it may be flawed? How do we deal with "noisy" network data in analysis? Are we getting to the point where only teams from Microsoft, Google, Akamai or AT&T (or some other big company) can publish in certain areas of networking because they're the only ones that can get good enough data? What are the useful ways mathematicians can contribute to the study of networking topology (yet another power law model does not seem to be compelling)?
I have to admit, I have a side worry with this appearing in the AMS. Given how it sometimes appears that mathematicians view computer scientists, I worry that this article will reinforce the belief in the minds of some mathematicians that computer science is "non-serious" or "non-rigorous", which clearly wasn't the intention of the authors. The problem of explaining the history of "enormous confusion" and "great potential" is the risk that too many readers will focus on the former rather than the latter.