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DOI: 10.4230/OASIcs.NINeS.2026.22

There Is More to Internet Invariants Than Meets the Eye

Authors: Chris Misa, Walter Willinger, Ramakrishnan Durairajan, and Reza Rejaie

Published in: OASIcs, Volume 139, 1st New Ideas in Networked Systems (NINeS 2026)

Abstract

A rich body of literature assembled over the last 30 years shows that traffic traversing wide-area Internet links is consistent with self-similar (temporal) scaling behavior and that sets of observed addresses have multifractal (spatial) scaling behavior. In view of this empirical evidence, these behaviors cannot be viewed as mere mathematical curiosities but should justifiably be called invariants of measured Internet traffic (Internet invariants, for short). At the same time, it is fair to say that the early architects of the Internet were largely unaware of these properties and certainly did not intend to design a network so that the traffic traversing its links would exhibit self-similar scaling in time or multifractal scaling in the IP address space. In this paper, we resolve this apparent disconnect between architectural intentions and observed behaviors by applying a three-part framework that leverages, at its core, the perspective of Highly Optimized Tolerance (HOT). In particular, we take inspiration from studies on the origins of (temporal) self-similarity in measured Internet traffic but focus on a fundamentally new approach to understanding multifractal (spatial) scaling behavior. Specifically, we examine whether this invariant can be viewed as a visible hallmark of underlying but largely unknown robust design efforts, and explore a reverse-engineering approach to determine the concrete nature of the constrained optimization problems that these robust designs solve. Based on the insights gained from such reverse-engineering efforts, we speculate on the benefits of future efforts at forward-engineering - systematically leveraging the identified robust designs in order to provide scientifically sound intellectual foundations and practical principles for designing future networked systems.

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Chris Misa, Walter Willinger, Ramakrishnan Durairajan, and Reza Rejaie. There Is More to Internet Invariants Than Meets the Eye. In 1st New Ideas in Networked Systems (NINeS 2026). Open Access Series in Informatics (OASIcs), Volume 139, pp. 22:1-22:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{misa_et_al:OASIcs.NINeS.2026.22,
  author =	{Misa, Chris and Willinger, Walter and Durairajan, Ramakrishnan and Rejaie, Reza},
  title =	{{There Is More to Internet Invariants Than Meets the Eye}},
  booktitle =	{1st New Ideas in Networked Systems (NINeS 2026)},
  pages =	{22:1--22:26},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-414-7},
  ISSN =	{2190-6807},
  year =	{2026},
  volume =	{139},
  editor =	{Argyraki, Katerina and Panda, Aurojit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.NINeS.2026.22},
  URN =		{urn:nbn:de:0030-drops-256077},
  doi =		{10.4230/OASIcs.NINeS.2026.22},
  annote =	{Keywords: Internet traffic, self-similarity, multifractal scaling, reverse-engineering}
}

Document

DOI: 10.4230/DagRep.3.8.27

The Critical Internet Infrastructure (Dagstuhl Seminar 13322)

Authors: Georg Carle, Jochen Schiller, Steve Uhlig, Walter Willinger, and Matthias Wählisch

Published in: Dagstuhl Reports, Volume 3, Issue 8 (2013)

Abstract

This report documents the program and the outcomes of Dagstuhl Seminar 13322 "The Critical Internet Infrastructure". The scope of the seminar includes three main topics, rethinking perspectives on the Internet backbone, methodologies to analyze the Internet structure, and paradigms overlaying IP connectivity. The results are based on fruitful discussions between people from the research and operational community.

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Georg Carle, Jochen Schiller, Steve Uhlig, Walter Willinger, and Matthias Wählisch. The Critical Internet Infrastructure (Dagstuhl Seminar 13322). In Dagstuhl Reports, Volume 3, Issue 8, pp. 27-39, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@Article{carle_et_al:DagRep.3.8.27,
  author =	{Carle, Georg and Schiller, Jochen and Uhlig, Steve and Willinger, Walter and W\"{a}hlisch, Matthias},
  title =	{{The Critical Internet Infrastructure (Dagstuhl Seminar 13322)}},
  pages =	{27--39},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2013},
  volume =	{3},
  number =	{8},
  editor =	{Carle, Georg and Schiller, Jochen and Uhlig, Steve and Willinger, Walter and W\"{a}hlisch, Matthias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.3.8.27},
  URN =		{urn:nbn:de:0030-drops-43416},
  doi =		{10.4230/DagRep.3.8.27},
  annote =	{Keywords: Internet, Backbone, Internet Services, Critical Infrastructure}
}

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Documents authored by Willinger, Walter

There Is More to Internet Invariants Than Meets the Eye

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The Critical Internet Infrastructure (Dagstuhl Seminar 13322)

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