Scaling phenomena in the Internet: Critically examining criticality
Abstract
Recent Internet measurements have found pervasive evidence of some surprising scaling properties. The two we focus on in this paper are self-similar scaling in the burst patterns of Internet traffic and, in some contexts, scale-free structure in the network's interconnection topology. These findings have led to a number of proposed models or “explanations” of such “emergent” phenomena. Many of these explanations invoke concepts such as fractals, chaos, or self-organized criticality, mainly because these concepts are closely associated with scale invariance and power laws. We examine these criticality-based explanations of self-similar scaling behavior—of both traffic flows through the Internet and the Internet's topology—to see whether they indeed explain the observed phenomena. To do so, we bring to bear a simple validation framework that aims at testing whether a proposed model is merely evocative, in that it can reproduce the phenomenon of interest but does not necessarily capture and incorporate the true underlying cause, or indeed explanatory, in that it also captures the causal mechanisms (why and how, in addition to what). We argue that the framework can provide a basis for developing a useful, consistent, and verifiable theory of large networks such as the Internet. Applying the framework, we find that, whereas the proposed criticality-based models are able to produce the observed “emergent” phenomena, they unfortunately fail as sound explanations of why such scaling behavior arises in the Internet.
Footnotes
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↵ † To whom reprint requests should be addressed. E-mail: walter{at}research.att.com.
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This paper results from the Arthur M. Sackler Colloquium of the National Academy of Sciences, “Self-Organized Complexity in the Physical, Biological, and Social Sciences,” held March 23–24, 2001, at the Arnold and Mabel Beckman Center of the National Academies of Science and Engineering in Irvine, CA.
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↵ ∥ Following widespread (but perhaps overly general) practice, we use the term self-organized criticality (SOC) to refer to highly interactive self-organized systems that display power law behavior.
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↵ ** In addition, TCP's flow control leads to a “self-clocking” structure that also introduces structure on the time scales of round-trip times, but one that is in this case separate from current network conditions.
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↵ †† We are not claiming that “closing the loop” is a new concept; for example, much of physics has been all about “closing the loop.” We simply argue here for applying the “closing the loop” concept in the context of Internet modeling, too.
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↵ ‡‡ The measurements were gathered by J. Mogul in 1995 and are available from the Internet Traffic Archive, http://www.acm.org/sigcomm/ITA/.
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↵ §§ The symbol ∼ means “behaves asymptotically as.”
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↵ ¶¶ We hasten to note, however, that without TCP, or some other form of congestion control, the highly variable session workloads are capable of creating aggregate link traffic that would be very different from what we observe in today's Internet.
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↵ ∥∥ It is important to note, however, that because of BGP-specific features such as address aggregation and policy routing, the NLANR-generated AS connectivity maps may provide a very incomplete picture of the actual AS connectivity in the Internet. We ignore in the following this largely unsolved problem, but resolving it is an area of active research.
- Abbreviations:
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IP, Internet protocol
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AS, autonomous system
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TCP, transmission control protocol
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BGP, border gateway protocol
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HTTP, hypertext transmission protocol
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LRD, long-range dependence
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BA, Barabasi–Albert
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- Copyright © 2002, The National Academy of Sciences
