Mathematics and the Internet: A Source of Enormous Confusion and Great Potential

Graph theory models the Internet mathematically, and a number of plausible mathematically intersecting network models for the Internet have been developed and studied. Simultaneously, Internet researchers have developed methodology to use real data to validate, or invalidate, proposed Internet models. The authors look at these parallel developments, particularly as they apply to scale-free network models of the preferential attachment type

Understanding Internet topology: principles, models, and validation

Building on a recent effort that combines a first-principles approach to modeling router-level connectivity with a more pragmatic use of statistics and graph theory, we show in this paper that for the Internet, an improved understanding of its physical infrastructure is possible by viewing the physical connectivity as an annotated graph that delivers raw connectivity and bandwidth to the upper layers in the TCP/IP protocol stack, subject to practical constraints (e.g., router technology) and economic considerations (e.g., link costs). More importantly, by relying on data from Abilene, a Tier-1 ISP, and the Rocketfuel project, we provide empirical evidence in support of the proposed approach and its consistency with networking reality. To illustrate its utility, we: 1) show that our approach provides insight into the origin of high variability in measured or inferred router-level maps; 2) demonstrate that it easily accommodates the incorporation of additional objectives of network design (e.g., robustness to router failure); and 3) discuss how it complements ongoing community efforts to reverse-engineer the Internet

A contrasting look at self-organization in the Internet and next-generation communication networks

This article examines contrasting notions of self-organization in the Internet and next-generation communication networks, by reviewing in some detail recent evidence regarding several of the more popular attempts to explain prominent features of Internet structure and behavior as "emergent phenomena." In these examples, what might appear to the nonexpert as "emergent self-organization" in the Internet actually results from well conceived (albeit perhaps ad hoc) design, with explanations that are mathematically rigorous, in agreement with engineering reality, and fully consistent with network measurements. These examples serve as concrete starting points from which networking researchers can assess whether or not explanations involving self-organization are relevant or appropriate in the context of next-generation communication networks, while also highlighting the main differences between approaches to self-organization that are rooted in engineering design vs. those inspired by statistical physics

Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (Extended Version)

Although the ``scale-free'' literature is large and growing, it gives neither a precise definition of scale-free graphs nor rigorous proofs of many of their claimed properties. In fact, it is easily shown that the existing theory has many inherent contradictions and verifiably false claims. In this paper, we propose a new, mathematically precise, and structural definition of the extent to which a graph is scale-free, and prove a series of results that recover many of the claimed properties while suggesting the potential for a rich and interesting theory. With this definition, scale-free (or its opposite, scale-rich) is closely related to other structural graph properties such as various notions of self-similarity (or respectively, self-dissimilarity). Scale-free graphs are also shown to be the likely outcome of random construction processes, consistent with the heuristic definitions implicit in existing random graph approaches. Our approach clarifies much of the confusion surrounding the sensational qualitative claims in the scale-free literature, and offers rigorous and quantitative alternatives.Comment: 44 pages, 16 figures. The primary version is to appear in Internet Mathematics (2005

FAIR: Forwarding Accountability for Internet Reputability

This paper presents FAIR, a forwarding accountability mechanism that incentivizes ISPs to apply stricter security policies to their customers. The Autonomous System (AS) of the receiver specifies a traffic profile that the sender AS must adhere to. Transit ASes on the path mark packets. In case of traffic profile violations, the marked packets are used as a proof of misbehavior. FAIR introduces low bandwidth overhead and requires no per-packet and no per-flow state for forwarding. We describe integration with IP and demonstrate a software switch running on commodity hardware that can switch packets at a line rate of 120 Gbps, and can forward 140M minimum-sized packets per second, limited by the hardware I/O subsystem. Moreover, this paper proposes a "suspicious bit" for packet headers - an application that builds on top of FAIR's proofs of misbehavior and flags packets to warn other entities in the network.Comment: 16 pages, 12 figure

Contrasting Views of Complexity and Their Implications For Network-Centric Infrastructures

There exists a widely recognized need to better understand and manage complex “systems of systems,” ranging from biology, ecology, and medicine to network-centric technologies. This is motivating the search for universal laws of highly evolved systems and driving demand for new mathematics and methods that are consistent, integrative, and predictive. However, the theoretical frameworks available today are not merely fragmented but sometimes contradictory and incompatible. We argue that complexity arises in highly evolved biological and technological systems primarily to provide mechanisms to create robustness. However, this complexity itself can be a source of new fragility, leading to “robust yet fragile” tradeoffs in system design. We focus on the role of robustness and architecture in networked infrastructures, and we highlight recent advances in the theory of distributed control driven by network technologies. This view of complexity in highly organized technological and biological systems is fundamentally different from the dominant perspective in the mainstream sciences, which downplays function, constraints, and tradeoffs, and tends to minimize the role of organization and design

Developing Robust VoIP Router Honeypots Using Device Fingerprints

As the telegram was replaced by telephony, so to Voice over IP (VoIP) systems are replacing conventional switched wire telephone devices, these systems rely on Internet connectivity for the transmission of voice conversations. This paper is an outline of ongoing preliminary research into malfeasant VoIP activity on the Internet. 30 years ago PABX systems were compromised by hackers wanting to make long distance calls at some other entities expense. This activity faded as telephony became cheaper and PABX systems had countermeasures installed to overcome attacks. Now the world has moved onto the provision of telephony via broadband enabled Voice over Internet Protocol (VoIP) this service is now being provided as a replacement for conventional fixed wire telephony by major telecommunication providers worldwide. Due to increasing bandwidth it is possible for systems to support multiple voice connections simultaneously. The networked nature of the Internet allows for attackers of these VoIP systems to enumerate and potentially attack and compromise a wide range of vulnerable systems