Abstract Fifty years of research in Networks coincides with 50 years of advances in resilience theory and applications. The purpose of this review is to identify how these two technical communities influenced each other in the past and can bolster each other in the future. Advances in resilience theory show that there are at least four ways networks demonstrate resilience: robustness, rebound, extensibility, and adaptability. Research published in Networks and by the broader network optimization community has focused primarily on technical methods for robustness and rebound. We review this literature to organize seminal problems and papers on the ability of networks to manage increasing stressors and return to normal activities after a stressful event. In contrast, the Networks community has made less progress addressing issues for network extensibility and adaptability. Extensibility refers to the ability to stretch current operations to surprising situations and adaptability refers to the ability to sustain operations into the future. We discuss ways to harness existing network optimization methods to study these forms of resilience and outline their limitations. We conclude by providing a research agenda that ensures the Networks community remains central to future advances in resilience while being pragmatic about the limitations of network optimization for achieving this task.

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.

Considerable attention is now being devoted to the study of "complexity science" with the intent of discovering and applying universal laws of highly interconnected and evolved systems. This paper considers several issues related to the use of these theories in the context of critical infrastructures, particularly the Internet. Specifically, we revisit the notion of "organized complexity" and suggest that it is fundamental to our ability to understand, operate, and design next-generation infrastructure networks. We comment on the role of engineering in defining an architecture to support networked infrastructures and highlight recent advances in the theory of distributed control driven by network technologies.

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.

The Internet is teeming with high variability phenomena, from measured IP flow sizes to aspects of inferred router-level connectivity, but there still exists considerable debate about how best to deal with this encountered high variability and model it. While one popular approach favors modeling highly variable event sizes with conventional, finite variance distributions such as lognormal or Weibull distributions, Mandelbrot has argued for the last 40 years that there are compelling mathematical, statistical, and practical reasons for why infinite variance distributions are natural candidates for capturing the essence behind high variability phenomena. In this paper, we elaborate on Mandelbrot's arguments and present a methodology that often allows for a clear distinction between the two approaches. In particular, by requiring the resulting models to be resilient to ambiguities (i.e., robust to real-world deficiencies in the underlying network measurements) and internally self-consistent (i.e., insensitive with respect the duration, location, or time of the data collection), we provide a rigorous framework for a qualitative assessment of the observed high variability. We apply the proposed framework to assess previously reported findings about measured Internet traffic and inferred router- and AS-level connectivity. In the process, we also discuss what our approach has to say about recent discussions concerning network traffic being Poisson or self-similar and router-level or AS-level connectivity graphs of the Internet being scale-free or not.

A detailed understanding of the many facets of the Internet's topological structure is critical for evaluating the performance of networking protocols, for assessing the effectiveness of proposed techniques to protect the network from nefarious intrusions and attacks, or for developing improved designs for resource provisioning. Previous studies of topology have focused on interpreting measurements or on phenomenological descriptions and evaluation of graph-theoretic properties of topology generators. We propose a complementary approach of combining a more subtle use of statistics and graph theory with a first-principles theory of router-level topology that reflects practical constraints and tradeoffs. While there is an inevitable tradeoff between model complexity and fidelity, a challenge is to distill from the seemingly endless list of potentially relevant technological and economic issues the features that are most essential to a solid understanding of the intrinsic fundamentals of network topology. We claim that very simple models that incorporate hard technological constraints on router and link bandwidth and connectivity, together with abstract models of user demand and network performance, can successfully address this challenge and further resolve much of the confusion and controversy that has surrounded topology generation and evaluation.