Efficient Behavior of Small-World Networks

We introduce the concept of efficiency of a network, measuring how efficiently it exchanges information. By using this simple measure small-world networks are seen as systems that are both globally and locally efficient. This allows to give a clear physical meaning to the concept of small-world, and also to perform a precise quantitative a nalysis of both weighted and unweighted networks. We study neural networks and man-made communication and transportation systems and we show that the underlying general principle of their construction is in fact a small-world principle of high efficiency.Comment: 1 figure, 2 tables. Revised version. Accepted for publication in Phys. Rev. Let

Generating Representative ISP Technologies From First-Principles

Understanding and modeling the factors that underlie the growth and evolution of network topologies are basic questions that impact capacity planning, forecasting, and protocol research. Early topology generation work focused on generating network-wide connectivity maps, either at the AS-level or the router-level, typically with an eye towards reproducing abstract properties of observed topologies. But recently, advocates of an alternative "first-principles" approach question the feasibility of realizing representative topologies with simple generative models that do not explicitly incorporate real-world constraints, such as the relative costs of router configurations, into the model. Our work synthesizes these two lines by designing a topology generation mechanism that incorporates first-principles constraints. Our goal is more modest than that of constructing an Internet-wide topology: we aim to generate representative topologies for single ISPs. However, our methods also go well beyond previous work, as we annotate these topologies with representative capacity and latency information. Taking only demand for network services over a given region as input, we propose a natural cost model for building and interconnecting PoPs and formulate the resulting optimization problem faced by an ISP. We devise hill-climbing heuristics for this problem and demonstrate that the solutions we obtain are quantitatively similar to those in measured router-level ISP topologies, with respect to both topological properties and fault-tolerance

Economic Small-World Behavior in Weighted Networks

The small-world phenomenon has been already the subject of a huge variety of papers, showing its appeareance in a variety of systems. However, some big holes still remain to be filled, as the commonly adopted mathematical formulation suffers from a variety of limitations, that make it unsuitable to provide a general tool of analysis for real networks, and not just for mathematical (topological) abstractions. In this paper we show where the major problems arise, and how there is therefore the need for a new reformulation of the small-world concept. Together with an analysis of the variables involved, we then propose a new theory of small-world networks based on two leading concepts: efficiency and cost. Efficiency measures how well information propagates over the network, and cost measures how expensive it is to build a network. The combination of these factors leads us to introduce the concept of {\em economic small worlds}, that formalizes the idea of networks that are "cheap" to build, and nevertheless efficient in propagating information, both at global and local scale. This new concept is shown to overcome all the limitations proper of the so-far commonly adopted formulation, and to provide an adequate tool to quantitatively analyze the behaviour of complex networks in the real world. Various complex systems are analyzed, ranging from the realm of neural networks, to social sciences, to communication and transportation networks. In each case, economic small worlds are found. Moreover, using the economic small-world framework, the construction principles of these networks can be quantitatively analyzed and compared, giving good insights on how efficiency and economy principles combine up to shape all these systems.Comment: 17 pages, 10 figures, 4 table

Computing in the RAIN: a reliable array of independent nodes

The RAIN project is a research collaboration between Caltech and NASA-JPL on distributed computing and data-storage systems for future spaceborne missions. The goal of the project is to identify and develop key building blocks for reliable distributed systems built with inexpensive off-the-shelf components. The RAIN platform consists of a heterogeneous cluster of computing and/or storage nodes connected via multiple interfaces to networks configured in fault-tolerant topologies. The RAIN software components run in conjunction with operating system services and standard network protocols. Through software-implemented fault tolerance, the system tolerates multiple node, link, and switch failures, with no single point of failure. The RAIN-technology has been transferred to Rainfinity, a start-up company focusing on creating clustered solutions for improving the performance and availability of Internet data centers. In this paper, we describe the following contributions: 1) fault-tolerant interconnect topologies and communication protocols providing consistent error reporting of link failures, 2) fault management techniques based on group membership, and 3) data storage schemes based on computationally efficient error-control codes. We present several proof-of-concept applications: a highly-available video server, a highly-available Web server, and a distributed checkpointing system. Also, we describe a commercial product, Rainwall, built with the RAIN technology