Several novel concepts and tools have revolutionized our understanding of the Internet topology. Most of the existing efforts attempt to develop accurate analytical models. In this paper, our goal is to develop an effective conceptual model: a model that can be easily drawn by hand, while at the same time, it captures significant macroscopic properties. We build the foundation for our model with two thrusts: a) we identify new topological properties, and b) we provide metrics to quantify the topological importance of a node. We propose the jellyfish as a model for the inter-domain Internet topology. We show that our model captures and represents the most significant topological properties. Furthermore, we observe that the jellyfish has lasting value: it describes the topology for more than six years. 1

Mapping the Internet is a major challenge for network researchers. It is the key to building a successful modeling tool able to generate realistic graphs for use in networking simulations. In this paper we provide a detailed analysis of the inter-domain topology of the Internet. The collected data and the resulting analysis began in November 1997 and cover a period of two and a half years. We give results concerning major topology properties (nodes and edges number, average degree and distance, routing policy, etc.) and main distributions (degree, distance, etc.). We also present many results about the trees of this network. The evolution of these properties is reviewed and major trends are highlighted. We propose some empirical laws that match this current evolution. Four new power-laws concerning the number of shortest paths between node pairs and the tree size distribution are provided with their detailed validation.

There is a growing interest in discovery of internet topology at the interface level. A new generation of highly distributed measurement systems is currently being deployed. Unfortunately, the research community has not examined the problem of how to perform such measurements efficiently and in a network-friendly manner. In this paper we make two contributions toward that end. First, we show that standard topology discovery methods (e.g., skitter) are quite inefficient, repeatedly probing the same interfaces. This is a concern, because when scaled up, such methods will generate so much traffic that they will begin to resemble DDoS attacks. We measure two kinds of redundancy in probing (intra- and inter-monitor) and show that both kinds are important. We show that straightforward approaches to addressing these two kinds of redundancy must take opposite tacks, and are thus fundamentally in conflict. Our second contribution is to propose and evaluate Doubletree, an algorithm that reduces both types of redundancy simultaneously on routers and end systems. The key ideas are to exploit the treelike structure of routes to and from a single point in order to guide when to stop probing, and to probe each path by starting near its midpoint. Our results show that Doubletree can reduce both types of measurement load on the network dramatically, while permitting discovery of nearly the same set of nodes and links. ∗ The authors are participants in the traceroute@home project.This work was supported by: the RNRT project

In this paper, we investigate two issues. First, what level of efficiency gain does multicast offer over unicast? Second, how does the shape of multicast trees impact multicast efficiency? We address the first issue by developing a metric to measure multicast efficiency for a number of real and synthetic datasets. We find that group sizes as small as 20 to 40 receivers offer a 60-70% reduction in the number of links traversed compared to separately delivered unicast streams. Addressing the second issue, we have found that almost all multicast trees have similar characteristics in terms of key parameters such as depth, degree frequency and average degree. A final contribution of our work is that we have taken multicast group membership data and multicast path data and compiled datasets which can be used to generate large, realistic multicast trees. Keywords---Multicast, measurement, modeling, tree characteristics. I.

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In our previous work, 1 we used a simplied model of routing policy in the Internet to study the impact of policy routing on Internet path-lengths. This prior work suered from two shortcomings|it was based on a single snapshot of the Internet topology, and our simplied policy model could generate AS paths that violate peering relationships. In this paper, we address these two shortcomings by re-examining our results with respect to a more recent snapshot of the Internet, and improving the policy model to avoid peering violation. We nd that our prior observations regarding the path ination due to routing policy appear to hold both across time and with respect to a more sophisticated model of routing policy. Keywords: Internet Paths, Paths, Routing Policy, Policy Routing, Path Ination 1.

Replication is a well-known technique to improve the accessibility of Web sites. It generally offers reduced client latencies and increases a site’s availability. However, applying replication techniques is not trivial, and various Content Delivery Networks (CDNs) have been created to facilitate replication for digital content providers. The

The development and deployment of distributed networkaware applications and services require the ability to compile and maintain a model of the underlying network resources with respect to (one or more) characteristic properties of interest. To be manageable, such models must be compact, and to be general-purpose, they should enable a representation of properties along temporal, spatial, and measurement resolution dimensions. In this paper, we propose MINT---a general framework for the construction of such metric-induced models using end-to-end measurements. We present the basic theoretical underpinnings of MINT for a broad class of metrics obeying certain properties. We instantiate MINT for two metrics of interest, namely packet loss rates and bottleneck bandwidth. For the loss rate metric, we leverage recently proposed end-to-end techniques for the estimation of shared losses to characterize loss topologies. We present results of simulations and Internet measurements that confirm the effectiveness and robustness of our loss topology constructions over a wide range of network conditions.

Internet topology discovery consists of inferring the inter-router connectivity (“links”) and the mapping from IP addresses to routers (“alias resolution”). Current topology discovery techniques use TTL-limited “traceroute ” probes to discover links and use direct router probing to resolve aliases. The often-ignored record route (RR) IP option provides a source of disparate topology data that could augment existing techniques, but it is difficult to properly align with traceroute-based topologies because router RR implementations are under-standardized. Correctly aligned RR and traceroute topologies have fewer false links, include anonymous and hidden routers, and discover aliases for routers that do not respond to direct probing. More accurate and feature-rich topologies benefit overlay construction and network diagnostics, modeling, and measurement. We present DisCarte, a system for aligning and cross-validating RR and traceroute topology data using observed engineering practices. DisCarte uses disjunctive logic programming (DLP), a logical inference and constraint solving technique, to intelligently merge RR and traceroute data. We demonstrate that the resultant topology is more accurate and complete than previous techniques by validating its internal consistency and by comparing to publicly available topologies. We classify irregularities in router implementations and introduce a divide-and-conquer technique used to scale DLP to Internet-sized systems.

Understanding the graph structure of the Internet is a crucial step for building accurate network models and designing efficient algorithms for Internet applications. Yet, obtaining this graph structure can be a surprisingly difficult task, as edges cannot be explicitly queried. For instance, empirical studies of the network of Internet Protocol (IP) addresses typically rely on indirect methods like traceroute to build what are approximately single-source, all-destinations, shortest-path trees. These trees only sample a fraction of the network’s edges, and a recent paper by Lakhina et al. found empirically that the resulting sample is intrinsically biased. Further, in simulations, they observed that the degree distribution under traceroute sampling exhibits a power law even when the underlying degree distribution is Poisson. In this paper, we study the bias of traceroute sampling mathematically and, for a very general class of underlying degree distributions, explicitly calculate the distribution that will be observed. As example applications of our machinery, we prove that traceroute sampling finds power-law degree distributions in both δ-regular and Poisson-distributed random graphs. Thus, our work puts the observations of Lakhina et al. on a rigorous footing, and extends them to nearly arbitrary degree distributions.