Scaling properties of the Internet graph

Abstract

As the Internet grows in size, it becomes crucial to understand how the speeds of links in the network must improve in order to sustain the pressure of new end-nodes being added each day. Although the speeds of links in the core and at the edges roughly improve according to Moore's law, this improvement alone might not be enough. Indeed, the structure of the Internet graph and routing in the network might necessitate much faster improvements in the speeds of key links in the network. In this paper, using a combination of analysis and extensive simulations, we show that the worst congestion in the Internet in fact scales poorly with the network size (n 1+Q^1 \ where n is the number of nodes), when shortest-path routing is used. We also show, somewhat surprisingly, that policy-based routing does not exacerbate the maximum congestion when compared to shortest-path routing. Our results show that it is crucial to identify ways to alleviate this congestion to avoid some links from being perpetually congested. To this end, we show that the congestion scaling properties of the Internet graph can be improved dramatically by introducing moderate amounts of redundancy in the graph in terms of parallel edges between pairs of adjacent nodes.

Connectivity Measures for Internet Topologies on the Level of Autonomous Systems

“…Apart from demonstrating the usability of our algorithms on realistic instances, our investigations also provide useful information on the similarities and differences between the topologies produced by the four different inference algorithms from Gao (2001), Subramanian et al (2002), Di Battista, Patrignani, and Pizzonia (2003), Erlebach, Hall, and Schank (2002). We believe that it is important to learn more about the characteristics of the topologies produced by different inference algorithms, as recent results about measurements on the AS level of the Internet have shown that there is a need for a simple and accurate algorithm to infer relationships; see Spring, Mahajan, and Anderson (2003) about path inflation in interand intra-domain routing, Akella et al (2003b) about multi-homing (i.e., the phenomenon that customers tend to have more than one external link to different providers, in order to guarantee the reliability of their network), and Akella et al (2003a) about scaling properties of the Internet regarding link congestion. Thus, in addition to the two connectivity measures, we study aspects such as the depth of the provider-hierarchy in the different topologies and the presence of so-called customer-provider cycles.…”

Evolution Versus “Intelligent Design”: Comparing the Topology of Protein-Protein Interaction Networks to the Internet

“…Edge congestion measures the amount of flows traveling through the edges of a network assuming a given traffic model and routing policy. In this study, we assume that one unit of flow between every pair of vertices is routed using the shortest-path routing policy 19,20 .…”

On the scaling of congestion in the internet graph

“…Specifically, we consider the model in which each link can be replaced by multiple links (between the same pair of nodes) that can share the traffic load 8 . Ideally, we would like to provide sufficient parallel links between a pair of nodes, so that the total congestion on the corresponding edge divided equally among these parallel 8 For results on alternate methods of alleviating congestion, please refer to a full version of this paper [4]. Avg.…”