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Register a new userTowards Modelling The Internet Topology - The Interactive Growth Model
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Added by
Shi Zhou
Publication date
2003
fields
Informatics Engineering
and research's language is
English
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The Internet topology at the Autonomous Systems level (AS graph) has a power--law degree distribution and a tier structure. In this paper, we introduce the Interactive Growth (IG) model based on the joint growth of new nodes and new links. This simple and dynamic model compares favorable with other Internet power--law topology generators because it not only closely resembles the degree distribution of the AS graph, but also accurately matches the hierarchical structure, which is measured by the recently reported rich-club phenomenon.
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Recently we introduced the rich-club phenomenon as a quantitative metric to characterize the tier structure of the Autonomous Systems level Internet topology (AS graph) and we proposed the Interactive Growth (IG) model, which closely matches the degree distribution and hierarchical structure of the AS graph and compares favourble with other available Internet power-law topology generators. Our research was based on the widely used BGP AS graph obtained from the Oregon BGP routing tables. Researchers argue that Traceroute AS graph, extracted from the traceroute data collected by the CAIDAs active probing tool, Skitter, is more complete and reliable. To be prudent, in this paper we analyze and compare topological structures of Traceroute AS graph and BGP AS graph. Also we compare with two synthetic Internet topologies generated by the IG model and the well-known Barabasi-Albert (BA) model. Result shows that both AS graphs show the rich-club phenomenon and have similar tier structures, which are closely matched by the IG model, however the BA model does not show the rich-club phenomenon at all.
Based on measurements of the Internet topology data, we found out that there are two mechanisms which are necessary for the correct modeling of the Internet topology at the Autonomous Systems (AS) level: the Interactive Growth of new nodes and new internal links, and a nonlinear preferential attachment, where the preference probability is described by a positive-feedback mechanism. Based on the above mechanisms, we introduce the Positive-Feedback Preference (PFP) model which accurately reproduces many topological properties of the AS-level Internet, including: degree distribution, rich-club connectivity, the maximum degree, shortest path length, short cycles, disassortative mixing and betweenness centrality. The PFP model is a phenomenological model which provides a novel insight into the evolutionary dynamics of real complex networks.
The internet structure is extremely complex. The Positive-Feedback Preference (PFP) model is a recently introduced internet topology generator. The model uses two generic algorithms to replicate the evolution dynamics observed on the internet historic data. The phenomenological model was originally designed to match only two topology properties of the internet, i.e. the rich-club connectivity and the exact form of degree distribution. Whereas numerical evaluation has shown that the PFP model accurately reproduces a large set of other nontrivial characteristics as well. This paper aims to investigate why and how this generative model captures so many diverse properties of the internet. Based on comprehensive simulation results, the paper presents a detailed analysis on the exact origin of each of the topology properties produced by the model. This work reveals how network evolution mechanisms control the obtained topology properties and it also provides insights on correlations between various structural characteristics of complex networks.
We present the first complete measurement of the Chinese Internet topology at the autonomous systems (AS) level based on traceroute data probed from servers of major ISPs in mainland China. We show that both the Chinese Internet AS graph and the global Internet AS graph can be accurately reproduced by the Positive-Feedback Preference (PFP) model with the same parameters. This result suggests that the Chinese Internet preserves well the topological characteristics of the global Internet. This is the first demonstration of the Internets topological fractality, or self-similarity, performed at the level of topology evolution modeling.
This paper takes a critical look at the usefulness of power law models of the Internet. The twin focuses of the paper are Internet traffic and topology generation. The aim of the paper is twofold. Firstly it summarises the state of the art in power law modelling particularly giving attention to existing open research questions. Secondly it provides insight into the failings of such models and where progress needs to be made for power law research to feed through to actual improvements in network performance.
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