Study On Characteristics And Model Of The Internet Topology At Autonomous System Level

Network topology along with network traffic and network protocols constitutes the three basic components of the simulated environment of the Internet. Researches on the Internet topology include:discovery, interpretation, modeling, validation and control. Current related researches focus on the first three, and then the topology characteristics and models of the Internet were validated and revised and quantified based on the empirical data.The layering method of the Internet topology was analyzed, and the model based on the five layers structure was given. The source of the BGP data for the Internet topology at AS level and the method collecting the BGP data were presented, and the implications of the BGP routing table was obtained.Firstly, the mathematical definition of the power-law was given, and the relationship between the power-law distribution and the scale-free property was analyzed. Secondly, the four kinds of the power-law distributions and the exponents of the power-law distributions based on the various kinds of the empirical data were summarized. Thirdly, the small-world effect of the Internet topology at the AS-level was analyzed and the formulas of the average path length and the clustering coefficients were given, and the betweenness centrality, the disassortativity and the rich-club phenomenon of the Internet topology were analyzed and discussed. Finally, the above characteristics of the Internet topology at AS-level were validated using the empirical data.Based on the parameters including the minimum node degree and the maximum node degree, the models of the Internet AS-level topology for the power-law distribution were presented. Next, the existing parameter estimations were compared, and then a new algorithm based on the Kolmogorov-Smirnov for estimating the parameters was obtained. In the end, the model and algorithm were analyzed and validated by using the empirical data of the Internet AS-level topology. We find that:(1) the Internet AS has the general characteristics of a complex network; (2) the power-law model introducing the minimum node degree and the maximum node degree is more suitable for modeling the Internet AS; (3) the parameter estimation algorithm based on KS is able to estimate the parameters of the power-law model.