On the Size Distribution of Autonomous Systems

We model the evolution of the Internet at the Autonomous System level as a process of competition for users and adaptation of bandwidth capability. We find the exponent of the degree distribution as a simple function of the growth rates of the number of autonomous systems and the total number of connections in the Internet, both empirically measurable quantities. This fact place our model apart from others in which this exponent depends on parameters that need to be adjusted in a model dependent way. Our approach also accounts for a high level of clustering as well as degree-degree correlations, both with the same hierarchical structure present in the real Internet. Further, it also highlights the interplay between bandwidth, connectivity and traffic of the network.PACS numbers: 87.23.Ge, 05.70.Ln A statistical physics approach to Internet modeling will be successful only if its large-scale properties can be explained and predicted on the basis of the interactions between basic units at the microscopic level [1,2]. Dynamical evolution rules acting at the local scale would then determine the behavior and the emergent structural properties of the whole Internet, which self-organizes under an absolute lack of centralized control [3,4]. This approach is at the core of a set of recent network models focusing on evolution, which recognise growth as one of the key mechanisms on network formation, along with preferential attachment or other utility rules [5,6,7,8,9,10]. While several of such models succeed in depicting some of the Internet features, none of them accounts for a complete description of the real topology [11,12,13]. In this paper, we present a new growing network model which, from competition and adaptation mechanisms, reproduces the topological properties observed in the autonomous system level maps of the Internet, namely: i) a scale-free distribution of the number of connections -or degree-of vertices k i , characterized by a power law P (k) ∼ k −γ , 2.1 ≤ γ < 2.5, ii) high clustering coefficient c k , defined as the ratio between the number of connected neighbors of a node of degree k and the maximum possible value averaged for all nodes of degree k, and, finally, iii) disassortative degree-degree correlations, quantified by means of the average nearest neighbors degree of nodes of degree k,k nn (k) [12].We start our analysis by looking at the growth of the Internet during the last three decades. We focus on the temporal evolution of the number of hosts present in the Internet [14] as compared to the number of distinct autonomous systems (ASs) and the total number of connections among them. We have reanalysed AS maps collected by the Oregon route-views project which has recorded the Internet topology at the AS level since November 1997 [15]. Let W (t), N (t) and E(t) be the total number of hosts (we assume that number of hosts is equivalent to number of users), number of ASs and edges among ASs at time t respectively. Fig.1 shows empirical measurements for these quantities revealing exponential gro...

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“…In the case of the Internet, α > ∼ β which implies an exponent smaller but close to 2. A similar result was obtained in [9].…”

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confidence: 88%

Competition and Adaptation in an Internet Evolution Model

2005

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“…But, if the victim has access to the global Internet map, then by seeing the connectivity between the routers, the victim can construct the attack graph. Again, the current size of the Internet being greater than 1.6e+08 hosts [24,25], obtaining the global Internet map is a non-trivial issue.…”

Section: 12mentioning

confidence: 99%

“…Number of ASes is far lesser than the number of routers in the Internet. The Internet consists around 14,000 ASes as compared to 1.6e+08 hosts [25]. Hence, obtaining an AS map of the Internet is feasible while obtaining Internet map itself is very difficult if not impossible.…”

Section: Design Motivationmentioning

confidence: 99%

“…2. In more than 99.5% cases, a packet passes through less than seven ASes before reaching its destination [24,25]. 3.…”

Section: Design Motivationmentioning

confidence: 99%

“…In this scheme, we reserve two fields -a 16-bit ASN field and a 3-bit AS_distance field -in the packet header. Note that 3 bits can represent up to a distance of 8 hops in terms of ASes traversed which is sufficient for almost all Internet paths [24,25,11].…”

Section: Autonomous System Based Ip Tracebackmentioning

confidence: 99%

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