By Robert B. Israel
Arthur S. Wightman (introduction)
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Extra resources for Convexity in the Theory of Lattice Gases
This difference in size is reﬂected in different administrative policies that make routing through the Internet a highly unpredictable and heterogeneous phenomenon. Also very important is the fact that the Internet is a self-organizing system, whose properties cannot be traced back to any blueprint or chart. 1 This means that routers and links are added by competing entities according to local economic and technical constraints, leading to a very intricate physical structure that does not comply with any globally optimized plan.
ASs were originally only a routing concept, but have eventually led to a more general abstract representation of the Internet. Also in this case we can use a graph-like representation to study the inter-AS connectivity, in which vertices represent ASs and edges are peering relationships5 among them. Mapping projects focus essentially on two levels of topological description. First, by inferring router adjacencies it has been possible to measure the Internet Router (IR) level graph. The second mapping effort concerns the AS level graph of the Internet obtained from AS routing path information.
4 This introduces a more precise identiﬁcation of AS classes based on their 3 It is worth mentioning that the early Internet was quite different, with an essentially tree-like inter-domain hierarchy. The NSFNET provided long-distance connectivity to regional providers. The latter in their turn were offering connectivity to campuses and other LANs. 4 Exceptions to this general picture can be found in the case of stubs connected by a stub-to-stub link. 22 Measuring the global Internet AS3 AS2 AS3 AS2 AS4 AS4 AS1 AS1 LAN Router level Autonomous system level Fig.
Convexity in the Theory of Lattice Gases by Robert B. Israel