A geographic directed preferential Internet topology model

The goal of this work is to model the peering arrangements between autonomous systems (ASes). Most existing models of the AS-graph assume an undirected graph. However, peering arrangements are mostly asymmetric customer-provider arrangements, which are better modeled as directed edges. Furthermore, it is well known that the AS-graph, and in particular its clustering structure, is influenced by geography. We introduce a new model that describes the AS-graph as a directed graph, with an edge going from the customer to the provider, but also models symmetric peer-to-peer arrangements. In addition, our model takes geography into account. We are able to mathematically analyze its power-law exponent and number of leaves. Beyond the analysis, we have implemented our model as a synthetic network generator called GDNG. Experimentation with GDNG shows that the networks it produces are more realistic than those generated by other network generators, in terms of its power-law exponent, fractions of customer-provider and symmetric peering arrangements, and the size of its dense core. We believe that our model is the first to manifest realistic regional dense cores that have a clear geographic flavor. Our synthetic networks also exhibit path inflation effects that are similar to those observed in the real AS graph.