Multilevel resilience analysis of transportation and communication networks

For many years the research community has attempted to model the Internet in order to better understand its behaviour and improve its performance. Since much of the structural complexity of the Internet is due to its multilevel operation, the Internet's multilevel nature is an important and non-trivial feature that researchers must consider when developing appropriate models. In this paper, we compare the normalised Laplacian spectra of physical- and logical-level topologies of four commercial ISPs and two research networks against the US freeway topology, and show analytically that physical level communication networks are structurally similar to the US freeway topology. We also generate synthetic Gabriel graphs of physical topologies and show that while these synthetic topologies capture the grid-like structure of actual topologies, they are more expensive than the actual physical level topologies based on a network cost model. Moreover, we introduce a distinction between geographic graphs that include degree-2 nodes needed to capture the geographic paths along which physical links follow, and structural graphs that eliminate these degree-2 nodes and capture only the interconnection properties of the physical graph and its multilevel relationship to logical graph overlays. Furthermore, we develop a multilevel graph evaluation framework and analyse the resilience of single and multilevel graphs using the flow robustness metric. We then confirm that dynamic routing performed over the lower levels helps to improve the performance of a higher level service, and that adaptive challenges more severely impact the performance of the higher levels than non-adaptive challenges.