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Shortest path models for scale-free network topologies: literature review and cross comparisons

Shortest path models for scale-free network topologies: literature review and cross comparisons

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The chapter focuses on Internet topology models. First, it investigated topology representations provided at different levels of granularity. Second, it reviewed topology models based on the graph theory and related topology generator tools. Third, it studied analytical models showing average shortest path and distribution of the shortest path length for scale-free networks. In fact, starting from these concepts, the accuracy of reference models for the shortest path are studied and compared through computer simulations. Obtained results demonstrate that available models are able to catch the average value and the distribution of the shortest path distribution over a very broad set of conditions. More specifically, when m = 1, the Gamma distribution shows the lowest distance for all N values. When m = 2 and m = 3, instead, the Weibull distribution provides the lowest error. The lognormal distribution always registers the worst behavior. On the contrary, all the evaluated models require a case-by-case tuning of their parameters, which represents an important limit to be solved in future research activities.

Chapter Contents:

  • 6.1 Mapping the Internet topology
  • 6.1.1 Interface level
  • 6.1.1.1 Active methodology based on traceroute
  • 6.1.1.2 IP options and subnet discovery
  • 6.1.2 Router level
  • 6.1.2.1 Alias resolution techniques
  • 6.1.2.2 Recursive router discovery
  • 6.1.3 AS level
  • 6.1.3.1 Passive methodology based on BGP and Internet Routing Registry
  • 6.1.3.2 Active methodology based on traceroute
  • 6.1.4 Geographic network topologies
  • 6.2 Internet models based on the graph theory
  • 6.2.1 Fundamental notions from the graph theory
  • 6.2.2 Topology models
  • 6.2.2.1 Regular and well-known topology models
  • 6.2.2.2 Random and small-world topology model
  • 6.2.2.3 Power-law topology models
  • 6.2.2.4 Scale-free topology model
  • 6.2.2.5 Hierarchical methods
  • 6.2.3 Topology generator tools
  • 6.2.3.1 Random topology generator tools
  • 6.2.3.2 Power-law topology generator tools
  • 6.2.3.3 Scale-free topology generator tools
  • 6.2.3.4 Hierarchical topology generator tools
  • 6.3 Shortest path models
  • 6.3.1 Parameters definition
  • 6.3.2 Shortest path models
  • 6.3.2.1 Gamma distribution
  • 6.3.2.2 Weibull distribution
  • 6.3.2.3 Lognormal distribution
  • 6.3.3 Cross-comparison among shortest path models
  • 6.3.4 Shortest path models applications
  • 6.4 Conclusion
  • Acknowledgment
  • References

Inspec keywords: gamma distribution; computer simulation; Internet; reviews; graph theory; telecommunication network topology

Other keywords: graph theory; Internet topology models; computer simulations; Gamma distribution; scale-free network topologies; reviewed topology models; case-by-case tuning; Weibull distribution; reference models; related topology generator tools; lognormal distribution

Subjects: Communication network design, planning and routing; Computer communications; Internet software; Other topics in statistics; Combinatorial mathematics; Other topics in statistics; Combinatorial mathematics

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