Effect of adding physical links on the robustness of the Internet modeled as a physical–logical interdependent network using simple strategies

In this work we model the Internet as a physical–logical interdependent network composed by the logical Internet network (Autonomous System level network), the physical Internet network (Internet backbone), and their interactions. We have tested the effect of adding physical links over the Internet’s robustness against both physical random attacks, and localized attacks. We add links using strategies that are simple enough to be used when information of the physical network is incomplete or not accurate enough to use more complex strategies. To measure the effect of adding links to the physical network our tests consider the logical network, and the set of interlinks to be constant. We tested four physical link addition strategies: random addition, distance addition, local hubs addition, and degree addition, over three different physical network models: Gabriel Graphs, n-nearest neighbors, and relative neighborhood graphs, and two extreme space shapes based on the geography of real countries: a long and narrow space with a width to length ratio of (1:25), and square space with a (1:1) width to length ratio. Our results show that there are High Damage Localized Attacks (HDLA): localized attacks that cause the failure of more than half of the logical network after removing less than 9% of the physical nodes. Some HDLA can even result in total failure. We found that HDLA are caused by the failure of “bridge nodes” in the logical network. Our results show that adding links to the physical network improves the robustness against localized attacks, and physical random attacks. Adding physical links also decreases the damage caused by HDLA, but does not fully prevent them. We found that degree and random addition strategies improve the Internet’s robustness the most, while distance addition is the most cost efficient link addition strategy in terms of robustness improvement. We also found that the high robustness and low cost efficiency of random strategy is related to the length of the links added, highlighting the importance of simple features such as the length of the links added over the robustness of physical–logical interdependent networks . Our findings suggest that given cost constraints it may be better to add more physical links using distance addition than it is to add fewer physical links using degree or random link addition strategies, and that more cost efficient versions of degree strategy could be obtained by simply limiting the length of the links added by the strategy.