Given the importance of the Internet network in our society, it is relevant to understand its behaviour under adverse scenarios. The Internet can be studied through di erent angles: by studying the Border Gateway Protocol (BGP) network, the Internet Backbone, the complete physical network, etc. However, these networks do not exist in isolation, but rather interact with one another (see gure 1). Furthermore, the robustness behaviour of interacting networks is di erent compared to their single network counterpart. In particular, it has been shown that networks can be more fragile when coupled [BPP+10]. Indeed, the single network approach to study the Internet's behaviour has been criticized in the past by Willinger et al. [WR13] as it does not capture the whole behaviour of it. Thus, to properly study the Internet we should model it as an interdependent network system.
We have previously presented an initial model [BBJ17]. Here, we modelled the Internet Backbone using a modi ed version of the relative neighborhood model [WKVM16], and the BGP network was modelled using a Scale-Free network with an appropriate value [FFF99] as it has been widely used to model BGP networks. In our modi ed version of the relative neighborhood model, each node is allocated into a 2-dimensional space, and any two nodes, u and v, get to be connected if there is no other node in the intersection area of the circles centered at u and v, each of radius d(u; v), where d(u; v) is the euclidean distance between node u and v. This can be interpreted as follows: two nodes will get to be connected if there is no other node closer to them in-between them.
However, in this model the interconnections between both networks are established at random, and thus do not represent the actual network pairing nature of the Internet. In order to further develop this model, the relation between Internet Backbone nodes, and BGP nodes must be studied. Here, the hypothesis is that the number of Internet Backbone nodes interacting with a BGP node is proportional to the degree of such BGP node. To test this hypothesis, data has been collected to determine whether high degree nodes on the BGP network are coupled to a proportional number of nodes on the Internet backbone or not. As an initial approximation of the Internet Backbone, the localization of BGP nodes per country has been established. Thus, for the present work the hypothesis is that the number of countries in which BGP nodes have counterparts, is proportional to the degree of such node. 3
The information to determine the country localization of BGP nodes was obtained from the Routing Information Service (RIS) project from RIPE NCC [rip], and GeoLite2 geolocalization database [geo]. Here, the fAS pre xes obtained from the BGP routing tables were used to determine their geographical localization using GeoLite2. The router geolocalization obtained from this kind of database has been demonstrated to be precise enough to perform localization analysis [GSH+17]. To obtain the degrees for BGP nodes, we used BGP routes obtained from RIS project and Traceroutes from RIPE Atlas.
We used the data obtained in this stage was to get a rst approximation about the relation of the BGP nodes degrees and the amount of physical counterparts of these nodes. 4
From the data obtained we can observe that there is no correlation between the amount of countries in which a BGP node has physical counterparts, and the degree of said node. Indeed, the Pearson correlation coe cient of this data was of 0.23, showing the lack of correlation between the parameters studied. This can be further appreciated in gure 2. These initial results show that in our initial model [BBJ17], the random coupling of both networks might be appropriate for modelling the Internet Backbone and the BGP network. However, we must note that the data used here to represent the Internet Backbone corresponds to an approximation using the number of countries in which a BGP node has physical counterparts, and therefore does not show the real amount of Backbone nodes coupled to each BGP node. Thus, to accurately determine the relation between the amount of Internet Backbone nodes interacting with a BGP node and the degree of said BGP node, we must determine the amount of Internet Backbone nodes associated to each BGP node within each country. As future work, we will study again the relation between the BGP node degree and the amount of Backbone nodes connected to said BGP node, this time looking for a non-linear relation. Also, further studies about the Internet Backbone, and the BGP network will be performed to continue the model development. In particular, this work will continue to research on data to determine a more precise approximation of Internet Backbone nodes. Once this work is completed, the possibility of adding other network infrastructures to the interdependent networks system model, that allow a better understanding of the Internet will be evaluated in order to improve the model.
This work was partially funded by CONICYT Doctorado Nacional 21170165. [ATG16]
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