There are numerous reasons that network failures could occur. It is a conse- quence of certain events such as cable cuts, hardware malfunctions, software errors, power outages, natural disasters (e.g., flood, fire, and earthquake), accidents, human errors (e.g., incorrect maintenance) and malicious physi- cal/electronic attacks [10]. One approach for network survivability analysis is to focus on isolated independent failures, which could be single or multiple, but not correlated. Independent, uncorellated failures are modelled usually by a random process. However, communication networks are generally very robust against the single random failures, and multiple simultaneous failures are less likely to happen. Another approach is to model a targeted attack, which is directed towards single or multiple important nodes. As shown in Figure 5.6, the critical group of nodes could consist of geographically dispersed points, hence the physical reasons such as natural disaster, accident or power
Geographically Correlated Failures 139 outage could not cause their simultaneous failure. However, many physical risks could affect relatively large areas and could interrupt the operation of numerous nodes in the vicinity.
Geographically correlated failures analysis relies on the position of nodes and links on a geographical plane. The geographical location of the network el- ements is usually mapped to the cartesian coordinate system [10]. Then, various strategies could be used to damage the network and the disturbance could be assessed by many means. Most commonly researchers use cuts of various sizes and shapes to remove the links [121], including circular and other two-dimensional figures, such as ellipses and various polygons. Although cir- cles could fairly approximate the affected geographical area, some failures demand other shapes in order to identify a critical region [122]. The resulting cut damages the network by altering its topology. The damage assessment is usually performed using several measures including [10]: weighted spec- tral distribution (WSD), algebraic connectivity (AC) and network criticality (NC). Neumayer et al. use additional measures to study the impact of geo- graphically correlated cuts such as: total expected capacity of the intersected links (TEC), average two terminal reliability of the network (ATTR), maxi- mum flow (MFST) and the average value of maximum flow between all pairs of nodes (AMF) [121].
Here, the shape of a spatial disturbance is modeled as a circle. For a node i, the circular area with radius r is marked. Then, all nodes within the radius are considered as failed. The Figure 5.7 illustrates an example of chosen areas around three nodes as centers The cascading failure is simulated for all nodes and circular areas around them for various r, where r = [5, 10, 20 . . . 100] measured in kilometers Note that links which seemingly fall within the radius remain intact in this simulation and only nodes are considered as failed. The reason for that is the unknown actual geographical path of links. In all figures, links are represented as straight lines, but their real path could take any shape, usually following major infrastructures such as roads or power lines. The data
High Lo w Criticalit y r = 30 r = 40 High Lo w Criticalit y r = 50 r = 70
Figure 5.8: Critical areas on the map. The areas are defined as circular cuts. The network damage is simulated in a way that all nodes within the area are removed together with associated links. The criticality of the area is then measured as the size of largest connected component after the cascade. The most critical areas are around the most critical
nodes with some exceptions.
about the actual paths is unknown and for that reason, only nodes within the radius and their adjacent links are removed.
This way we can identify the critical areas of various sizes. A measure of the damage is the size G of the largest connected component remaining after the cascade. This simulation is a variation of multiple simultaneous node failures, where the nodes are chosen by its geographical location. In Figure 5.8 the critical areas are plotted on the map. The most critical areas are concentrated around critical nodes. That is aligned with the innate characteristic of the
Geographically Correlated Failures 141 communication network as an example of a scale-free network. The power law is everpresent in almost all analyses regarding the node importance. The European NREN network is not an exception. There is a relatively small number of very important nodes and many nodes whose removal would cause negligible damage.
r = 50 r = 70
Figure 5.9: Location of the most critical areas. The most critical areas are located around the most critical nodes. Depending on the r of the circular cut, many areas could include the same important node, which can cause the group of geographically close areas to be identified as critical. The smaller the r the geographical distribution of critical areas
becomes more dispersed.
The damage distribution of critical areas and critical nodes are similar but with slightly larger exponent value (Figure 5.10). It means that there are more important areas than important nodes. However, the relative number of important areas still remains small even for the large r. Depending on the radius of the circular cut, many areas could include a very important nodes, whose removal would cause a substantial damage. In Figure 5.9, the concentration of critical areas around the most important nodes are evident. With small r, critical areas tend to become more geographically dispersed and with even smaller r, the geographical distribution of critical areas becomes very similar to the distribution of individual nodes. The reason for such geographical distribution is the fact that for relatively large r, the individual critical nodes become covered with circular cuts which are centered in many
0 100 200 300 400 500 600 700 800 900 1,000 1,100 1,200 200 400 600 800 1,000 1,200
Areas around nodes sorted by G
G Radius r 5km 10km 20km 30km 40km 50km 60km 70km 80km 90km 100km 0 10 20 30 40 50 60 70 200 400 600 800 1,000
Figure 5.10: Main frame: The distribution of the extent of damages caused by the circular cuts of various radii. The damage is quantified as the size of the largest remaining connected component G after the cascade. The majority of cuts do not cause greater damage, but the small number of critically positioned cuts could cause devastating impact.
Inset: An excerpt from the greater graph, showing the damage of the
most critical areas. Even the areas with small radius could potentially cause big damage. Note that lower value of G represents bigger damage.
neighboring nodes. The node which is in the ”epicenter” of the cut, might not be important but the cut affects a central node within the radius. The most critical node in the area adds the most to network damage. Therefore, to avoid a substantial damage in case of a geographically correlated failures, the most important nodes should not be concentrated in the narrow geographical area.
The damage caused by the circular cuts around nodes with various radii is plotted in Figure 5.10. For each radius, the areas are sorted by the damage the cut makes. The damage is quantified as the largest remaining connected component G after the cascade. This figure illustrates that there is a relatively small number of critical areas. The vast majority of areas do not cause the extensive damage, even for the large r.
External Risks to European NRENs 143 An interesting phenomenon has been noticed. Sometimes, damaging the wider area around a single node could cause the smaller cascading effect than dam- aging narrower area. This phenomenon which appears to be some sort of a paradox could be used as a mean for active network protection against cascades. After the initial failure of the node or group of nodes within the geographical area, deliberately shutting down the nodes in their vicinity can stop the cascade or decrease the overall damage. More details about that and other means of active protection is provided in Section 5.4.