# Formal Algebraic Model of an Edge Data Center with a Redundant Ring Topology
## 4 Implementing AI on the System Proposed  
AI may be implemented in any of the three kinds of remote computing levels exposed, such as on edge servers, fog servers and cloud servers. As explained above, the systems proposed only use the cloud premises for backup and offload services, thus the application of AI techniques at that level makes improve the backup competences and the offload capabilities, hence getting better performance for the overall system. In addition, AI may export some proper data from the cloud level to the lower levels in order to influence their performance. For instance, there may be a coefficient \(c_{c1}\) associated with the storage backup process, whose value may be _nil_ if such a process in the cloud premises are being undertaken at full extent, whereas such a value might obtain a non-zero value if some kind of congestion is detected, where that value might grow as the level of congestion does. Analogously, another  
Figure 2: Migration diagram. coefficient \(c_{c2}\) may become associated with the offloading capabilities, whose functionality may follow the same pattern of behavior as the former. It is to be remarked that non-zero values of any of both coefficients may penalize the VM migration process among fog servers, as it is a high-resource consumption operation and congestion on the cloud level might affect the backup and offloading tasks right after the migration is conducted. Centering on the fog level, the application of AI techniques may induce some coefficients about the VM migration processes referred to orchestrators, such as \(c_{f1i}\) gets associated with the occupation rate of resources in host \(i=\{1\cdots 4\}\), such as their values may stand to _nil_ in cases of low occupation, and it may grow as such a rate increases. In addition, another coefficient \(c_{f2}\) may be associated to the fact that some interhost link may be down, thus increasing the traffic flows going through the rest of the links, leading to a higher probability of saturation of those links. Similarly, another coefficient \(c_{f3}\) may be defined for the case of having some host down, thus rising the traffic being cursed for the rest of hosts. Focusing on the edge level, applying AI techniques may incorporate some coefficients regarding VM migration processes referred to brokers, resulting in some of them being analogous as those in the fog case, such as \(c_{e1i}\) being related to the occupation rate of host \(i=\{1\cdots 4\}\), \(c_{c2}\) being attached to some interhost link down, and \(c_{c3}\) being associated with having some host down. Additionally, \(c_{c4}\) being related to a high error bit rate in the air interface due to interferences, or \(c_{c5}\) being associated with some error in any sensor or actuator. All of those coefficients are related to the system itself, even though other external parameters might also be taken into account, such as current network load, stated by \(c_{n}\), historical data, given by \(c_{h}\), variation over the baseline, cited by \(c_{b}\), or network intelligence data, quoted by \(c_{d}\). As a summary, here they are the list of coefficients conveniently grouped. * Edge: \(c_{c1}\), \(c_{c2}\)
* Fog: \(c_{f11}\), \(c_{f12}\), \(c_{f13}\), \(c_{f14}\), \(c_{f2}\), \(c_{f3}\)
* Cloud: \(c_{e11}\), \(c_{e12}\), \(c_{e13}\), \(c_{e14}\), \(c_{e2}\), \(c_{c3}\), \(c_{e4}\), \(c_{e5}\)
* Others: \(c_{n}\), \(c_{h}\), \(c_{b}\), \(c_{d}\)  
Eventually, the target is to craft an objective function, whose aim is to search for the goal proposed, whilst applying some penalties referred to all of the aforesaid coefficients \(c_{j}\), each one being multiplied by a certain particular value \(\lambda_{j}\), established by an AI tool after the appropriate training, as exhibited in (1), where the goal is obtained to the fullest if no penalization exist, although the goal gets reduced in a given percentage related to the weighted sum of the value of the coefficients not being zero.