# Formal Algebraic Model of an Edge Data Center with a Redundant Ring Topology
## 3 Basics of the System Proposed
On the contrary, brokers operating with drones will need to be migrated along to the quadrant where a drone is located at a given time so as to be the closest to it, thus reducing the power necessary for the wireless transmissions between the drone and its corresponding VM, and also lowering the latency, thus speeding up the processing times, as well as the energy expenses. Additionally, the orchestrator will also be allocated within any of the hosts, where at least a pair of them would need to be used to obtain two synchronized copies of that VM allocated in different hosts for redundancy purposes. With respect to the operativity, let us suppose a drone acting as an edge device, whose role is to fly around the square field in order to take pictures of the crops being planted over there and their corresponding environment in order to spot plagues or traces of other harmful situations. This way, the drone would act as an end device, thus capturing the pictures obtained by the camera acting as a sensor, and in turn, forwarding those images to the proper broker, meaning the corresponding VM, in order for it to process them. The messages between the drone, which acts as a publisher of data, and the edge server, playing the role of a broker, needs to be forwarded through a wireless technology, whose type will depend on the maximum distances within a quadrant, which occurs to be its diagonal, whose distance is given by the square root of 2 multiplied by half of the side length of the whole square. Hence, such a distance would establish the necessary wireless technology to be used, that being either short-range such as Wi-Fi or ZigBee, or middle-range such as WiMAX, or cellular technology for longer distances, or even satellite technology to access any type of environment. Otherwise, the rest of the sensors may be located in fixed locations in order to measure some key environmental indicators, such as temperature or humidity, in certain parts of the field. In this case, wireless technologies may also be employed to communicate with the edge servers, although a better option would be to employ wired technologies such as fiber optical runs, which might be deployed so as to speed up such communications, even though some civil engineering infrastructure would need to be implemented. This way, the best solution is to evaluate the balance between the costs incurred and the benefits obtained in terms of throughput. In summary, data obtained by a fixed sensor are forwarded to the corresponding VM acting as a broker, allocated in the host within the quadrant where such a sensor is ubicated, which will in turn process the data, and then, it will send a response to the appropriate actuator to do a certain action to alleviate that condition, or otherwise, it will not send any response whatsoever if there is no need to. Moreover, another VM acting as an orchestrator will supervise the operation and it will forward some extra information so as to influence the decision-making process of the broker. Otherwise, data obtained by a moving sensor, which in this case are the pictures taken by the drone, are also forwarded to its corresponding VM acting as a broker, but its location will be into the quadrant where the drone is flying over. The processing of such data matches that exposed for the fixed sensor case, ending up with an appropriate response to the actuators so as to cope with the potential issue being detected, or otherwise, no response is expected in case no relevant event is detected. However, the moving sensor case requires a handover action of the VM associated to the drone, which successfully transfers that VM from one host to another. The point where the handover needs to be made gets indicated by the fact of crossing the coordinate axes at any point, in a way that when a drone traverses any of those, then it happens that the distance to the host within the new quadrant is shorter than that to the old one, thus handover needs to be accomplished to revert that situation.