# Formal Algebraic Model of an Edge Data Center with a Redundant Ring Topology
## 1 Introduction  
To start with, artificial Intelligence (AI) could be formally defined as \"a cross-disciplinary approach to understanding, modeling, and replicating intelligence and cognitive processes by invoking various computational, mathematical, logical, mechanical, and even biological principles and devices\", as stated by [PERSON] and [PERSON] in 2014 [1]. However, it is to be noted that, at this point, there is no widely accepted definition of AI, as well as that AI is still mathematically undefined after some 65 years since its foundation [2]. An interesting definition of an AI algorithm is \"a set of rules or processes that aims to solve a problem or a task\" [3]. In this sense, two types may be distinguished, such as static ones, where a fixed sequence of actions is performed, or otherwise, dynamic ones, where they can interact with the environment, thus being able to learn and evolve [4]. Those are usually called machine learning (ML) algorithms, which are further divided into supervised, unsupervised and reinforcement learning [5]. Basically, AI methods are just tools to analyze data, whereas ML might be seen as a meeting point between AI and statistics [6], providing ML solutions with the ability to achieve great results in basically any field, such as medicine [7], engineering [8], science [9], accessibility [10], knowledge management [11], general learning [12] and even incidental learning [13]. ML may be seen as the capability to learn out of specific training data to automatically build a model in an analytical way so as to solve related tasks [14]. ML may be divided into shallow learning and deep learning (DL), where the latter usually refers to learning with neural networks with several hidden layers [15], whilst the rest of instances are included in the former [16], even though the boundary between them is a bit blurred as there is no consensus in the literature. In fact, the development of DL marked a milestone in the ML paradigm [17], as 2010 is considered to be the transition from the pre-DL era to the DL era, where training compute doubled every 20 months approximately in the former, whilst in the latter, it did in about 6 months. Later on, 2015 is considered to be the transition from the DL era to the Large-Scale era, where training compute became 10- to 100-fold higher [18]. AI may be applied to enhance many types of processes by dynamically adjusting them. In this sense, this paper proposes a multipurpose field monitoring system, which may well be fit for agricultural purposes, where moving end devices such as drones, furnished with some sensors, will be flying around so as to check for undesired conditions as plagues, whilst fixed end devices, such as measuring poles, also equipped with some sensors, will be testing for environmental conditions so as to keep track of them. The data collected by all sensors involved are going to be sent to an edge data center powered with AI in order to obtain faster processing, whereas sustainability is achieved by implementing computing resource migration among hosts in order to minimize the distance between each resource and its associated owner, thus reducing the power consumption, leading to lower the carbon footprint. Additionally, a formal algebraic model will be exposed and further verified. Hence, the contribution of this paper is related to the establishment of a framework focused on field monitoring system in order to obtain its formal algebraic model from the point of view of distributed networking. First of all, its characteristics and functionality are described, and after that, it is outlined how to enhance its behavior by means of an AI tool. Afterwards, the focus is set on the topology of the data center proposed, and eventually, a formal algebraic model of the whole system is presented, followed by its formal algebraic verification.