Fog and Edge Computing are two models that reached maturity in the last decade. Today, they are two solid concepts and plenty of literature tried to develop them. Also corroborated by the development of technologies, like for example 5G, they can now be considered de facto standards when building low and ultra-low latency applications, privacy-oriented solutions, industry 4.0 and smart city infrastructures. The common trait of Fog and Edge computing environments regards their inherent distributed and heterogeneous nature where the multiple (Fog or Edge) nodes are able to interact with each other with the essential purpose of pre-processing data gathered by the uncountable number of sensors to which they are connected to, even by running significant ML models and relying upon specific processors (TPU). However, nodes are often placed in a geographic domain, like a smart city, and the dynamic of the traffic during the day may cause some nodes to be overwhelmed by requests while others instead may become completely idle. To achieve the optimal usage of the system and also to guarantee the best possible QoS across all the users connected to the Fog or Edge nodes, the need to design load balancing and scheduling algorithms arises. In particular, a reasonable solution is to enable nodes to cooperate. This capability represents the main objective of this thesis, which is the design of fully distributed algorithms and solutions whose purpose is the one of balancing the load across all the nodes, also by following, if possible, QoS requirements in terms of latency or imposing constraints in terms of power consumption when the nodes are powered by green energy sources. Unfortunately, when a central orchestrator is missing, a crucial element which makes the design of such algorithms difficult is that nodes need to know the state of the others in order to make the best possible scheduling decision. However, it is not possible to retrieve the state without introducing further latency during the service of the request. Furthermore, the retrieved information about the state is always old, and as a consequence, the decision is always relying on imprecise data. In this thesis, the problem is circumvented in two main ways. The first one considers randomised algorithms which avoid probing all of the neighbour nodes in favour of at maximum two nodes picked at random. This is proven to bring an exponential improvement in performance with respect to the probe of a single node. The second approach, instead, considers Reinforcement Learning as a technique for inferring the state of the other nodes thanks to the reward received by the agents when requests are forwarded.
Moreover, the thesis will also focus on the energy aspect of the Edge devices. In particular, will be analysed a scenario of Green Edge Computing, where devices are powered only by Photovoltaic Panels and a scenario of mobile offloading targeting ML image inference applications.
Lastly, a final glance will be given at a series of infrastructural studies, which will give the foundations for implementing the proposed algorithms on real devices, in particular, Single Board Computers (SBCs). There will be presented a structural scheme of a testbed of Raspberry Pi boards, and a fully-fledged framework called ``P2PFaaS'' which allows the implementation of load balancing and scheduling algorithms based on the Function-as-a-Service (FaaS) paradigm
