Arithmetic Framework to Optimize Packet Forwarding among End Devices in Generic Edge Computing Environments.

Multi-access edge computing implementations are ever increasing in both the number of deployments and the areas of application. In this context, the easiness in the operations of packet forwarding between two end devices being part of a particular edge computing infrastructure may allow for a more efficient performance. In this paper, an arithmetic framework based in a layered approach has been proposed in order to optimize the packet forwarding actions, such as routing and switching, in generic edge computing environments by taking advantage of the properties of integer division and modular arithmetic, thus simplifying the search of the proper next hop to reach the desired destination into simple arithmetic operations, as opposed to having to look into the routing or switching tables. In this sense, the different type of communications within a generic edge computing environment are first studied, and afterwards, three diverse case scenarios have been described according to the arithmetic framework proposed, where all of them have been further verified by using arithmetic means with the help of applying theorems, as well as algebraic means, with the help of searching for behavioral equivalences.