Formal Algebraic Modelling for Fog Computing Network Architecture

Abstract

Fog computing is basically an extension of cloud computing where the computing resources are located on the edge of the network, allowing for better performance regarding latency and bandwidth. Hence, data centres (DC) being used in fog computing may be far smaller and so may the number of hosts and switches in use. In this context, the present thesis dissertation undertakes the modelling of some DC designs for fog computing, setting the focus on just simple network topologies, even though more complex ones might achieve better performance. Such topologies may be modelled in different ways, exposing the minimal path, or equal-cost multiple paths, through which a live Virtual Machine (VM) migration of computing assets may take place from a source to a destination host. This way, a user moving throughout a fog domain will have their computing assets following it as close as possible with a minimal time interval, which is the key point in Internet of Things (IoT) moving environments. It is to be stressed that the models are going to be exposed by following an analytical approach, with the combination of different mathematical branches to get the models ready, such as geometry and topology to obtain the appropriate designs, arithmetic to forward the moving assets to the proper destination, logic to implement those actions in flow charts and pseudocode, or algebra to exhibit a formal description of the whole model. The main contribution in this thesis dissertation goes about obtaining models of optimal paths for VM migrations in DC topologies related to fog computing deployments by means of an abstract process algebra called Algebra of Communicating Processes (ACP), which has been used in order to formally specify and verify such models, as it allows to reason about process terms on an analytical basis, getting back to basics regarding the information technology field. In summary, regarding each topology, different models may be proposed, such as by means of flow charts, pseudocode and a formal algebraic model, followed by the presentation of a formal algebraic model for a whole fog/cloud system.