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Edge computing applications leverage advances in edge computing along with the latest trends of convolutional neural networks in order to achieve ultra-low latency, high-speed processing, low-power consumptions scenarios, which are necessary for deploying real-time Internet of Things deployments efficiently. As the importance of such scenarios is growing by the day, we propose to undertake two different kind of models, such as an algebraic models, with a process algebra called ACP and a coding model with a modeling language called Promela. Both approaches have been used to build models considering an edge infrastructure with a cloud backup, which has been further extended with the addition of extra fog nodes, and after having applied the proper verification techniques, they have all been duly verified. Specifically, a generic edge computing design has been specified in an algebraic manner with ACP, being followed by its corresponding algebraic verification, whereas it has also been specified by means of Promela code, which has been verified by means of the model checker Spin.