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Despite the importance of fog computing, few works using formal techniques have been interested in the modelling and verification of fog architectures to ensure their security. The present work fits into this context and proposes a generic formal model (CA-BRS), extending the BRS with control agents. This offers the possibility to specify a fog architecture consisting of a set of secure fog nodes that act both as filters to reduce the amount of data sent to the cloud and as processing units close to the data collected. This formal setting makes possible the description of the multi-layers' collaboration requirements (IoT, fog, and cloud) and the analysis of certain security requirements with regard to identity management and resource access management. The execution of CA-BRS model through the framework supporting tool: “Maude-based Tool for CA-BRS” allows the formal analysis of the reliability and availability properties of an illustrative fog system example which is an oil/gas refinery plant.