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Smart buildings in big cities are now equipped with an internet of things (IoT) infrastructure to constantly monitor different aspects of people's daily lives via IoT devices and sensor networks. The malfunction and low quality of service (QoS) of such devices and networks can severely cause property damage and perhaps loss of life. Therefore, it is important to quantify different metrics related to the operational performance of the systems that make up such computational architecture even in advance of the building construction. Previous studies used analytical models considering different aspects to assess the performance of building monitoring systems. However, some critical points are still missing in the literature, such as (i) analyzing the capacity of computational resources adequate to the data demand, (ii) representing the number of cores per machine, and (iii) the clustering of sensors by location. This work proposes a queuing network based message exchange architecture to evaluate the performance of an intelligent building infrastructure associated with multiple processing layers: edge and fog. We consider an architecture of a building that has several floors and several rooms in each of them, where all rooms are equipped with sensors and an edge device. A comprehensive sensitivity analysis of the model was performed using the Design of Experiments (DoE) method to identify bottlenecks in the proposal. A series of case studies were conducted based on the DoE results. The DoE results allowed us to conclude, for example, that the number of cores can have more impact on the response time than the number of nodes. Simulations of scenarios defined through DoE allow observing the behavior of the following metrics: average response time, resource utilization rate, flow rate, discard rate, and the number of messages in the system. Three scenarios were explored: (i) scenario A (varying the number of cores), (ii) scenario B (varying the number of fog nodes), and (iii) scenario C (varying the nodes and cores simultaneously). Depending on the number of resources (nodes or cores), the system can become so overloaded that no new requests are supported. The queuing network based message exchange architecture and the analyses carried out can help system designers optimize their computational architectures before building construction.