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Nowadays, Unmanned Aerial Vehicles (UAVs) are being used in several novel applications, especially in the telecommunication domain. However, ensuring UAV communication and networking for the purpose of a specific application is still challenging. Indeed, due to the mobility of a UAV in a vast area, permanent connectivity over the back-haul is very sporadic and might be lost. In this paper, we consider an aerial mesh network where each UAV can serve as a flying base station to boost terrestrial base station in case of damaged infrastructure case for example, or/and provide connectivity for uncovered or poorly covered nodes, and behaves as a relay to establish communication between two components owing to a lack of reliable direct communication link between them. We then detail a case study where a UAV-fleet are used to collect data from the ground Internet of Things (IoT) devices and forward it to cloud for further processing passing by a remote gateway. We aim here to build a queueing framework including network layer, MAC layer, and physical layer and investigate both uplink and downlink communication links. Next, we derive some closed forms allowing us to predict the network performance in terms of traffic intensity at every UAV of the aerial mesh network, end-to-end (E2E) throughput and e2e delay of ongoing streams. Next, we conduct extensive simulations to illustrate the benefit of our framework. Results discussion and numerous insights on parameter setting, target quality of service and design consideration are also drawn.