Deep learning technology has been widely used in edge computing. However, pandemics like covid-19 require deep learning capabilities at mobile devices (detect respiratory rate using mobile robotics or conduct CT scan using a mobile scanner), which are severely constrained by the limited storage and computation resources at the device level. To solve this problem, we propose a three-tier architecture, including robot layers, edge layers, and cloud layers. We adopt this architecture to design a non-contact respiratory monitoring system to break down respiratory rate calculation tasks. Experimental results of respiratory rate monitoring show that the proposed approach in this paper significantly outperforms other approaches. It is supported by computation time costs with 2.26 ms per frame, 27.48 ms per frame, 0.78 seconds for convolution operation, similarity calculation, processing one-minute length respiratory signals, respectively. And the computation time costs of our three-tier architecture are less than that of edge+cloud architecture and cloud architecture. Moreover, we use our three-tire architecture for CT image diagnosis task decomposition. The evaluation of a CT image dataset of COVID-19 proves that our three-tire architecture is useful for resolving tasks on deep learning networks by edge equipment. There are broad application scenarios in smart hospitals in the future.