Title: FedMes: Speeding Up Federated Learning with Multiple Edge Servers. Abstract: We consider federated learning with multiple wireless edge servers having their own local coverages. We focus on speeding up training in this increasingly practical setup. Our key idea is to utilize the devices located in the overlapping areas between the coverage of edge servers; in the model-downloading stage, the devices in the overlapping areas receive multiple models from different edge servers, take the average of the received models, and then update the model with their local data. These devices send their updated model to multiple edge servers by broadcasting, which acts as bridges for sharing the trained models between servers. Even when some edge servers are given biased datasets within their coverages, their training processes can be assisted by coverages of adjacent servers, through the devices in the overlapping regions. As a result, the proposed scheme does not require costly communications with the central cloud server (located at the higher tier of edge servers) for model synchronization, significantly reducing the overall training time compared to the conventional cloud-based federated learning systems. Extensive experimental results show remarkable performance gains of our scheme compared to existing methods.