This paper studies a federated learning (FL) system, where textit{multiple} FL services co-exist in a wireless network and share common wireless resources. It fills the void of wireless resource allocation for multiple simultaneous FL services in the existing literature. Our method designs a two-level resource allocation framework comprising emph{intra-service} resource allocation and emph{inter-service} resource allocation. The intra-service resource allocation problem aims to minimize the length of FL rounds by optimizing the bandwidth allocation among the clients of each FL service. Based on this, an inter-service resource allocation problem is further considered, which distributes bandwidth resources among multiple simultaneous FL services. We consider both cooperative and selfish providers of the FL services. For cooperative FL service providers, we design a distributed bandwidth allocation algorithm to optimize the overall performance of multiple FL services, meanwhile cater to the fairness among FL services and the privacy of clients. For selfish FL service providers, a new auction scheme is designed with the FL service owners as the bidders and the network provider as the auctioneer. The designed auction scheme strikes a balance between the overall FL performance and fairness. Our simulation results show that the proposed algorithms outperform other benchmarks under various network conditions.
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