  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.
