  In the rapidly advancing field of federated learning (FL), ensuring efficient
FL task delegation while incentivising FL client participation poses
significant challenges, especially in wireless networks where FL participants'
coverage is limited. Existing Contract Theory-based methods are designed under
the assumption that there is only one FL server in the system (i.e., the
monopoly market assumption), which in unrealistic in practice. To address this
limitation, we propose Fairness-Aware Multi-Server FL task delegation approach
(FAMuS), a novel framework based on Contract Theory and Lyapunov optimization
to jointly address these intricate issues facing wireless multi-server FL
networks (WMSFLN). Within a given WMSFLN, a task requester products multiple FL
tasks and delegate them to FL servers which coordinate the training processes.
To ensure fair treatment of FL servers, FAMuS establishes virtual queues to
track their previous access to FL tasks, updating them in relation to the
resulting FL model performance. The objective is to minimize the time-averaged
cost in a WMSFLN, while ensuring all queues remain stable. This is particularly
challenging given the incomplete information regarding FL clients'
participation cost and the unpredictable nature of the WMSFLN state, which
depends on the locations of the mobile clients. Extensive experiments comparing
FAMuS against five state-of-the-art approaches based on two real-world datasets
demonstrate that it achieves 6.91% higher test accuracy, 27.34% lower cost, and
0.63% higher fairness on average than the best-performing baseline.
