  Federated learning (FL) is a collaborative machine learning paradigm, which
enables deep learning model training over a large volume of decentralized data
residing in mobile devices without accessing clients' private data. Driven by
the ever increasing demand for model training of mobile applications or
devices, a vast majority of FL tasks are implemented over wireless fading
channels. Due to the time-varying nature of wireless channels, however, random
delay occurs in both the uplink and downlink transmissions of FL. How to
analyze the overall time consumption of a wireless FL task, or more
specifically, a FL's delay distribution, becomes a challenging but important
open problem, especially for delay-sensitive model training. In this paper, we
present a unified framework to calculate the approximate delay distributions of
FL over arbitrary fading channels. Specifically, saddle point approximation,
extreme value theory (EVT), and large deviation theory (LDT) are jointly
exploited to find the approximate delay distribution along with its tail
distribution, which characterizes the quality-of-service of a wireless FL
system. Simulation results will demonstrate that our approximation method
achieves a small approximation error, which vanishes with the increase of
training accuracy.
