  Time-triggered federated learning, in contrast to conventional event-based
federated learning, organizes users into tiers based on fixed time intervals.
However, this network still faces challenges due to a growing number of devices
and limited wireless bandwidth, increasing issues like stragglers and
communication overhead. In this paper, we apply model pruning to wireless
Time-triggered systems and jointly study the problem of optimizing the pruning
ratio and bandwidth allocation to minimize training loss under communication
latency constraints. To solve this joint optimization problem, we perform a
convergence analysis on the gradient $l_2$-norm of the asynchronous multi-tier
federated learning (FL) model with adaptive model pruning. The convergence
upper bound is derived and a joint optimization problem of pruning ratio and
wireless bandwidth is defined to minimize the model training loss under a given
communication latency constraint. The closed-form solutions for wireless
bandwidth and pruning ratio by using KKT conditions are then formulated. As
indicated in the simulation experiments, our proposed TT-Prune demonstrates a
40% reduction in communication cost, compared with the asynchronous multi-tier
FL without model pruning, while maintaining the model convergence at the same
level.
