# Asynchronous Hierarchical Federated Learning Based on Bandwidth Allocation and Client Scheduling
## 2 Related Works  
In order to address the issue of low communication efficiency with peripheral devices, [PERSON] et al. proposed an FL framework with cooperative mobile edge networking [5]. The structure involves the use of multiple edge cloud servers collaborating instead of a single cloud server, which allows devices located at the periphery to upload parameters to the cloud server at a lower cost, enabling it to cover a broader range of clients. The authors in [6] designed a compression control scheme to balance the energy consumption of local computing and wireless communication from the long-term learning perspective. Several approaches have been proposed to address the straggler effect in FL, including works in [7; 8; 9]. [PERSON] et al. in [7] introduced the FedAsync algorithm, which enables clients to promptly upload their local models to the server upon completing an update. However, these uploaded models may become outdated by the time they reach the server. To mitigate the influence of obsolete models on the global model, some researchers attempted to incorporate the FedAsync algorithm with an obsolescence function as a hyperparameter. [PERSON] et al. proposed the FedBuff algorithm [8], which involves the server establishing a buffer of a specific capacity and leveraging trusted execution environments to enhance privacy protection. In this approach, clients asynchronously upload their updated models to the buffer. Once the buffer holds a sufficient number of models, the server conducts a round of aggregation. The FedBuff algorithm has faster convergence compared to the FedAsync algorithm while also preserving privacy. [PERSON] et al. introduced an aggregation method based on update awareness in the asynchronous FL framework [9]. This approach effectively addresses the negative impact of variations in local training speeds on aggregation parameters by appropriately controlling parameter proportions among clients. Furthermore, the aggregation parameters of slower clients are dynamically updated in this method.  
While these algorithms can improve model training efficiency and reduce data traffic, several challenges still require further investigation. For example, optimization algorithms tend to exhibit longer processing times for non-IID (non-Independent and Identically Distributed) data compared to IID data, resulting in increased time costs [10]. Additionally, compression algorithms, capable of reducing the data volume of communication, may also have a significant impact on convergence performance, posing a challenge for achieving a balance between communication efficiency and convergence [11]. Consequently, there is an urgent need for effective algorithms that can overcome issues related to non-uniform computing capacity and discrete distribution in the context of a large number of clients.  
In response to the challenges posed, we introduce an innovative asynchronous hierarchical FL approach and the main contributions of this work are summarized as follows.  
* To mitigate the straggler effect, we introduce an asynchronous hierarchical FL approach which jointly optimizes bandwidth allocation and client scheduling.
* In order to realize load balance, we dynamically assign clients to edge servers taking into account client mobility during training. Then, we propose a client schedulingalgorithm which selects clients with high-quality data and low latency to achieve fast convergence and high model accuracy.
* We accelerate model parameter uploading by taking into account the remaining bandwidth of the edge servers.
* The simulation results validate the potential of the proposed asynchronous HFL approach in improving the overall performance and scalability in the context of a large number of clients.