# A Novel Multi-Server Federated Learning Framework in Vehicular Edge Computing
## 4 Proposed MS-FL Framework
### Inter-Server Model Aggregation  
At the server level, we introduce the collaborative operation of servers through a decentralized multi-server FL framework. This decentralized framework supports direct exchanges among servers, thereby reducing the dependency on a single central server. Inter-server model aggregation comprises two main phases: evaluation and aggregation. During the evaluation phase, each server measures the performance of both its own model and the models received from peer servers against a validation dataset. This dataset may be shared among all servers, or each server can maintain its own validation set for model evaluation. In real-world deployments, each server would maintain an evolving validation set that reflects site-specific conditions--lighting variations, sign wear, and background clutter--without relying on private client data. Over time, servers could augment their validation corpus with fresh imagery from designated data-collection vehicles operating under explicit consent, or from third-party vendors and synthetic generation pipelines. When traffic sign distributions and environmental conditions are largely consistent across RSUs, a single shared validation set may suffice; otherwise, each server uses its own tailored subset to ensure that the performance metrics remain relevant and accurate. In our simulations, we simplify this process by assuming comparable signage environments and applying an 80/20 train/validation split of the original dataset. In practice, manufacturers would provision the initial validation corpus and then update it regularly--adding new or modified signs and reflecting changing weather and lighting--to keep evaluations aligned with the actual operating conditions. This evaluation involves measuring the accuracy and loss of each server model against the validation dataset. Suppose a server wants to evaluate a model, \(w^{(s)}(s\in\{1,2,\,\dots,\,N\})\), and let \(D_{v}^{(s)}=\left\{\left(x_{j},y_{j}\right)\right\}_{j=1}^{I}\) be the server's validation dataset. Then the accuracy of the model \(w^{(s)}\) against \(D_{v}^{(s)}\) is computed as follows:  
\[A_{s}=\frac{1}{j}\sum_{j=1}^{J}I(y_{j}=\text{argmax}(w^{s}(x_{j}))), \tag{1}\]  
where \(w^{s}(x_{j})\) is the model's output for input \(x_{j}\), and \(I(\cdot)\) is the indicator function that returns 1 if the predicted label (obtained via argmax) matches the true label \(y_{j}\), and 0 otherwise. J is the number of validation data samples at server \(s\). Next, in the aggregation phase, the server combines these models using an aggregation method. In this paper, we propose and compare four distinct aggregation strategies: Sequential Aggregation (SA), Binary Aggregation (BA), Dynamic Weighted Averaging Aggregation (DWAA), or Statistical Performance-Aware Aggregation (SPAA). * Sequential Aggregation (SA) In this method, server \(s\) incorporates a peer's model \(w^{(s^{\prime})}(t),\ (s^{\prime}\in\{1,2,\,\dots,\,N\})\) via a weighted average using the equation below: \[w^{(s)}(t)\leftarrow\ (1-\lambda)w^{(s)}(t)+(\lambda)w^{(s^{\prime})}(t),\] (2) where \(\lambda\in[0,\ 1]\) controls how much influence the peer's parameters have. We choose the following: \[\lambda=\frac{\left|D^{(s^{\prime})}\right|}{\left|D^{(s)}\right|+\left|D^{(s^ {\prime})}\right|},\] (3) where \(\left|D^{(s^{\prime})}\right|\) and \(\left|D^{(s)}\right|\) denote the total number of training samples used by peer server \(s^{\prime}\) and server \(s\), respectively, so that a server trained on more data (for example, in a high-traffic area) contributes more heavily. After forming the candidate update, server \(s\) evaluates the performance of its new model on its validation dataset using (1). If the updated model shows improved accuracy, the contribution from server \(s^{\prime}\) is accepted, and the server proceeds to integrate updates from the next peer. If not, the update is discarded, and the server proceeds to the next peer server, without incorporating the parameters from \(s^{\prime}\).