# A Novel Multi-Server Federated Learning Framework in Vehicular Edge Computing
## 3 System Model and Problem Definition  
### System Model  
This section outlines the fundamental architecture of the vehicular network under investigation. The system consists of two main components:  
* A set S of N RSUs., each hosting an FL server. * A set V of K vehicles across N RSUs. In VEC, RSUs serve as edge servers strategically positioned along roadways, serving as access points that provide extensive communication, computational, and storage resources compared to vehicles. RSUs are responsible for identifying nearby vehicles, aggregating model updates from both vehicles and peer RSUs, and managing overall network operations. Communication between vehicles and RSUs occurs over wireless links and cellular technologies (e.g., 5G, 6G), while RSUs connect to the internet via reliable backhaul links [22; 23]. Each vehicle is equipped with advanced communication interfaces that enable Vehicle-to-RSU (V2R) communication, robust onboard computing and storage resources for local processing and training, and a variety of sensors, such as cameras, radars, and GPS that allow it to monitor both internal diagnostics (e.g., engine performance, GPS data) and external conditions (e.g., road status, traffic, environmental data). Vehicles act as data collectors by continuously gathering critical information from both their onboard systems and external environments. This sensor data is then used to train and update machine learning models, typically neural networks that perform essential tasks such as object detection, image classification, and route optimization. By integrating diverse data sources, these models significantly enhance real-time decision-making, ultimately improving driving safety and operational efficiency. To capture the system dynamics, the network's operation is divided into discrete time intervals, \(\mathsf{t}\in\{1,2,3,\ldots\}\). At each time step, the system undergoes a series of interactions, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **Latency** & **Handover** & **Pre-Aggregation** & **Server-Level** & **Strengths** & **Weaknesses** \\ \hline Single-server FL (Vanilla FL) [6] & Edge-only & No & No & No & Lower communication overhead compared to cloud-based. & Poor performance under non-IID data; no inter-server collaboration. \\ \hline Cloud-based FL (Hierarchical) [10] & Edge + Cloud & No & No & Yes & Global aggregation improves IID performance & High end-to-end latency. \\ \hline FedMes [18] & Edge-only & No & No & No & Exploits overlapping coverage, faster convergence due to aggregation at clients. & Depends on clients in overlap regions for convergence— insufficient overlap can degrade performance. \\ \hline Trust-based [21] & Edge-only & No & Yes & No & Considers clients’ preferences to select the next model. & Requires feedback from clients, high communication overhead. \\ \hline MS-FL (ours) & Edge-only & Yes & Yes & Yes & Quality-aware model aggregation among servers, continuous training for moving vehicles. & Slightly higher compute per round for evaluation steps. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of FL methods. The table contrasts key features—communication latency, support for model handover, and the presence of pre-aggregation evaluation and server-level aggregation—alongside each method’s strengths and weaknesses. The data collected using vehicle i during time step t is represented as \(\text{d}_{\text{i}}(\text{t})\), while the state of the machine learning model within vehicle i at the end of that time step is denoted by \(\text{w}_{\text{i}}(\text{t})\), the model's parameters. The state of the machine learning model within server s at the end of time step t is represented by \(\text{w}^{\text{(s)}}(\text{t})\). An overview of the vehicular network with multiple servers is illustrated in Figure 1.  
For simplicity, we assume that each vehicle is equipped with its own distinct, pre-loaded, and labeled dataset, which is used for real-time training whenever a vehicle is selected by a server.