## 3 Problem Definition  
This section outlines the modeling of the infrastructure environment and the problems addressed in this study. Consistent with previous works on RSU deployment [19], we assume RSUs are deployed at urban crossroads. In line with established standards [7], it is further assumed that all the RSUs at a given crossroad are connected to a TFC equipped with a RSCE unit, forming a star topology. The TFCs are interconnected to ensure multiple paths between any pair of nodes, providing enhanced reliability in terms of connectivity. In the proposed model, each TFC is equipped with a TSN switch to enable TSN functionalities. Additionally, each RSU is equipped with cellular or wireless communication technology and a global navigation satellite system (GNSS), which are utilized to establish V2I communications. Figure 1 illustrates the proposed infrastructure architecture at a crossroad. By deploying synchronous network systems such as TSNs, the model achieves very high levels of reliability and ultralow delays, with submillisecond latency. The I2I infrastructure consists of a network of interconnected TFC nodes, equipped with a secure credential management system (SCMS) and integrated with the TMS of various service operators via a high-capacity TSN fixed network. Each node of the I2I network features a TSN switch, enabling the creation of low-latency service channels between the TFC nodes and their corresponding service operators. These channels are designed to be reliable and secure, ensuring that the controlled traffic between different service providers remains independent. The proposed architecture is based on a centralized TSN network governed by a control plane. This control plane is managed by MARL algorithms, which automate the processes for creating, maintaining, and closing the service channels of the  
Figure 1: Proposed model for a roadside transportation field controller (TFC). data plane. This real-time operation eliminates the need for human intervention, ensuring seamless and efficient management of the infrastructure. As shown in Figure 2, the communication control plane is composed of a centralized user configuration (CUC) module and a centralized network configuration (CNC) module. The CUC module is responsible for handling end-user service requests and processing basic network parameters. The CNC module, on the other hand, receives these service requests from the CUC and configures the TSN switches accordingly to meet the user demands. Our proposed models are designed to be integrated into the CNC module, enabling it to efficiently manage the communication data plane in response to dynamic service requests over time. This integration ensures seamless operation and adaptability to changing network requirements, leveraging the CNC module's centralized control capabilities. The TSN network connecting all of the infrastructure devices is modeled as a directed graph \(G=(V,E)\), where \(V\) represents the set of TSN switches located within TFCs and TMSs, and E denotes the set of directed links connecting these entities. The cumulative delay introduced by an edge from source node \(i\) to destination \(j\) is defined as \(d_{i,j}\), which accounts for transmission, propagation, and queuing delays. One of the simulated topologies is depicted in Figure 3. In the figure, arrows indicate unidirectional edges between TFCs and TMSs, while the numbers next to the edges represent the delays \(d_{i,j}\) in milliseconds. Although the figure focuses on the data plane, it is essential to note that entities of the control plane are also included in this study, following the centralized approach described earlier. The TSN architecture provides an infrastructure capable of handling critical services, ensuring that information frames are transmitted synchronously with a transmission period chosen by the transmitting and receiving entities through the CUC module.