## 3 Proposed Approach and Methodology
### System Architecture
#### 3.1.1 VLC-Enabled Infrastructure  
Arterial traffic signal control refers to managing intersections formed by crossing two or more main roads that are either radial or circular in design. The layout and spacing between intersections vary depending on traffic volume, road capacity, and network design. Each approach at an intersection comprises multiple lanes to accommodate different vehicle movements, such as left turns, right turns, and through-traffic. These intersections are governed by standard traffic rules, with priority movements determined by the traffic signals in place. The scenario was idealized to reflect a futuristic urban environment tailored for autonomous vehicles. Key aspects include the following:  
* Multiple lanes on each arm of the junction to reduce queuing and enhance traffic flow. * Exclusive pedestrian phases to ensure complete pedestrian safety by segregating vehicle and pedestrian movements. * The scenario assumes that autonomous vehicles pre-plan their routes, enabling seamless navigation within designated lanes. * These assumptions align with a forward-looking vision of urban traffic management, optimizing safety and efficiency while accommodating future technological advancements. The traffic scenario analyzed in this study is depicted in Figure 2. It includes three uniform 4-arm junctions, spaced at varying distances. The lane between junctions C0 and C1 is 400 m long, while the lane between C1 and C2 is only 200 m long. Figure 4 presents the simulated environment for each four-legged intersection, showcasing the optical infrastructure (Xij), the generated footprints (#1-#9), and the interactions between connected vehicles and pedestrians. The streetlights along the lanes, denoted as \(X_{ij}\), are identified by integers that follow the opposite direction of traffic (N, S, E, W), starting from _streetlight 0_ at the required signalized intersection and extending, in line, towards _streetlights K,L,M, N_ at the neighboring junction. Figure 4: Simulated scenario for each junction: four-legged intersection and environment with the optical infrastructure (Xij), the generated footprints (#1–#9), and the connected cars and pedestrians. Dush lines show the sidewalks. Each arm of the junction has two lanes: one for left turns and another for vehicles to continue straight or turn right. This design is tailored for CAVs. Using VLC (Figure 1), the vehicle gathers information about the junction's footprint regions, lanes, and surroundings to select the appropriate lane. Once positioned, the vehicle communicates its intention to cross to the Intersection Manager (IM) via V2I technology. The environment also includes sidewalks with designated pedestrian waiting zones at each intersection, ensuring safe waiting areas until the crossing phase is activated for pedestrians to use the zebra crossings. The traffic signal phase timing is determined by factors like traffic demand, intersection layout, and traffic management objectives (e.g., minimizing delays, maximizing traffic flow). Traffic signals typically operate in phases, with green lights allowing movement in one direction while red lights restrict conflicting movements. In this study, we design eight vehicle signal phases and one exclusive pedestrian phase for each intersection, as illustrated in Figure 5a. For vehicles, there is a north-south phase (P1) where they can either proceed straight or turn right, followed by a phase where vehicles coming from the north can cross in all directions (P2), and another phase where vehicles from the south can do the same (P3). Additionally, there is a phase where vehicles traveling from both the north and the south can only turn left (P4). The same phase structure applies to the east-west direction (P5, P6, P7, P8). Pedestrians have an exclusive phase during which all vehicle traffic lights are red, allowing them to cross safely without interference from vehicles. This exclusive phase ensures pedestrian safety by preventing any crossover between pedestrians and vehicles at the crossings.