## 3 The Proposed Method and Scenarios
### Testing Scenarios  
Figure 4 shows three case scenarios for the experimentation of the system. The first scenario, as shown in Figure 4a, focuses on a suburban area. In this scenario, we utilized 100 vehicles, four Roadside Units (RSUs), and one Traffic Analysis System (TAS). The limited number of RSUs is justified by the relatively low density of the suburban environment, which does not necessitate a large number of vehicles. The experiments were conducted using the Tsushima Campus area maps in Okayama, Japan, as shown in Figure 5a. The maps are generated by using Openstreet Maps, licensed under the Open Database License (ODbL) and inserted into SUMO tools to simulate the VANET. SUMO  
Figure 3: Main parts of the Kerberos-blockchain VANETs system.  
is distributed under the Eclipse Public License (EPL), which is a permissive open-source license. In the first scenario, the TAS is placed in the middle of the network, surrounded by RSU1, RSU2, RSU3, and RSU4.  
The second scenario is an urban scenario with 1 TAS, as shown in Figure 3(b), characterized by higher vehicle density. In this case, we increased the number of vehicles from 100 to 200. Given the greater availability of infrastructure in the city, we also doubled the number of Roadside Units (RSUs) from 4 to 8. This scenario was conducted in the densely populated area around Okayama Station in Okayama City, Japan, as highlighted in Figure 4(b). The objective is to determine whether or not the performance of the authentication system remains within acceptable limits when the number of vehicles increases. Specifically, we aimed to assess if the authentication delay in the VANET environment stays below the critical threshold of 100 milliseconds, as stipulated in [6]. We placed the TAS in the centre of the maps, surrounded by the 8 RSUs. The small yellow dots in the maps indicate the vehicles.  
The third scenario, depicted in Figure 3(c), was also implemented using the urban area maps depicted in Figure 4(c). In this case, we employed more than one Trusted Authority Server (TAS) to ensure the system's performance in an environment requiring additional infrastructure. Specifically, we utilized 8 RSUs, 200 vehicles, and 2 TAS units. The introduction of multiple TAS units aimed to distribute the authentication management tasks effectively, accommodating the increased number of vehicles. In the third scenario, the TASs are positioned on the right and left sides of the map, unlike the central placement in scenarios 1 and 2, to achieve balanced load distribution. This configuration is intended to prevent load imbalances that could negatively impact TAS performance.  
The number of vehicles in a VANET system varies based on factors like area size, use case, and simulation goals. Denser urban areas have higher vehicle counts, while less populated areas have lower values. In one study [25], the authors chose 50-200 vehicles to evaluate routing protocols in a city scenario with high-density traffic. In a separate analysis [26], authors selected 0-120 vehicles to study urban traffic congestion and system effectiveness. In another study [27], authors chose 10-100 vehicles to simulate low and moderate traffic scenarios in real-world vehicular environments. This range helps analyze how increasing vehicle density impacts key performance metrics such as packet delivery ratio and delays. The selection of vehicle numbers for simulations depends on balancing real-world traffic patterns with available computational resources.  
Figure 4: Experiment case scenarios: (a) suburban, (b) urban with 1 TAS, and (c) urban with 2 TASs.