## 4 Implementation and Discussion
### The Network Performance Result
#### 4.2.1 Delay
In this case, the authentication delay reduces to 74 ms, which also meets the requirement for VANETs. This is because an additional TAS can help to distribute the load more effectively. Even when the authentication requests rise due to the increase of vehicles, this additional TAS can handle requests more efficiently throughout the network, reducing the delay associated with data transmission and processing. Another delay observed in our study is the handover delay. Handover delay is quantified from the vehicle's exit from the previous RSU's coverage to its re-authentication by the new RSU [37]. The data indicate that, in every scenario, the handover delay is consistently lower than the initial authentication delay. However, the handover delay values exhibit a linear relationship with the changes in the authentication delay, increasing or decreasing correspondingly. In this proposed method, the handover delay indicates the re-authentication process associated with transitioning between RSU coverage areas; the vehicle needs re-authentication to make sure it has the correct credentials. From all of our experiments, the handover delay for scenarios 1, 2, and 3 are 55 ms, 69 ms, and 44 ms, respectively. Due to the authentication delay requirements, all the scenarios in our experiments still have values below the maximum limit (100 ms) of authentication delay. This indicates that our system functions well in the case of handover delay in all the cases, including the suburban and the urban areas. The period required for a packet to traverse from its origin to its target location is termed end-to-end delay [38]. This is established by evaluating the time the packet leaves the source vehicle and the time it reaches the destination vehicle. Equation (13) delineates the method for accurately calculating the end-to-end delay, denoted as EED, with TA representing arrival time and TS representing sending time [39]. Based on the ETSI TS 122 186 criteria regarding the service specifications for upgraded V2X scenarios [40], the maximum permissible end-to-end delay for information interchange between an On-Board Unit (OBU) and a Roadside Unit (RSU) while platooning must be less than 20 ms. Figure 9 illustrates that scenarios 1 and 3 exhibit end-to-end delays of 15 ms and 9 ms, respectively, which meet this requirement. Conversely, scenario 2 records a 27 ms delay, surpassing the acceptable limit. This suggests that the urban scenario with 200 vehicles necessitates more than 1 TAS to meet the ETSI standard's ETSI TS 122 186 [40] end-to-end delay requirement. \[EED=\sum T_{A}\ -\ T_{S}. \tag{13}\]  
In this study, the vehicle serves as the source node while the TAS acts as the destination node. The delay includes propagation, transmission, queuing, and processing delays. Additionally, the end-to-end delay is consistently less than the authentication delay and handover delay. The variation patterns in the end-to-end delay observed in our proposed system closely follow the authentication delay values due to their intrinsic correlation. The authentication delay is derived from the Kerberos authentication process, which includes the processing time at each node and the time taken to exchange multiple messages among entities. So, the total delay in authentication within our system is notably affected by the end-to-end delay. In an urban setting with 2 TASs scenario (scenario 3), it shows that all types of delay are reduced compared to the other two scenarios. This reduction is attributed to the increased number of TASs. However, the reduction of the delay is not exactly 50% due to the addition of 2 TASs compared to the scenario with 1 TAS. It is only 40.3%. This discrepancy is influenced by the Ad-Hoc On-Demand Distance Vector (AODV) routing protocol utilized in the VANET system. It is a popular routing protocol for VANETs that only establishes routes when needed [41].