## 5 Performance Evaluation and Comparative Analysis
### Performance Evaluation  
We considered _M/M/1/K_ queueing systems where the arrival and services processes are (_M_)_emoryless_, there is only one server within a single queue, and \(K\) represents the  
Figure 12: Event-driven multi-queue and delay broker framework. Queues represent virtualised network components (e.g., SDN gateway, gNB, edge servers) that form the distributed 5G Infrastructure. Resource groups denote the corresponding flow rules and tables deployed for data processing. system capacity. Each queue is modelled as a single _M/M/1_ queue with \(K\) capacity. The processing of critical vehicular data, including Camera, LiDAR, and RADAR, with similar QoS requirements but varying transmission rates and packet sizes, creates the problem of service differentiation to ensure optimal QoS. The proposed model follows the FIFO (First-In-First-Out) packet processing methodology. From our analysis, the management of diverse critical vehicular data on distributed and shared resources creates the problem of longer delays, particularly for sensors with lower transmission rates and packet sizes, like RADAR. Considering the observed results in Table 1, where the arrival rates are consistently equivalent to the service rates observed at the SDN gateway and VXLAN link to gNB. \[\rho=\lambda/\mu\ \approx\ 1\]  
The queue-utilisation function (\(\rho\)) is approximately equal to 1 across the three tests. This implies that the SDN gateway and VXLAN link to gNB were operating at full utilisation across the three tests. The arrival rate at the gNB is the rate on VXLAN links. Therefore, the relatively higher service rates observed at the gNB (as illustrated in Table 2) indicate \(\rho<1\) at the gNB for all test scenarios. At the gNB, the system utilisation increased by a small margin between test 1 and test 3 (as illustrated in Table 3), possibly due to increasing arrival rates. However, the maximum utilisation (\(\rho\)) of approximately 36% suggests that the gNB is far from full utilisation. For queueing systems with finite capacity, \(K\) is the maximum number of packets that can be in the system. Calculating the average number of packets in the system and the waiting time often involves state probabilities and considering the probability of packet loss due to full utilisation. Assuming a \(K\) of 1940, 1169, and 780 for Camera, LiDAR, and RADAR, respectively, during the third test (as illustrated in Table 4), we can calculate the probability of the system being full _P_(_K_) when \(\rho=1\) as follows:  
\[P(K)=\frac{1}{K+1}\]  
where \(K\) is the number of packets the system can hold, excluding the one currently being served. The probabilities that the system is full for the Camera, LiDAR, and RADAR queues formed in the system are therefore approximately 0.0005%, 0.0009%, and 0.0013%, respectively, during the third test. These low probabilities imply that even though the SDN gateway and VXLAN links currently operate at near full utility, it is unlikely that their performance will deteriorate under the current system dynamics. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sensor Type** & **TEST 1 (PPS)** & **TEST 2 (PPS)** & **TEST 3 (PPS)** \\ \hline CAMERA & 8.4 & 14.7 & 18 \\ LIDAR & 4.3 & 9.0 & 11 \\ RADAR & 2.4 & 4.4 & 5.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Service rates at gNB (Packets per Second (PPS)). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sensor Type** & **TEST 1 (\(\rho\))** & **TEST 2 (\(\rho\))** & **TEST 3 (\(\rho\))** \\ \hline CAMERA & 0.27 & 0.31 & 0.36 \\ LIDAR & 0.33 & 0.31 & 0.36 \\ RADAR & 0.25 & 0.30 & 0.32 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: System utilisation at gNB (\(\rho\)). Taking into consideration the above low probabilities and the 100% packet delivery rate observed across all tests, we can assume that the current capacity \(K\) is the average number of packets processed in a queue (\(Lq\)).