# Joint Deployment Optimization of Parallelized SFCs and BVNFs in Multi-Access Edge Computing
## 5 Performance Evaluation
### The Impact of the Number of Mobile Users on Different Algorithms  
We first analyze the impact of the number of mobile users on network performance. Figure 7 shows that the average delay increases with the number of mobile users. As the number of mobile users increases, the resource capacities of nearby edge servers are \begin{table}
\begin{tabular}{c c c} \hline \hline
**Notation** & **Explanation** & **Value** \\ \hline \(|U|\) & Number of mobile users & 50, 100, 150, 200, 250 \\ \(|V|\) & Number of edge servers & 50, 75, 100, 125 \\ \(|L_{i}|\) & Number of VNFs in SFC & 6, 8, 10, 12, 14 \\ \(|R|\) & Reliability of each VNF & 0.6, 0.7, 0.8, 0.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List of important parameters in this paper. not enough to deploy the critical VNF. The critical VNF needs to be deployed in further edge servers. Meanwhile, DRPD is superior to BMPD and SRPD in terms of the difference between the average delay and the average delay requirement. DRPD deploys parallel instances for critical VNFs with the highest delay between the previous server and the next server, while BMPD deploys it for critical VNFs with the highest delay between the previous server and the current server. However, SRPD does not deploy parallel instances for critical VNF. Then, we define the average reliability provided by all parallel instances for each VNF as the average VNF reliability. When there is only one instance that is deployed for each VNF, we define the average reliability of each VNF as the base reliability. In Figure 7b, BMPD is superior to our proposed algorithm in terms of the number of parallel VNF instances and average VNF reliability. DRPD selects VNF with the highest delay between the previous server and the current server as the critical VNF. When replacing edge servers in the comparison set with the target edge server, the number of all feasible sets that satisfy the delay requirement is lower than BMPD. The reason for this probably is that after replacement, the delay of the user request traversing the target edge server in DRPD is higher than the delay before replacement. Thus, BMPD can deploy more parallel instances than DRPD. The enhancement of VNF reliability in BMPD is also higher than in DRPD. In Figure 7c, we can observe that the difference between VNF reliability and base reliability decreases with the increase in the number of mobile users. As the number of  
Figure 7: (**a**) Average delay and average delay requirement of all accepted user requests when the number of users changes; (**b**) the number of VNF instances consisting of active VNF instances and BVNF instances and average VNF reliability provided by all active VNF instances of all accepted user requests when the number of users changes; (**c**) the average reliability provided by one VNF instance, all active VNF instances and all VNF instances of all accepted user requests when the number of users changes; (**d**) throughput when the number of users changes. mobile users increases, algorithms may deploy VNFs on further target edge servers. The increase in delay leads to a decrease in the number of all feasible sets about the target edge server, thus resulting in a decrease in reliability. For SRPD, the increase in delay leads to an increase in the number of parallel VNFs, thus decreasing reliability. Figure 7b,c also show that there is no significant performance difference in terms of the number of instances for each VNF and the final reliability provided by all instances among the three algorithms. This is because, to satisfy the reliability requirement, the average reliability for each VNF in SFC provided by active and backup VNFs remains the same. The number of BVNFs needed to satisfy reliability generally remains the same in SRPD. Additionally, we select BVNFs for which the number of feasible sets exceeds the length of the comparison set. Thus, the reliability enhancement is close to the reliability improvement of deploying one BVNF.