## 6 Numerical Results
The TO solution is investigated when the number \(N_{s}\) of servers in each NFVI-PoP equals 4. Figure 10: Composition of the Service Function Chain; four types are considered: the first one composed of a Firewall (FW) (**a**), the second one composed of an FW and an Intrusion Detection System (IDS) (**b**); the third one composed of an FW, an IDS and a Network Address Translator (NAT) (**c**); and the fourth one composed of an FW, an IDS, a NAT and a Proxy (**d**). SFCs offered. We show the results in the case of type-b and type-d offered SFCs and when the number \(N_{s}\) of servers is equal to 2, 4 and 6. As you can observe from Figure 12, the SRCBA execution times of the SO are independent of \(N_{s}\) because the the Resource Orchestrator is able to abstract the NFVI-PoP network topology and exposes the NS orchestrator information about the cloud resources (number of available cores) only. Conversely, we also observe from Figure 12 how the SRCBA execution time increases as the number \(N_{s}\) of servers increases. For example, when the number \(N\) of type-d SFCs equals 1500, the SRCBA execution time equals 1246 ms, 9902 ms and 41,243 ms for \(N_{s}\) equal to 2, 4 and 6, respectively. The increase is according to the expression of the computational complexity \(C_{TO}=O(NM_{max}N_{s}^{2}log(M_{max}N_{s}))\) of the SRCBA algorithm in the TO solution [7]. Finally, we notice as the SRCBA execution time equals 1645 ms in SO solution, allowing for an execution time percentage reduction equal to 66%, 96% and 99% with respect to TO solution for number \(N_{s}\) of servers equal to 2, 4 and 6, respectively. Next, we study the impact of the number of NFVIs on the SRCBA execution time. We report in Figure 13 the SRCBA execution time versus the number of SFC requests for the TO and SO solutions. We consider the NSFNET network with a number of NFVI-PoPs equal to 4, 7, 10 and 14 and located as shown in Figure 9. We report the SRCBA execution time for both TO and SO solutions and \(N_{s}=4\) servers are located in the NFVI-PoPs for the TO case. Type-b SFCs are considered. From Figure 13, we can observe the increase in the SRCBA execution time when the number of NFVI-PoPs is increased for both TO and SO solutions. The reduction of the SRCBA execution time is confirmed even varying the number \(N_{NFVI}\) of NFVI-PoPs; for example, when the number \(N\) of SFCs equals 3500, the percentage reduction in SRCBA execution time of the SO solution with respect to the TO one equals 91%, 98%, 99% and 99% for \(N_{NFVI}\) equal to 4, 7, 10 and 14, respectively. Figure 12: SRCBA execution time versus the number of SFC requests for the TO and SO solutions and when the Deutsche Telekom network is considered. The TO solution is investigated when the number \(N_{s}\) of servers in each NFVI-PoP is equal to 2, 4 and 6. We compare the TO and SO solution in terms of total cost given by the sum of the cloud and bandwidth resource costs. We report in Figure 14 the total cost as a function of the number \(N\) of SFCs. Type-b SFCs are considered and the results are provided for the NSFNET network with a number of NFVI-PoPs equal to 4, 7, 10 and 14. From Figure 14, we can observe similar costs for the TO and SO solutions; the reason is due to the operation mode of SRCBA that is analogue for the TO and SO cases. Finally, notice how the aggregate knowledge of the resources of SO may lead to a high loss of SFC requests when the NFVI-PoP bandwidth and cloud resources are limited. This analysis is out of the scope of this work and we believe that the problem is of little interest since the NFVI-PoP resources are over-dimensioned with respect to the network ones. Figure 14: Total cost versus the number of SFC requests for the TO and SO solutions. The number \(N_{\text{NVFI}}\) of NFVIs is varied from 4 to 14 and the NFVIs are located as shown in Figure 9. The TO solution is investigated when the number \(N_{s}\) of servers in each NFVI-PoP is equal to 4. Figure 13: SRCBA execution time versus the number of SFC requests for the TO and SO solutions.