## 6 Numerical Results  
We provide some results to compare the computational complexity of the Traditional Orchestration (TO) and proposed Scalable Orchestration (SO) solutions. In particular, we evaluate the execution times of SRCBA algorithms proposed in [7] and in Section 5.1 for TO and SO solutions, respectively. The times are measured on a Personal Computer characterized by a 3.40 GHz Intel i7-3770 processor and by an 8 GB RAM memory (Intel Core i7-3770). The comparison is carried out when two realistic network scenarios are considered. The first one is reported in Figure 8 and considers a medium distance network such as Deutsche Telekom (Germany) in which \(N_{NFVI}\) = 4 NFVI-PoPs are considered as illustrated in Figure 8. The second one is reported in Figure 9 and considers a long distance network as NSFNET with 16 switches and 25 links; the four cases with a number \(N_{NFVI}\) of NFVI-PoPs equal to 4 (a), 7 (b), 10 (c) and 14 (d) are considered. For these four case studies, the NFVI-PoPs are placed as illustrated in Figure 9a-d, respectively. The NFVI-PoPs are equipped with \(N_{core}=96\) processing cores. The link bandwidth of the network interconnecting the NFVI-PoPs is fixed equal to 40 Gb/s. The NFVI-PoP network topology is  
Figure 7: Construction of the multi-stage graph for the SO solution of the SRCBA algorithm. The cases \(x=35\) (a) and \(x=85\) (b) for the bandwidth interconnection cost between NFVI-PoP-1 and NFVI-PoP-3 of Figure 4 are reported. assumed to be a fat tree. We assume a core cost \(c^{core}\) equal to 1 \(\$/\)h while the bandwidth cost \(c_{b}\) equals 0.1 cent/KmGb. We consider four Service Functions: Firewall (FW), Intrusion Detection System (IDS), Network Address Translator (NAT) and Proxy. VNF instances can be instantiated in the NFVI-PoPs to support these SFs. They are supported by software modules characterized by the maximum processing capacity and by the number of cores reported in Table 1. The possible compositions of the SFs in SFC are reported in Figure 10, where the nodes \(v_{s}\) and \(v_{e}\) are the access nodes originating and terminating the SFC. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Maximum Processing Capacity (\(C^{pr,max}\))** & **Number of Cores Allocated (\(n^{c}\))** \\ \hline
**FW** & 0.9 Gbps & 4 \\
**IDS** & 0.6 Gbps & 8 \\
**NAT** & 0.9 Gbps & 2 \\
**Proxy** & 0.9 Gbps & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Maximum processing capacity and allocated number of cores for the software modules implementing FW, IDS, NAT and Proxy. Figure 8: Deutsche Telekom network with four NFVI-PoPs. Figure 9: NSFNET (USA) network composed of 16 switches and 25 links. The four cases with a number \(N_{NIVI}\) of NFVI-PoPs equal to 4 (a), 7 (b), 10 (c) and 14 (d) are considered. We assume that \(N\) SFC requests are generated. The bandwidth values of the SFCs are chosen equal to 20 Mbps. The ingress and egress nodes of each SFC are randomly chosen. We illustrate in Figure 11 for the Deutsche Telekom network the SRCBA execution time as a function of the number of SFC requests for the Traditional Orchestration (TO) and Scalable Orchestration (SO) cases. The number \(N_{s}\) of servers in each NFVI-PoP equals 4. We report the results when SFCs with one SF (SFC-a), two SFCs (SFC-b), three SFCs (SFC-c) and four SFCs (SFC-d) of Figure 10 are offered. We can observe how our proposed scalable orchestration allows for a remarkable reduction in SRCBA execution time. For example, when 2500 type-b SFCs are offered, SRCBA execution times equal 6642 ms and 536 ms for TO and SO, respectively, with an advantage in computation time by 92%. The impact of the number \(N_{s}\) of servers on the SRCBA execution time is analyzed in Figure 12 for Deutsche Telekom. In this figure, we report the SRCBA execution time as a function of the number \(N\) of  
Figure 11: SRCBA execution time versus the number of SFC requests for the TO and SO solutions and when the Deutsche Telekom network is considered.