## 5 Numerical Results
The SFC required bandwidth in the peak SI is chosen according to a ZIP distribution among the values 1 Gbps, 1.5 Gbps, 2 Gbps, 2.5 Gbps and 3 Gbps. We report in Table 5 the total cost as a function of the maximum number of reconfigurable lightpaths when the proposed heuristic is applied and the ILP problem described in Appendix A is solved. The percentage error is also evaluated. From the values reported in Table 5 we can observe how in the case of small networks the heuristic allows for percentage errors lower than 25%. Unfortunately the high running times of the optimization problem does not allow for analysis of more complex scenario. For this reason we only provide the results of the heuristic in the network scenario of Figure 4. The total number of cores in each NFVI-PoP is 4092. We assume a core cost unbalancing for the NFVI-PoP-1, NFVI-PoP-2, NFVI-PoP-3 and NFVI-PoP-4. The expression of the core cost for the four NFVI-PoPs is \(4c_{av}\frac{1-\alpha}{1-\alpha^{4}}\alpha^{i}\) (\(i=0,1,2,3\)) where \(\alpha\) is the cost unbalancing factor and \(c_{av}\) is the average core cost. \(c_{av}\) is assumed to be equal to 1$/h. The choice of \(\alpha=1\) corresponds to the uniform cost case. The bandwidth cost is 0.001 cent/KmGHzhour and the number of frequency slots in each fiber is 600. The SFC type and their bandwidth are chosen as in the small network scenario. A classical daily profile is considered with 8 SIs. The total offered traffic is 800 Gbps in the peak SI. The traffic reduction in the low traffic SI is 80% the one in the peak SI. We report the total cost, the processing cost, the bandwidth cost and the number of reconfigured switches as a function of the maximum number \(R\) of switch reconfigurations in Figure 6a-d respectively. We evaluate the performance index as a function of the parameters \(R\) ranging from 0 to 20,000 in order to investigate the performance in the case of optical switches with different reconfiguration characteristics. The cost unbalancing parameter \(\alpha\) is varied from 1 to 1.5. From the Figure 6 we can remark that:  
* the increase in maximum number \(R\) of switch reconfigurations leads to lower total costs up a saturation value depending on the chosen value of \(\alpha\) (Figure 6a);
* the cost advantage is due to the consolidation of the VMs toward less costly NFVI-PoPs and consequently to lower processing costs (Figure 6b);
* the bandwidth cost has little impact on the total cost for the typical choice of the bandwidth cost per GHz and Km (Figure 6c);
* fewer lightpath configurations are needed in the case of uniform cost because the consolidation has little impact on the processing cost (Figure 6d). \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \(R\) & 0 & 100 & 200 & 300 & 400 & 500 \\ \hline ILP & 172243 & 172243 & 172243 & 170710 & 159959 & 158465 \\ \hline Heuristic & 131925 & 131190 & 130958 & 130958 & 130958 \\ \hline Percentage Error & 23\% & 24\% & 24\% & 23\% & 18\% & 17\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison between cost of the Integer Linear Programming (ILP) and heuristic as a function of the maximum number \(R\) of switch reconfigurations. Finally, we provide some results for the USNET network topology of Figure 5 and when the unbalancing factor \(\alpha\) is varied from 1 to 3. We illustrate the total cost and the percentage cost saving in Figure 7a,b respectively. Notice that the percentage cost saving is evaluated for each value of \(\alpha\) with respect to the cost achieved when no reconfigurations are applied. We can observe from Figure 7a,b how the reconfiguration is more effective for larger values of \(\alpha\) that lead to an advantages in consolidating towards lower cost NFVI-PoP. In particular in the case of \(\alpha=3\) the percentage cost saving is 20% when a number of switch reconfigurations larger than 10,000 is allowed.