## 6 Modified Priority-Based Greedy Heuristic
However, the values obtained for the same set of experiments using the PG algorithm correspond to a higher number of non-allocated SFCrs (around 4% in the first scenario and 2% in the second scenario whatever the percentage of P-SFCrs). Although there are enough resources, the mapping order set by the PG algorithm penalizes SFCrs, which without being cataloged as P-SFCrs, have high latency restrictions. The same trend is observed considering 400 and 500 SFCrs. As mentioned previously, in both scenarios and independent of the algorithm, as the number of SFCrs increases for the same amount of available CPU and memory resources, the inability to map SFCrs increases. This fact can be deduced from the result obtained by ModPG in the first scenario considering 500 SFCrs with 25% P-SFCrs and in the second scenario considering 600 SFCrs with 25% P-SFCrs. In these cases, the percentage of non-allocated SFCrs is almost equal using the ModPG solution and the PG solution, and this is because there are not enough resources to allocate such a high number of highly demanding SFCrs. Figures 5 and 6 corroborate the previous conclusions. The figures show the total amount of non-allocated SFCrs considering the size of the potential set of MDCs assigned by the SFCr classification procedure. It is important to remember that an SFCr is classified as a P-SFCr if the number of potential MDCs is only one. The results shown in Figure 5 correspond to four of the simulations considering 600 SFCrs with 15% P-SFCrs. It can be observed that the PG algorithm penalizes SFCrs with high latency restrictions, that is with a low number of potential MDCs, but that have not been cataloged as P-SFCrs because the value was not just one. The results obtained using the ModPG solution indicate that there are enough resources, but the mapping order set by the PG solution prevents their suitable allocation. The same behavior is observed in Figure 6. In this case, as observed before, the total number of non-allocated SFCrs is higher due to the shortage of resources. SFCrs with less strict delay requirements, and consequently with a higher number of potential MDCs, are not allocated. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Scenario 1**} & \multicolumn{3}{c}{**Scenario 2**} \\ \hline  & & **1\%** & **15\%** & **25\%** & **1\%** & **15\%** & **25\%** \\ \hline \multirow{2}{*}{**300 SFCrs**} & ModPG & 0\% & 0.23\% & 1.97\% & 0\% & 0.17\% & 0.87\% \\  & PG & 4.10\% & 4.20\% & 4.43\% & 1.73\% & 1.97\% & 2.30\% \\ \hline \multirow{2}{*}{**400 SFCrs**} & ModPG & 0\% & 1.38\% & 4.68\% & 0\% & 0.20\% & 1.40\% \\  & PG & 11.18\% & 9.58\% & 8.70\% & 4.93\% & 5.30\% & 3.20\% \\ \hline \multirow{2}{*}{**500 SFCrs**} & ModPG & 1.78\% & 10.98\% & 15.96\% & 0.04\% & 1.06\% & 4.88\% \\  & PG & 17.22\% & 18.58\% & 17.82\% & 6.64\% & 10.38\% & 7.62\% \\ \hline \multirow{2}{*}{**600 SFCrs**} & ModPG & – & – & – & 0.27\% & 2.65\% & 13.37\% \\  & PG & – & – & – & 14.7\% & 11.55\% & 14.27\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Percentage of non-allocated SFCrs: mean values. #### 7.2.2 Utilization of Network Resources

In this section, the total number of activated MDCs, the total BRC cost, and the bandwidth cost are analyzed. Figures 3b and 4b show the number of activated MDCs after successfully allocating the corresponding number of SFCrs. In the first scenario, both solutions offer similar results. The slight increment observed in the ModPG solution is due to the fact that, as evaluated in the previous section, the total number of allocated SFCrs is higher than when using the PG solution. Consequently, more MDC resources are needed. In the second scenario, where the total number of CPU and memory resources offered by MDCs is higher, the ModPG solution also presents positive results. In the case of 300 and 400 SFCrs to be mapped, the PG solution activates a lower number of MDCs.