## 6 Modified Priority-Based Greedy Heuristic
The virtualization of each network function in a node requires CPU and memory BRCs to be instantiated (as in the referenced work, both BRC values were set to 20 units), and a particular VNFr demands CPU and memory consumption (as in the referenced work, both requirements were randomly assigned following a uniform distribution of (40,80) units). The bandwidth consumption of each SFCr obeys a uniform distribution of (10,50). Similarly, assuming the delay values considered in [13], a set of experiments was performed considering that the \(D_{\gamma}^{MDC}\) of each SFCr obeys a uniform distribution of (1,2) and that \(D_{\gamma}^{CDC}\) obeys a uniform distribution of (5,10). Analyzing the obtained results, from the point of view of SFCr classification as P-SFCrs or R-SFCrs, these delay distributions lead to a reduced amount of P-SFCrs. In particular, the number of P-SFCrs corresponds to around just 1% of the total number of SFCrs. Because the main objective of this performance evaluation is to verify the improvement of the proposed ModPG heuristic against the original PG heuristic when the percentage of P-SFCrs increases, two other sets of experiments were executed, where the percentage of P-SFCrs increased to around 15% and around 25%. ### Results

Two scenarios were considered: the first scenario where the CPU and memory resources of each MDC were set to 3000 units; and the second scenario where the CPU and memory resources of each MDC were set to 4000 units. The second scenario replicates the simulation parameters defined in the baseline work [13]. To extend the evaluated scenarios, a more reduced capacity of MDCs was considered in the first scenario to study and compare the behavior of both proposals in a tightener situation. For each scenario, different simulations were executed for different sets of SFCrs. Each experiment was executed 10 times. The percentage of non-allocated SFC requests, the total number of activated MDCs, the total BRC cost, and the bandwidth cost were the obtained values for each simulation. The last three parameters were used in [13] to evaluate the performance of the PG. In addition, the first parameter allows us to evaluate the suitability of the proposed ModPG solution when the number of SFCrs with strong low-delay requirements is significant. Figures 3 and 4 represent the evaluated parameters corresponding to the first and second scenario, respectively. The mean value is shown, and the 95% confidence interval is represented in the figures. Both figures compare the evaluated parameters using the proposed ModPG algorithm and the original PG algorithm. In both cases, the VNFr merging algorithm defined in Section 6.2 was implemented. #### 7.2.1 Performance Comparison Focused on Successful SFCr Allocation

The main objective of this work is to solve the weakness found in the referenced work as the percentage of SFC requests with strong low-delay restriction increases. As analyzed before in this work, this behavior affects the number of non-allocated SFCrs. Therefore, the first parameter to be evaluated is the percentage of non-allocated SFCrs, which is shown in Figure 3a and Figure 4a. First of all, as expected, as the number of total SFCrs increases, the percentage of non-allocated SFCrs increases as well, because of the limited CPU and memory capacity of the MDCs. The maximum set of SFCrs in the first scenario was 500 and 600 in the second scenario. Figure 4: Scenario 2: CPU and memory capacity of MDCs set to 4000. Figure 3: Scenario 1: CPU and memory capacity of MDCs set to 3000. On the other hand, taking into account the percentage of P-SFCrs shown in Figure 4a (and summarized in Table 2), the ModPG algorithm always results in a lower number of non-allocated SFCrs than the PG algorithm. Analyzing the obtained values in the case of 300 SFCrs, the percentage of non-allocated SFCrs using the ModPG algorithm is very low. That is, there are enough CPU and memory resources in the network to allocate almost all the SFCrs, even when the percentage of P-SFCr is 25%.