## 6 Modified Priority-Based Greedy Heuristic
When the set size of the SFCrs increases, the ModPG solution activates a similar number of MDCs, but in a more efficient manner, because the proportion of non-allocated SFCrs is lower. From Figures 3c and 4c, it can be observed that the total cost due to BRC increases as the proportion of SFCrs with high latency restrictions grows. When the set of potential MDCs of the SFCrs is limited due to the latency restrictions, the VNFr merging algorithm is less efficient, which means an inability to reduce this cost. Again, the higher results obtained in the case of 500 SFCrs in the first scenario and 600 SFCrs in the second scenario is associated with the higher successful allocation rate. Figure 5: Detailed analysis of non-allocated SFCrs. Sets of 600 SFCrs with 15% P-SFCrs. Scenario 2: CPU and memory capacity of MDCs set to 4000. Figure 6: Detailed analysis of non-allocated SFCrs. Sets of 600 SFCrs with 25% P-SFCrs. Scenario 2: CPU and memory capacity of MDCs set to 4000. Finally, the bandwidth consumption behavior shown in Figures 3d and 4d results in the same conclusions that were already exposed. ## 8 Conclusions

This work proposes and evaluates a solution for the Virtual Network Function (VNF) placement problem in Micro Data Center (MDC)/Cloud Data Center (CDC) edge computing networks. This scenario defines a hierarchical and geo-distributed data center structure, where micro data centers are closer to service requesters than remote cloud data centers. This is a suitable scenario to solve the VNF placement problem when Service Function Chains (SFCs) present strict delay restrictions. In this paper, we propose a VNF placement solution that takes into account the latency and resource requirements imposed by the SFCs, the bandwidth and resource restrictions imposed by the network and the micro data centers, as well as the instantiation cost of VNFs. Due to the fact that the optimization objective, the minimization of the total substrate resource cost, is an NP-hard problem, a heuristic solution is proposed. The Modified Priority-based Greedy heuristic (ModPG heuristic) is coded and compared to a previously proposed solution (the PG heuristic) taking into account as an important factor the percentage of SPC requests with strong low-delay restrictions. Both solutions are compared considering the presence of 1%, 15%, and 25% of SFCs with strong low-delay restrictions. For the performance evaluation, the following parameters are considered: the percentage of non-allocated SFCs, the number of activated MDCs, the BRC, and the bandwidth cost. The results show that the ModPG heuristic obtains the objective, the optimization of the target cost, similar to the original proposal, and at the same time, it obtains the reduction of non-allocated SFC requests. As future work, we plan to evaluate the proposal performance considering different weighing parameter values (\(\alpha\), \(\beta\), \(\rho\), and \(\varsigma\)) defining the total substrate resource cost. In addition, it will be interesting to evaluate the results offered by the ModPG heuristic in a wider set of network topologies, establishing specific NFV resource requirements and MDC and CPC capacities expressed in terms of the number of cores and memory units. Conceptualization, [PERSON]-L., [PERSON], and [PERSON]; methodology, [PERSON]-L., [PERSON], and [PERSON]; software, [PERSON]-L.; validation, [PERSON]-L., [PERSON], and [PERSON]; formal analysis, [PERSON]-L., [PERSON], and [PERSON]; investigation, [PERSON]; resources, [PERSON]; data curation, [PERSON]; writing, original draft preparation, [PERSON], [PERSON], and [PERSON]; writing, review and editing, [PERSON]; visualization, [PERSON]; supervision, [PERSON]; project administration, [PERSON]; funding acquisition, [PERSON]. All authors read and agreed to the published version of the manuscript. This work was supported by the AEI/FEDER, UE Project Grants TEC-2016-76465-C2-1-R (AIM). The authors declare no conflict of interest. The following abbreviations are used in this manuscript: