## 3 Technical Background  
The problem of VNF placement and resource optimization in mixed Micro Data Center (MDC)/Cloud Data Center (CDC) edge computing networks has been addressed in [13]. In this work, the networking scenario is described as a hierarchical and geo-distributed architecture that involves, from the edge to the core network, Service Access Routers (SARs), Micro Data Centers (MDCs), and remote Cloud Data Centers (CDCs). The hierarchical definition of the edge computing architecture allows the definition of two kinds of latency constraints in the SFC request: the latency constraint from SARs to MDCs and the latency constraint from the SARs to CDCs. The delay sensitive part of the SFC request will be served by one or more MDCs and the rest by remote CDCs. Unlike other VNF placement solutions, this work includes the instantiation method of VNFs as a cost to be considered in the VNF placement problem. A VNF is hosted on one Virtual Machine (VM), and each VM has its own guest operating system and hypervisor, so some basic resources are needed when instantiating a VNF. This cost is called Basic Resource Consumption (BRC). For the sake of isolation, different VNF instances cannot share the BRCs. To save BRCs, the VNF instances are all assumed to support multi-tenancy software architecture, which allows multiple VNF requests to be hosted on the same VNF instance. This VNF combination strategy was also considered in [19], where a VNF deployment algorithm was proposed for fog-based radio access networks in 5G mobile networks. Mapping all the VNF requests (VNFrs) of an SFC request (SFCr) on the same MDC reduces the bandwidth consumption because the flows between the VNFs do not go through network links. However, many copies of the same VNF will be placed across the network, meaning more node resource consumption due to the BRCs. BRCs can be reduced by reducing the instantiating of VNFs of the same type, but this implies longer paths between MDCs to map the SFC requests, increasing the bandwidth consumption and the latency from the SARs to the involved MDCs. The problem was described in [13] by the following example (see Figure 1). SFCr 1 (in blue) and SFCr 2 (in red) access the service from SAR 1 and SAR 3, respectively. SFCr 1 chains \(\{VNFr^{a1},VNFr^{b1},VNFr^{c1},VNFr^{e1},VNFr^{f1}\}\), and SFCr 2 chains \(\{VNFr^{a2},VNFr^{c2},VNFr^{d2},VNFr^{f2}\}\), in the indicated order. If VNFrs are mapped as shown in the figure, the consumed BRCs will be seven, owing to the multi-tenancy technology, allowing only one instance of \(VNF^{a}\) to map \(VNFr^{a1}\) and \(VNFr^{a2}\) on MDC 6. If the mapping position of \(VNFr^{c1}\) changes from MDC 8 to MDC 7, the consumed BRCs will be reduced, and MDC 8 will be free; consequently, CAPEX/OPEX will be saved. However, the flow path of SFCr 1 may change from \(1\to 6\to 2\to 8\to 4\to 9\) to \(1\to 6\to 3\to 7\to 5\to 4\to 9\), which involves more link hops, so the bandwidth consumption increases. A Priority-based Greedy (PG) heuristic was defined in [13] to solve the VNF placement problem. The PG heuristic consists of a priority-based SFC mapping algorithm and a subsequent VNFr merging algorithm. In a first stage, the SFC request (SFCr) mapping algorithm defines as many clusters as MDCs in the network topology. Then, each SFCr is assigned to all the clusters that fulfil the latency constraints (the SAR to MDC latency constraint and the MDC to CDC latency constraint). As can be expected, there will be SFCrs that are assigned to just one cluster (or MDC), but others will be assigned to more than one. For the first ones, the SFCrs assigned to just one cluster are called Poor SFCrs (P-SFCrs), and the others are called Rich SFCrs (R-SFCrs). According to the number of assigned P-SFCrs, the clusters (MDCs) receive a priority value. The more P-SFCrs, the higher the processing priority of the corresponding clusters is. Once the MDC processing sequence is obtained, the MDCs are processed in order. Thus, the P-SFCrs and the R-SFCrs assigned to the processed MDC are mapped on it.