## 2 Related Works  
Given that the literature of the NFV-RA problem contains hundreds of published works, we tried our best to summarize the most recent and important ideas in the literature. In general, the NFV-RAproblem evolved from the Virtual Network Embedding (VNE) problem, which focuses on the placement of NFs on physical network. Then, the placement problem was studied for the chains of NFs and the scheduling of the tasks on virtual networks, which was known as Virtual Network Function Problem (VNF-P). After that, the placement of service function chains was studied in three stages, namely the composition stage (VNF-FG), embedding stage (VNF-FGE) and scheduling stage (VNF-SCH) [16]. The NFV-RA inherited the embedding stage from the VNE and the scheduling from the VNF-P while the composition of service function in their VNF Forwarding Graphs (VNF-FG) was influenced by the policy-based requirements for different parties, such as the infrastructure provider, network operator and/or tenants/users (For further details on the literature of NFV-RA, we suggest reading reference [16]). Table 1 presents a brief comparison of the most recent work. A basic form of the placement (resource allocation) problem has been introduced in the form of embedding Virtual Machines (VM) on cloud, which has been surveyed in Reference [25]. The placement of a collection of VMs and the interconnection between them was introduced in SDNs and named a Virtual Network Embedding (VNE), as surveyed in Reference [26]. In the VM and VNE placement problems, the main target is to find the optimal location to place the VMs and the required link to steer the traffic demand between VMs of the service requests. However, the main objective of solving the VNE problem in the recent literature was to maximize the revenues. The work in Reference [27] introduced a framework for Green Virtual Network Embedding (GVNE) in order to minimize energy consumption on cloud computing. Maximizing revenues in Reference [28] was expressed in terms of minimizing the service request rejection on optical data center by a Markov chain model that computes the ranking of Top-of-the-Rack switches. The objective of maximizing revenue was also targeted in References [29; 30; 31], while Reference [29] proposed a sum of virtual node resources algorithm and Reference [30] proposed two algorithms based on multi-commodity flow and a Markov decision processes framework. In Reference [31], the VNE was formulated as a K-supplier optimization problem and an adaptive heuristic algorithm was proposed to solve the formulated problem. Moreover, VNF-P was formulated in Reference [32], where the VM embedding requests were separated from the resource allocation of the service requests in order to share virtual networks between multiple tenants/users. Then, solving this VNF-P as two separated problems, the mapping of VNFs and then scheduling tasks from different service requests over the mapped VNFs, was proposed in References [33; 34; 35; 36]. In Reference [33], the objective was to maximize the revenues, while References [34; 35] aimed at minimizing the transmission latency and the scheduling delay, respectively. A proof of the concept that NFV management can be extended to the radio segment of mobile network was introduced in Reference [36], while minimizing the operational cost and physical resource fragmentation was considered in Reference [37]. The work in Reference [38] solved the VNF-P for two conflicting objectives on mobile network, to minimize end-to-end path length between evolved NodeB (eNB) and respective data anchor gateway and also to optimize users sessions' mobility by minimizing the re-placement of mobility anchor according to users' mobility behaviors. It is worth to mention that VNF-P was studied as a service chain on NFV with applying the ordering constraint of the chain and the possibility of mapping \(n\) VNFs on one physical node [12].