# Joint Pricing, Server Orchestration and Network Slice Deployment in Mobile Edge Computing Networks
## 3 System Model  
### Infrastructure Model  
We consider the network model shown in Figure 1, where the InP owns the infrastructure such as base stations and MEC servers. In the network initialization phase, tenants make requests to the InP to create and deploy slices. The InP leverages SDN and NFV-enabled infrastructure (NFVI), such as base stations and MEC servers, to instantiate a set of VNFs to dynamically deploy slices on demand. As shown in Figure 1, the base stations and MEC servers are connected to the virtual infrastructure manager (VIM), which is responsible for managing the NFVI using SDN [8]. The VIM is connected to the NFV/MEC orchestrator (NFVO/MECO), which orchestrates services and manages the lifecycle of the network slices through the VIM. We use \(\mathcal{N}=\{1,\ldots,n,\ldots,N\}\) to represent the set of slices. There is a set of base stations \(\mathcal{M}=\{1,\ldots,m,\ldots,M\}\) within the region. They possess only the fundamental capabilities of communicating and receiving service requests. In this paper, we only consider downlink transmissions, and each base station has a downlink bandwidth capacity of \(W_{m}^{max}\). The InP is required to select base stations (in 5G NR, the specific applications of the access functions, such as access control, signal transmission and reception, data forwarding and radio resource management, are performed by the remote radio unit (RRU), distributed unit (DU), and centralized unit (CU). Here, we collectively refer to these three functional modules as the base station) for each slice to deploy access functions, with radio bandwidth resources being allocated accordingly. We use \(x=[x_{m,n}]_{M\times N}\) to denote the deployment indication of the access functions, where \(x_{m,n}=1\) means that the access function of slice \(n\) is deployed on base station \(m\), and \(x_{m,n}=0\) otherwise.  
We assume that each base station is equipped with one MEC server (actually, the number of equipped MEC servers can be less than or equal to the number of base stations, which does not affect our problem modeling. The exact number of MEC servers to be equipped can be decided by the InP, and here we just give an example). Due to factors such as energy consumption, only a subset of servers can be activated simultaneously [8; 14].  
Figure 1: System model.  
For the sake of illustration, we denote the set of MEC servers by \(\mathcal{V}=\{1,\ldots,v,\ldots,V\}\), where \(V=M\). Furthermore, \(\mathbf{p}=[p_{v}]_{1\times V}\) represents the server activation indication, where \(p_{v}=1\) means that server \(v\) is activated, and \(p_{v}=0\) otherwise. A base station can only forward service requests to its associated MEC server. The association between base stations and servers is denoted by \(\mathbf{a}=[a_{v,m}]_{V\times M}\), where \(a_{v,m}=1\) means that base station \(m\) is associated with server \(v\), and \(a_{v,m}=0\) otherwise. The computational and storage capacities of server \(v\) are \(E_{v}^{max}\) and \(S_{v}^{max}\), respectively. The InP is required to select MEC servers for slices to deploy VNF chains and allocate computational and storage resources to them. Let \(\mathbf{k}=[k_{v,n}]_{V\times N}\) be the VNF chain deployment indication, where \(k_{v,n}=1\) means that the VNF chain of slice \(n\) is deployed on server \(v\), and \(k_{v,n}=0\) otherwise.