# Towards Efficiently Provisioning 5G Core Network Slice Based on Resource and Topology Attributes
## 3 Problem Description and System Model
### 5G Core Slice Provisioning Problem Description  
The InP supplies 5G core physical infrastructure. It consists of physical nodes deployed in different locations and physical links connecting physical nodes. Physical nodes have computing, storage, and network forwarding capabilities. Virtual machine (VM) or container [27] technologies can be used to enable a physical node to host logically isolated virtual routers or VNFs (e.g., firewall, proxy, etc.). High-speed fiber optic cables are deployed in 5G core networks as physical links which have attributes such as bandwidth. Slice links are hosted on physical links or paths.  
Slice tenants request 5G core network slices from the SP. A core network slice instance consists of virtual network functions and virtual links. In this study, we assume that slice nodes offer the same type of virtual network function, which is virtual computing function. Slice nodes and links request computing resources, storage resources, bandwidth resources, etc. from the slice provisioning system. Without loss of generality, we only consider computing resources and bandwidth resources here. In addition, a slice node may have a location constraint instead of being arbitrarily deployed.  
The slice provisioning process includes mapping slice nodes to physical network nodes that satisfy the resource and deployment location requirements and mapping slice links onto physical paths that meet the bandwidth requests. The slice request is only accepted if the requirements of all nodes and links of the slice are satisfied; otherwise, it is rejected. We make the following assumptions for the slice provisioning problem:  
* The topology of the slice remains unchanged during the life cycle of the slice, which means slice reconfiguration is not considered here.
* Slice nodes from the same 5G core network slice request can only be mapped to different physical nodes, that is, co-hosting is not allowed [28].
* Slice links cannot be split. They can only be hosted by one physical path [28].  
\begin{table}
\begin{tabular}{c l} \hline \hline
**Notation** & **Description** \\ \hline \(G^{l}\) & 5G core infrastructure topological graph. \\ \(V^{l}\) & Set of physical nodes. \\ \(E^{l}\) & Set of physical links. \\ \(c_{0}(v^{l})\) & Initial total CPU capacity of physical node \(v^{l}\). \\ \(c_{a}(v^{l})\) & Available CPU capacity of physical node \(v^{l}\). \\ \(c_{u}(v^{l})\) & Total CPU capacity of physical node \(v^{l}\) allocated to slice nodes. \\ \(loc(v^{l})\) & Location of physical node \(v^{l}\). \\ \(\phi(v^{l}_{i},v^{l}_{j})\) & Euclidean distance between physical nodes \(v^{l}_{i}\) and \(v^{l}_{j}\). \\ \(b_{0}(e^{l})\) & Initial total bandwidth of physical link \(e^{l}\). \\ \(b_{a}(e^{l})\) & Available bandwidth of physical link \(e^{l}\). \\ \(b_{u}(e^{l})\) & Total bandwidth of physical link \(e^{l}\) allocated to slice links. \\ \(P^{l}(v^{l}_{i},v^{l}_{j})\) & Set of loop-free physical paths between \(v^{l}_{i}\) and \(v^{l}_{j}\). \\ \(L(p^{l}(v^{l}_{i},v^{l}_{j}))\) & Set of links in \(p^{l}(v^{l}_{i},v^{l}_{j})\). \\ \hline \(G^{S}\) & 5G core network slice request topological graph. \\ \(V^{S}\) & Set of slice nodes. \\ \(E^{S}\) & Set of slice links. \\ \(c(v^{S})\) & CPU capability required by slice node \(v^{S}\). \\ \(loc(v^{S})\) & Expected deployed location of slice node \(v^{S}\). \\ \(r(v^{S})\) & Maximum deployed deviation allowed by slice node \(v^{S}\). \\ \(b(e^{S})\) & Bandwidth required by slice link \(e^{S}\). \\ \hline \hline \end{tabular}
\end{table}
Table 1: System model notations.