## 4 Proposed Strategies for NSR Deployment
### PROMETHEE-II Strategy for NIRA Preparation
\begin{table}
\begin{tabular}{c c c c c} \hline  & \(f_{1}(f_{NCF})\) & \(f_{1}(f_{NNF})\) & \(f_{1}(f_{NNF})\) & \(f_{4}(f_{NCC})\) \\ \hline \(n_{1}\) & \(f_{1}(n_{1})\) & \(f_{2}(n_{1})\) & \(f_{3}(n_{1})\) & \(f_{4}(n_{1})\) \\ \(n_{2}\) & \(f_{h}(n_```
Input:\(G_{P},G_{NSR}\) Output:\(Nodeallocation\) for each node \(N_{P}(i)\) of \(G_{P}\)do  Calculate \(f_{NCF,i},f_{NTF,i},f_{NSCF,i},f_{NBF,i}\) \(\emptyset(i)\) for Physical infrastructure using PROMETHEE-II endfor for each node \(N_{NSR}(j)\) of \(G_{NSR}\)do  Calculate \(f_{NCF,i},f_{NTF,i},f_{NSCF,i},f_{NBF,j}\)  Prepare \(\emptyset(j)\) for NSR using PROMETHEE-II endfor  Set allocationTrack=0 for each node \(\emptyset(i)\) of \(G_{P}\)do if\(\emptyset(j)\) is not empty then for each node \(\emptyset(j)\) of \(G_{NSR}\)do if\(CPU_{NSR,j}<CPU_{available,i}\) and \(BW_{requested}(k)<BW_{available}(l)\)then  node Allocation \(N_{P}(l)\) to \(N_{NSR}(k)\)  Update \(CPU_{served,l}\) and \(a_{l,served}\forall N_{P}(l)\) of \(G_{P}\) and \(BW_{l,served}\forall E_{P}(l,j)\)  Update \(f_{NCF,l},f_{NTF,l},f_{NSCF,l},f_{NBF,l}\) else  Move to next node endif endfor elseif allocationTrack=\(N_{NSR}\)then  Return NSR node allocation unsuccessful else  Return NSR node allocation success endif endfor return nodeAllocation
```

**Algorithm 1** Node allocation through PROMETHEE-II

### SLE Strategy for SPA Preparation

Identifying the shortest route for the NSR nodes in the physical infrastructure is the primary goal of this SLE technique. Regarding NSR, it is clear that sometimes the most direct route is not the best one. In certain cases, a connection in the chosen shortest route may be connected to the already supplied NSRs. This makes an identification of all of the connections linking NSR nodes and organizing them in SPA in a non-increasing order according to the length of their individual pathways very necessary. This array may be used for the establishment of a connection for NSRs. It is anticipated that the shortest pathways indicated would be referred to one after another throughout the connection building process. The SPA chooses the path with the shortest length among those that are not engaged for link provisioning. Algorithm 2 is used to explain the process of preparing SPA. ```
1:Input:\(G_{P}=(N_{P},E_{P})\), \(L_{i,j}\) of all \(E_{P}\)
2:Output:\(SPA\)
3:Set, \(SN\): source node \(DN\): destination node \(K\): the number of shortest paths between \(SN\) and \(DN\) \(P_{n}\): a path from \(SN\) to \(u\) \(SPA\): a heap structure keeps paths \(P\): set of shortest paths from \(SN\) and \(DN\) \(countu\): number of shortest paths for node \(u\)
4: Initialize, \(P=empty,countu=0,L=0\)
5:for all \(u\) node in \(N_{P}\)do
6: Insert path \(P_{SN}=SN\) into \(SPA\) with cost 0
7:endfor
8:while\(SPAxxxempty\&\&countDN<K\)do
9:\(SPA=SPA-Pu\)
10:\(countu++\)
11:if\(u=DN\)then
12:\(P=PUPu\)
13:endif
14:if\(countuwwwK\)then
15:for each \(E_{P}\) adjacent to node \(u\)do
16:\(P_{v}\) new path with \(L=L+L_{i},u\)
17: Insert \(P_{v}\) into SPA
18:endfor
19:endif
20:endwhile
21:return\(SPA\)
```

**Algorithm 2** SLE for SPA preparation

### Hybrid PROMETHEE-II and SLE Approach for Deployment

This operation allots a node and establishes a connection between the nodes of the NSRs that have been received during the time interval from 0 to \(T_{max}\). Throughout this study, it was assumed that all of the required NSR nodes belong to a single category, such as eMBB, mMTC, or URLLC. A NSR should be able to request any slice type at any point in time. The PROMETHEE-II method was used to allocate nodes for the NSRs, and the SLE algorithm, which is based on [PERSON]'s shortest route algorithm, was used to construct links between them. The hybrid PROMETHEE-II and SLE algorithms were used to obtain the best possible optimum provisioning for the NSR. In the physical infrastructure, the NIRA and SPA were updated in accordance with the lifetime of the received NSR, which allows for the identification of the most appropriate and optimum provisioning for the next arrival of NSR.