## 3 Proposed System Model
### NSR Deployment Strategy  
Each NSR was deployed on the physical network in two successive steps. First, the NSR's nodes were allocated in accordance with the NIRA developed for both physical and logical networks. Second, the creation of links was carried out based on the SPA through SLE. Basically, the NIRA is a dynamic array that must be updated once each slice request is processed. Link mapping begins once nodes are allocated through the mapping of NIRAsfor the physical and logical networks. SPA is created for link mapping using the SLE method, which employs [PERSON]'s algorithm [34] to determine the shortest route between two nodes. Figure 2 illustrates the phases involved in the NSR deployment method. * NSR Acceptance Ratio (NAR): This metric provides the direct measurement of the adapted network slicing technique on the given physical infrastructure. It is measured by taking the ratio between successfully completed NSRs and unsuccessful NSRs for a given time \(T_{max}\), which is expressed as \[P_{NAR}=\frac{\sum_{t=0}^{T_{max}}NSR_{success}(t)}{\sum_{t=0}^{T_{max}}NSR_{ unsuccessful}(t)}\] (2) where \(NSR_{success}(t)\) and \(NSR_{unsuccess}(t)\) are served and unserved NSR at time \(t\), respectively. * Resource Efficiency (RE): This metric is measured by calculating the achieved revenue and the investment cost made for providing the physical infrastructure. The revenue can be determined from the CPU capacity of nodes and link bandwidth requested for the NSRs. The investment cost is estimated from the physical infrastructure for the case. The expression for calculating RE is given by \[P_{RE}=\sum_{t=0}^{T_{max}}\frac{NSR_{revenue}(t)}{PSI_{cost}(t)}\] (3) \[NSR_{revenue}(t)=CPU_{requested,t}+BW_{requested,t}\] (4) \[PSI_{cost}(t)=CPU_{requested,t}+BW_{requested,t}.L_{t}\] (5) where \(NSR_{revenue}(t)\) is the revenue of NSR at time \(t\), \(PSI_{cost}(t)\) is the utilized physical infrastructure for the NSR at time \(t\), \(CPU_{requested,t}\) and \(BW_{requested,t}\) are the requested  
Figure 2: NSR deployment strategy with NIRA and SPA. numbers of CPU and BW of NSR at time \(t\), and \(L_{t}\) is the length of the shortest path for NSR at time \(t\). * Problem Formulation: It is understandable that effective network slicing results in the maximum utilization of physical network resources while minimizing slice provisioning costs [27]. As a result, the problem of minimizing the cost of slice provisioning is formulated using the integer linear programming model in conjunction with the necessary constraints as shown below. \[ \begin{split}\text{\emph{min}},\sum_{N_{k,NSR}\in N_{NSR}}\sum_{N_{ k,p}\in N_{p}}b_{i,k}(1+SPL_{i,p}(CPU_{i,NSR})+\sum_{E_{il,NSR}\in E_{NSR}}\sum_{E_{ij,p} \in E_{p}}a_{ij,kl}BW_{kl,NSR}\end{split} \] (6)  
\[ \begin{split}\text{\emph{Subjectto}},\sum_{N_{k,p}}x_{i,k}=1, \forall N_{i,P}\in N_{P}\end{split}  \tag{7}\]  
\[\sum_{N_{i,j}\in NSR}x_{i,k}\leq 1,\forall N_{j,NSR}\in N_{NSR} \tag{8}\]  
\[x_{i,k}CPU_{k,NSR}\leq CPU_{i,p},\forall N_{i,p}\in N_{p},\forall N_{j,NSR}\in N _{NSR} \tag{9}\]  
\[x_{i,k}SPL_{k,NSR}\leq SPL_{i,p},\forall N_{i,p}\in N_{p},\forall N_{j,NSR}\in N _{NSR} \tag{10}\]  
\[\sum_{N_{i,p}}(a_{ij,kl}-a_{ji,kl})=x_{i,k}-x_{i,l},\forall N_{i,p}\in N_{P}, \forall E_{kl,NSR}\in E_{NSR} \tag{11}\]  
\[\sum_{N_{i,p}}a_{ij,kl}BW(E_{kl,NSR})\leq BW(E_{ij,p}),\forall E_{ij,p}\in E_{p} \tag{12}\]  
\(b_{i}^{k}\in(0,1)\) is a binary variable, where \(b_{i}^{k=1}\) indicates that \(N_{NSR}\) is served onto \(N_{P}\), and is otherwise \(0\). \(a_{ij,kl}\) indicates whether the link \(E_{ij,p}\) hosts the request link \(E_{kl,NSR}\): the value will be \(1\) if the link exists; otherwise, it will be \(0\). Network providers use some additional resources to ensure the security level of nodes. Along with CPU capacity and bandwidth, we also considered the link capacity, delay rate, and jitter resources to improve the allocation of resources and accuracy of node slice creation. Constraint (7) guarantees that each request node is allocated onto the physical node.