# A Novel Cloud Energy Consumption Heuristic Based on a Network Slicing-Ring Fencing Ratio
## 3 Materials and Methods
### Iterative Heuristic Energy-Aware Non-Convex Equation  
To enhance QoS, the minimum and maximum latency constraints such as \(\beta_{i}^{j}D_{\text{min}}^{j}\) and \(\alpha_{i}^{j}D_{\text{max}}^{j}\) are incorporated, where the respective weights \(\alpha_{i}^{j}\) and \(\beta_{i}^{j}\) coupled with latencies \(D_{\text{min}}^{j}\) and \(D_{\text{max}}^{j}\) are incorporated to ensure performance-sensitive applications, as in [5]. To provide energy-aware scheduling for techniques such as dynamic adaptation and smart sleeping, DVS with \(\tau S^{3}u_{i_{i}}\) is included in [5]. To clarify the terms, the full list is shown below: \begin{tabular}{l|l}
**Energy Component** & **Mathematical Expression** \\ \hline Central Cloud Energy & \(\frac{1}{\text{\zeta CC}}\left(P_{\text{compute}}^{\text{CC}}+P_{\text{cool}}^ {\text{CC}}\right)T\) \\ Network CPU Processing Energy & \(\frac{p_{\text{proc}}^{\text{CC}}}{\text{\zeta CC}}\sum_{s\in S}\sum_{u\in U_{s }}d_{\text{CPU},u,rf}\) \\ Network Resource and Ring Fence Energy & \(\sum_{\text{NS}\in\text{Network}}\text{RFF}\times\text{NS} \left(\frac{1}{\text{\zeta RF}}P_{\text{static}}^{\text{RF}}T\right.\) \\  & \(+\sum_{u\in U_{s}}E_{u,rf}^{\text{NR}}\) \\ Inter-Network Slice Communication Energy & \(\sum_{s\in S}\sum_{s^{\prime}\in S}B_{s,s^{\prime}}P_{s,s^{\prime}}^{\text{ comm}}T\) \\ Latency Constraint & \(\sum_{j\in S}\sum_{i\in U_{s}}\left(\alpha_{i}^{j}D_{\text{max}}^{j}+\beta_{i}^ {j}D_{\text{min}}^{j}\right)\) \\ DVS Energy & \(\tau\sum_{s\in S}\sum_{u\in U_{s}}S^{3}t_{u_{i}}\) \\ \end{tabular}   
With these requirements in mind, the optimisation equation shall now be formulated as the sum of the aforementioned constraints:  
\(E_{\text{total}_{1}}=\) 'Central Cloud Energy'  
+ 'Network CPU Processing Energy' +  
'Network Resource and Ring Fence Energy' +  
'Inter-Network Slice Communication Energy' +  
'Latency Constraint' +  
'DVS Energy'. \[ \begin{split} E_{\text{total}_{2}}=&\ \frac{1}{\xi_{\text{CC}}}\Big{(}P_{\text{compute }}^{\text{CC}}+P_{\text{cool}}^{\text{CC}}\Big{)}T\\ &+\frac{P_{\text{proc}}^{\text{CC}}}{\xi_{\text{CC}}}\sum_{s\in S }\sum_{u\in U_{s}}d_{\text{CPU},u_{\tau f}}\\ &+\sum_{\text{NS}\in\text{Network}}\sum_{\text{RF}\in\text{NS}} \Bigg{(}\frac{1}{\xi_{\text{RF}}}P_{\text{static}}^{\text{RF}}T+\sum_{u\in U_ {s}}E_{u_{\tau f}}^{\text{NR}}\Bigg{)}\\ &+\sum_{s\in S}\sum_{s^{\prime}\in S}B_{s,s^{\prime}}P_{s,s^{ \prime}}^{\text{comm}}T\\ &+\sum_{j\in S}\sum_{i\in U_{s}}\Big{(}a_{i}^{j}D_{\text{max}}^{ j}+\beta_{i}^{j}D_{\text{min}}^{j}\Big{)}\\ &+\tau\sum_{s\in S}\sum_{u\in U_{s}}S^{3}t_{u_{i}}\end{split}  \tag{5}\]  
where \(\sum_{s\in S}\tau S^{3}t_{u_{i}}\) incorporates the power consumption of the CPU according to the DVS technique. Here, \(\tau\) is the coefficient subject to chip design, \(S\) is the computational speed of the CPU, and \(t_{u_{i}}\) is the task execution time for user \(u_{i}\). Thus, the IHEA-NC optimisation equation models a network slicing-ring fencing ratio for cloud infrastructure. The defined \(E_{\text{total}_{2}}\) in (5) of this research paper is described as a pseudocode that efficiently satisfies the degree of convergence. With the initialisation and initial calculation described in Algorithm 1, we can now proceed with the gradient descent optimisation part by evaluating each heuristic against the convergence criterion.