# A Novel Cloud Energy Consumption Heuristic Based on a Network Slicing-Ring Fencing Ratio
## 3 Materials and Methods
### Proposed Iterative Energy-Aware Non-Convex Optimisation Heuristic  
**Total energy consumption of the network**: The total energy consumption of the network can be expressed as the sum of the energy consumption in the central cloud model, the network slice, and the ring fence [15]. In addition, centralised cooling is considered for the core computational tasks.  
**Energy consumption of the central cloud:** The required parameters starting with the central cloud computational power consumption and the cooling power consumption can be incorporated as:  
\[E_{\text{CC}}=\frac{1}{\xi_{\text{CC}}}\Big{(}P_{\text{compute}}^{\text{CC}}+P _{\text{cool}}^{\text{CC}}\Big{)}T \tag{1}\]  
where \(\xi_{\text{CC}}\) is the power efficiency of the central cloud. T is the total operation time of all network slices. \(P_{\text{compute}}^{\text{CC}}\) and \(P_{\text{cool}}^{\text{CC}}\) represent the computational power and the cooling power consumption of the cloud.  
**Energy consumption of a network slice:** Next, the energy consumption \(E_{\text{NS}}\) of a network slice NS with a ring fence RF can be represented as:  
\[E_{\text{NS}}=\sum_{\text{RF}\in\text{NS}}E_{\text{RF}} \tag{2}\]  
**Energy consumption of a ring fence within a network slice:** To actualise the energy consumption, the energy consumption of a ring fence should be incorporated within that network slice.  
This is expressed as follows:  
\[E_{\text{RF}}=\frac{1}{\xi_{\text{RF}}}P_{\text{static}}^{\text{RF}}T \tag{3}\]  
where \(\frac{1}{\xi_{\text{RF}}}\), \(P_{\text{static}}^{\text{RF}}\), and \(T\) represent the efficiency of the ring fence, static power consumption, and total operating time, respectively. Static power consumption is independent of circuit power and cooling.  
**Incorporating parameters of network resources:** Modelling the total network energy consumption taken from each slice according to [15], the equation should include the bandwidth, processing demands, and the energy consumption of network resources. Hence, the modified energy equation is now given as:  
\[\begin{split} E_{\text{total}}&=\frac{1}{\xi_{ \text{CC}}}\Big{(}P_{\text{compute}}^{\text{CC}}+P_{\text{cool}}^{\text{CC}} \Big{)}T+\frac{P_{\text{proc}}^{\text{CC}}}{\xi_{\text{CC}}}\sum_{s\in S} \sum_{u\in U_{s}}d_{\text{CPU},u,rf}\\ &+\sum_{\text{NS}\in\text{Network}}\sum_{\text{RF}\in\text{NS }}\Bigg{(}\frac{1}{\xi_{\text{RF}}}P_{\text{static}}^{\text{RF}}T+\sum_{u\in U _{s}}E_{u,rf}^{\text{NR}}\Bigg{)}\\ &+\sum_{s\in S}\sum_{s^{\prime}\in S}B_{s,s^{\prime}}P_{s,s^{ \prime}}^{\text{comm}}T\end{split} \tag{4}\]where \(E_{u,rf}^{\text{NR}}\) is the energy consumption of the network resource \(u\) within each ring fence \(rf\) and \(\frac{p_{\text{PC}}^{\text{PC}}}{\text{\zeta CC}}\sum_{s\in S}\sum_{u\in U_{s}}d_{ \text{CPU},u,rf}\) represents the energy consumed due to the CPU processing of all network resources within each ring fence \(rf\) considering the processing power consumption \(p_{\text{proc}}^{\text{CC}}\).  
\(\sum_{s\in S}\sum_{s^{\prime}\in S}B_{s,s^{\prime}}p_{s,s^{\prime}}^{\text{ comm}}T\) represents the energy consumption due to communication between different layers of the network \(s\) and \(s^{\prime}\), considering the bandwidth \(B_{s,s^{\prime}}\) and the power consumption \(P_{s,s^{\prime}}^{\text{comm}}\) over time \(T\). Next, the non-convex optimisation equation above shall be incorporated with end-to-end constraints for the heuristic approach.