# Multi-Objective Service Placement Scheme Based on Fuzzy-AHP System for Distributed Cloud Computing
## 3 Proposed Method
### Steps of the Proposed Scheme
Figure 5 presents an example of the AHP structure of user requirements in order to decide among cloud service candidates. A number of the previous studies [9; 10; 11; 12; 13; 19; 20; 21; 22; 23; 24; 41; 42; 43; 44; 45; 46] considered RU as a metric when services were placed or migrated. In this paper, we also considered the RU metric in the evaluation of all such cases with respect to parameters such as performance and energy efficiency. The CSP can decide to assign the weight according to relevant requirements. SP is performed from VM as well as other devices operated by the user. Therefore, RU is calculated to depend on the user's mobility and the probability of the utilization of resources based on the previous usage demonstrated over time, which is shown in Equation (4). The equation for RU is as follows. \[\textit{Utilization}_{VM_{j}}\ =\ \frac{\sum_{i=1}^{n}p}{\textit{time}} \tag{4}\]  
For example, low ET is better than a high ET, so we must get a high score. Thus, we present a mathematical method for a reciprocal number. In Equations (5) and (6), we represent two metrics, cpu utilization (CU) and memory utilization (MU), based on RU in order to apply them to situations, such as underload and overload. CU: CU is the average percentage of utilization (p) of the resource for VM. CU is used for weight calculation. According to weight, it can decide priority. Based on priority, we can get an alternative for target machine selection. The equation for CU is as follows. \[\text{CU}=\ \left\{ \begin{array}{cc}p&p\leq 70\\ 140-p&p>70\end{array} \right. \tag{5}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **M1** & **M2** & \(\dots\) & **Mn** \\ \hline M1 & S1/S1 & S1/S2 & \(\dots\) & S1/Sn \\ M2 & S2/S1 & S2/S2 & \(\dots\) & S2/Sn \\ \(\dots\) & \(\dots\) & \(\dots\) & \(\dots\) & \(\dots\) \\ Mn & Sn/S1 & Sn/S2 & \(\dots\) & Sn/Sn \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Relative value-based weight. \begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Description** \\ \hline M1 & Resource utilization of VM \\ M2 & Capacity of VM \\ M3 & The number of VM migrations for SP \\ M4 & The time of delay during the SP \\ M5 & Response time during SP \\ Mn & Metric n \\ Sn & Relative score n \\ Wn & Sum of weight \\ Wm & Weight for metric \\ RU & Resource utilization of VM \\ CU & CPU utilization of VM \\ MU & Memory utilization of VM \\ P & Percentage of resource utilization \\ RT & Response time of service \\ WT & Waiting time of service \\ NM & Number of VMs \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Notation used in this paper. The score for CU is equal to or under 70%. If it is higher than the threshold, the score is decreased. If CU is 65%, we get a score of 65. If CU is 90%, we get a score of 50. The reason we calculate the equation this way is that, when the CU gets a hotspot, service leads to latency [1]. MU: MU is the average utilization (p) of VM resources. The following equation calculates the MU scores for weight. \[\text{MU}=\ \left\{ \begin{array}{cc}p&p\leq 50\\ 100-p&p>50\end{array} \right. \tag{6}\]  
We propose an SP scheme with metrics that combine score demand based on the user requirements. In this equation, t represents the average amount of time taken for the system to process a request. The following equation obtains a score for RT. \[\text{RT}=\ \frac{1}{t} \tag{7}\]  
\(\bullet\) _Step 10._ Calculate the final weight for selecting the service. Equation (8) determines the target machine with values such as RU, RT, and prediction of WT. In addition, we can calculate selection VM through Equations (8)-(10). \[Target\ Service_{p}=RU+RT+WT \tag{8}\]  
\[Target\ Service_{e}=RU+NM \tag{9}\]  
\[\text{Selection Service}=\text{Max}(Target\ service_{i}) \tag{10}\]  
\(\bullet\) _Step 11. Action of placement._ After making decision of the target machine for SP, then we operate on SP.