# Multi-Objective Service Placement Scheme Based on Fuzzy-AHP System for Distributed Cloud Computing
## 4 Evaluation
### Result of Evaluation
#### 4.3.2 Proposed Placement Scheme Efficiency for Performance and Energy Efficiency  
In this section, as shown in Table 12, we define the policy of each individual case. The fuzzy rule used in order to measure the effectiveness of metrics is as follows. Table 12 shows an explanation of the metric with policy. To measure the impact of policy considered in the rules on the target machine, we apply the calculation results for the case. As shown in Figure 11, we calculated the weight values according to the alternatives in the AHP system based on Table 12. For example, it can be seen that, in M1 and M3, A5 is selected as the best alternative. To prove the efficiency of the proposed SP scheme, we divided them into two cases (performance and energy efficiency). \begin{table}
\begin{tabular}{c c} \hline \hline
**Metric** & **Fuzzy Rule** \\ \hline CU & \\ MU & \\ RU & \\ Power & \\ NM & \\ WT & \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Policy of case 1. Figure 10: EC with the number of VMs according to a (a) scenario and (b) policy. Although most of the existing work focused on the cloud service decision for SP in CDCs, the studies have been limited to a single metric. However, in this study, both single and multiple decision analysis approaches are performed by considering different metrics for performance, energy, and costs in the decision problem to determine the importance of different metrics. Our technique was also used to select the best service among different service providers based on the weights of different decision-making metrics. * Case 1: Performance  
In this case, for placement performance, we consider three metrics RU, RT, and WT. Figure 12a shows the selection VM for different alternatives. As shown in Figure 12, we calculate weight. Figure 12b shows total alternative ranks for case 1 for the performance, in the following order (from best to worst): A2, A1, A4, A1, and A5. Figure 11: Result of weight. Figure 12: Weight rank for case 1 according to the metrics: (**a**) weight value and (**b**) alternative score. We tested the performance of the scheme by measuring the ET during the entire experimental period. Each experiment was tested 30 times to ensure objectivity. Then we calculated the average for the worst-case execution time (WCET). We selected the target machine based on the results shown in Figure 12b. According to the result of the AHP score for the proposed scheme, we compared the results of the ET for SP with LR, Random, and LSTM. In Figure 13, we show that the decrease in ET of LSTM was approximately 9.5% less than that of the proposed scheme. This proves that our scheme increases SP efficiency better than existing schemes. * Case 2: Energy efficiency  
In this case, for placement energy efficiency, we consider five metrics CU, MU, RU, PW, and NM, as shown in Figure 14a. Figure 14b shows the total alternative ranks for case 2 for the energy efficiency, in the following order (from best to worst): A2, A1, A3, A4, and A5. We selected the target machine based on Figure 14b that shows the result of the AHP score. Then, we performed the placement by selecting the target machine, according to the result in Figure 14b. Through our scheme, we selected the target machine based on Figure 14b and then performed SP. We compared the result of the EC with Threshold, LR, ARIMA, and LSTM in this paper. As shown in Figure 15, the evaluation results of the proposed scheme verified lower EC than the other methods. Regarding energy, the proposed scheme showed an EC decrease about 23% lower when compared to the threshold scheme. For the test and evaluation, we constantly increased the number of VMs. When the number of VMs was smaller, the difference in EC became larger, as shown in Figure 15. Thus, the test result confirmed that our scheme is efficient in small data centers like distributed cloud environments. Figure 16 also shows the importance of considering and configuring the metric from Fuzzy (sc1) to Fuzzy (sc3) by the policy. According to the result of the configuring metric, its weight changed.