# Optimizing Energy Efficiency in Cloud Data Centers:
## 7 Results and Discussion
Figure 8 displays the percentage of service level agreement (SLA) violations. Our model surpasses other schemes in both iqr_1.5 mc and lr_1.2 mmt strategies, maintaining a  
Figure 5: Average energy consumption (Kwh). Figure 6: Comparison of virtual machine migration counts under different loads. Figure 7: Average number of migrations. consistently low value over the ten days. The SLA is upheld by QL with Firefly due to its lower migration count. To rigorously evaluate our approach, we conducted an in-depth statistical analysis of energy consumption over a 10-day simulation period. Table 8 summarizes several key descriptive metrics: mean, standard deviation, minimum, maximum, median, interquartile range (IQR), variance, and coefficient of variation (CV%). This analysis goes beyond a simple comparison of average results, offering a more comprehensive view of each method's energy performance and robustness:  
* The mean provides a general measure of energy efficiency. * The standard deviation, variance, and CV% reveal how consistent and predictable the methods are across different workload conditions. A lower CV indicates more stable energy consumption, which is essential in real-world data center operations. * The median and IQR give additional insight into the distribution of results, reducing the influence of occasional spikes or anomalies. Among all the evaluated methods, QL_Ir_mmt_1_2 stands out with the lowest average consumption (22.43 kWh) and one of the most stable profiles (CV = 20.43%). This balance between efficiency and consistency highlights the strength of reinforcement learning (QL), which can dynamically adapt to changing workloads while maintaining steady energy usage. In contrast, traditional approaches such as GA and PSO not only consume more  
Figure 8: SLA violation under different workload datasets. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Method** & **Mean** & **Std Dev** & **Min** & **Max** & **Median** & **IQR** & **Variance** & **CV (\%)** \\ \hline QL\_lr\_mmt\_1\_2 & 22.43 & 4.58 & 16.68 & 32.21 & 21.51 & 4.46 & 21.00 & 20.43 \\ \hline QL\_lqr\_mc\_1\_5 & 23.05 & 4.99 & 16.68 & 32.20 & 22.54 & 6.96 & 24.91 & 21.66 \\ \hline PABFD\_lr\_mmt\_1\_2 & 23.64 & 5.33 & 16.68 & 35.45 & 23.26 & 4.12 & 28.40 & 22.54 \\ \hline PABFD\_lqr\_mc\_1\_5 & 25.84 & 6.78 & 16.68 & 38.38 & 26.54 & 8.66 & 45.95 & 26.24 \\ \hline PSO\_lqr\_mc\_1\_5 & 26.64 & 6.40 & 18.06 & 37.38 & 26.04 & 9.03 & 41.00 & 24.04 \\ \hline PSO\_lr\_mmt\_1\_2 & 25.29 & 5.61 & 17.68 & 36.45 & 23.77 & 6.12 & 31.46 & 22.17 \\ \hline GA\_lqr\_mc\_1\_5 & 27.35 & 5.98 & 18.90 & 38.78 & 26.80 & 5.93 & 35.79 & 21.87 \\ \hline GA\_lr\_mmt\_1\_2 & 25.11 & 5.41 & 17.50 & 36.47 & 24.54 & 4.77 & 29.24 & 21.54 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Statistical analysis of energy consumption over 10-day simulation. energy on average but also display higher variability (e.g., CV > 24%), suggesting a greater risk of inconsistent performance. From a practical standpoint, these findings imply that using QL-based strategies could help cloud providers lower energy costs while improving service reliability. This marks a clear departure from conventional VM placement methods, which often depend on static or manually tuned heuristics that lack adaptability. By contrast, our RL-based approach offers a more autonomous and resilient solution--especially important in dynamic, real-world environments. In summary, the statistical evidence not only confirms the quantitative benefits of our approach but also reinforces its practical value: methods that combine low average consumption with high stability reduce operational risks and improve cost efficiency, which is crucial for meeting service level agreements (SLAs) in modern cloud infrastructures. Our model excels by effectively integrating reinforcement learning with the Firefly algorithm to optimize virtual machine (VM) placement.