# Seamless Weather Data Integration in Trajectory-Based Operations Utilizing Geospatial Information
## 3 Performance Evaluation of the 4 DT-Wx Prototype System
### Performance Analysis of MET Data Processing on 4 DT-Wx Prototype System
#### 3.2.2 Comparative Analysis of Parallelization Performance  
In this study, we applied the model proposed by [PERSON] et al. [55] along with [PERSON]'s and Gustafson's laws to analyze the parallelization performance of our Spark-based big data processing system. By applying and comparing these three models to the actual performance data of our system, we can explain the performance characteristics of various Spark workloads and evaluate the efficiency of the implemented parallelization. Therefore, we aimed to understand our system's parallelization characteristics by analyzing the alignment of each model with the actual data, identifying the strengths and potential areas for improvement in the current implementation. [PERSON]'s and [PERSON]'s laws are fundamental theories for understanding the benefits and limitations of parallel processing. [PERSON]'s law focuses on the serial portion of the task that limits the speedup, while [PERSON]'s law evaluates the effectiveness of parallelization under the assumption that the problem size can scale with the processing capability, suggesting that the efficiency of parallel processing can be maintained as the problem size increases. In contrast, the model proposed by [PERSON] et al. offers a new approach that is adjusted for specific characteristics observed in the data, providing a more tailored prediction of the parallelization performance. The analysis was performed using only the BOff condition. This approach prevents additional delays and performance variations caused by buffers, allowing for a clearer observation of the actual effects of parallelization, and similar patterns to those demonstrated in the previously presented results (i.e., BOn). The analysis results indicate that the model proposed by [PERSON] et al. explains the actual data patterns of our system most accurately. The experimental results show that [PERSON] et al. 's model demonstrated high \(R^{2}\) values, ranging from 0.819 to 0.982, for all numbers of API requests, particularly achieving very high accuracy with \(R^{2}\) values above 0.95 for 500 or more API requests (Table 3). This validates our implemented parallelization approach as being particularly effective for large-scale data processing. In contrast, [PERSON]'s law showed a generally low explanatory power, and [PERSON]'s law was also not suitable for most of our dataset. This suggests that our Spark workload performance does not scale in the manner assumed by these two models (Figure 8). Classical models like [PERSON] et al. 's model and [PERSON]'s law assume fixed ratios of parallel and serial portions. However, our Spark-based system exhibits different characteristics, with its performance following more complex patterns than these models predict. While these classical models provide a basic understanding, they fail to accurately capture our system's performance characteristics. In conclusion, the high accuracy and consistency of [PERSON] et al. 's model strongly support the effectiveness of our parallelization strategy, both theoretically and practically. It performs excellently in large-scale data processing, effectively handling the complex performance patterns that arise in real distributed environments. These findings suggest \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Number of API Requests**} & \multicolumn{3}{c}{\(R^{2}\)} \\ \cline{2-4}  & **[PERSON] et al.’s Model** & **Amdahl’s Law** & **[PERSON]’s Law** \\ \hline
50 & 0.835 & 0.475 & 0.823 \\
100 & 0.819 & 0.067 & 0.387 \\
500 & 0.982 & 0.324 & 0.211 \\
1000 & 0.956 & 0.319 & 0.292 \\
1500 & 0.971 & 0.318 & 0.263 \\
2000 & 0.971 & 0.313 & 0.271 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: \(R^{2}\) estimates for parallelization models ([PERSON] et al.’s model, [PERSON]’s law, and [PERSON]’s law) under the BOff condition.