## 4 Performance Evaluation, and Result Analysis and Discussion
### Experimental Results and Analysis of the Results  
This section shows and analyzes the experimental results. The three main metrics in our experiments were convergence time, convergence deviation, and cache hit ratio. Through the convergence time and deviation, we show the quickness and stability of EDCrammer. Through the cache hit ratio, we show the effectiveness of this framework. Tables 3-5 show representative performance evaluation results from 30 experiments. As a lightweight rate-control algorithm, EDCrammer adopts and enhances the existing PID controller. EDCrammer can provide agile rate-control for in- and outflows and caching of streaming data on resource-limited edge nodes. As shown in the graphs of the results, the three algorithms for all four scenarios reached the desired cache utilization (_setpoint_) within a few iterations. Furthermore, the result graphs show that EDCrammer immediately computed and compensated for the amount of caching data by using the current cache utilization (_feedback_). It is possible to maintain the stability of cache utilization according to the _setpoint_. Therefore, we conclude that EDCrammer quickly reaches and maintains the desired cache utilization in any situation. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Basic PID Algorithm** \\ \hline \hline  & Scenario 1 (Periodic and equal) & Scenario 2 (Periodic and unequal) \\ \hline  & Scenario 3 (Aperiodic and equal) & Scenario 4 (Aperiodic and unequal) \\ \hline  & Scenario 4 (Aperiodic and unequal) \\ \hline  & Scenario 5  
based on the setpoint is suitable to represent the performance of EDCrammer, thus we used that to check its stability of EDCrammer. \[error_{i}=setpoint-feedback_{i} \tag{6}\]  
\[STDEV=\sqrt{\frac{\sum_{i=1}^{n}(feedback_{i}-setpoint)^{2}}{n}}=\sqrt{\frac{ \sum_{i=1}^{n}(error_{i})^{2}}{n}} \tag{7}\]  
The performance evaluation was conducted 30 times, and the average of the standard deviation represents the average convergence deviation for the existing and proposed algorithms as follows. \[\overline{STDEV}=\frac{\sum_{i=1}^{n}STDEV_{i}}{n},(n=30)\]  
Table 6 shows the average performance of the existing and proposed algorithms over 30 experiments. Each experiment performed a different number of caching operation for about 30 s. A caching operation (_an iteration_) takes 0.15 s on average. Experiments using the basic PID algorithm were performed as a basis for comparison. The existing algorithm that reflects the rate of change in PID output has an advantage in environment with low rate of change. The proposed algorithm also reflects the rate of change in the PID output and increases sensitivity. This algorithm has an advantage in dynamically changing environment. In Scenarios 1 and 2, the existing algorithm showed better performance than the proposed one and the basic PID one because those are relatively stable scenarios compared to Scenarios 3 and 4. In detail, in Scenario 1, the average convergence time of the existing algorithm was the fastest of the three. It was 27% faster than that of the proposed one and 24% faster than that of the basic PID one. The average convergence deviation of the existing algorithm was the most stable of the three. It was 9% more stable than that of the proposed one and 5% more stable than that of the basic PID one. In Scenario 2, the average convergence time of the existing algorithm was the fastest of the three. It was 8% faster than that of the proposed one and 85% faster than that of the basic PID one. The average convergence deviation of the existing algorithm was the most stable of the three. It was 1% more stable than that of the proposed one and 2% more stable than that of the basic PID one. On the other hand, the proposed algorithm showed better performance than the existing one and the basic PID one in Scenarios 3 and 4. In Scenario 3, the average convergence time of the proposed algorithm was the fastest of the three. It was 14% faster than that of the existing one and 77% faster than that of the basic PID one.