## 4 Simulation Results and Discussion
### Case 2: Sensitivity Analysis with Criterion Variation Within \(\pm 10\%\)
#### 4.3.6 Sensitivity Analysis  
Figure 15 shows the variation rates of the scores for the Scenario 1, in comparison with the initial case. We observe that the SD-TOPSIS algorithm is the most robust, as it shows the lowest score variation rate of 9.87%, whereas the Entropy-TOPSIS and Importance-TOPSIS exhibit variation rates of 11.44% and 12.1%, respectively. Figure 16 shows the variation rates for the Scenario 2. We observe that the SD-TOPSIS algorithm is still the most robust, as it shows the lowest score variation rate of 14.54%, whereas the Entropy-TOPSIS and Importance-TOPSIS exhibit variation rates of 15.07% and 16%, respectively. Figure 17 shows the variation rates for the Scenario 3. We observe that the SD-TOPSIS algorithm is still the most robust, as it shows the lowest score variation rate of 27.85%, whereas the Entropy-TOPSIS and Importance-TOPSIS exhibit variation rates of 32  
Figure 19 presents the standard deviation in the score values for a variation range of \(-5\leq x\leq 5\), while Figure 20 illustrates the standard deviation for a wider variation range of \(-10\leq x\leq 10\). A low standard deviation indicates that the scores remain relatively stable, implying greater robustness, whereas a high standard deviation reflects significant variability in the scores, indicating higher sensitivity to changes in the criteria values. A low standard deviation indicates that the scores remain relatively stable. Figure 19: Standard deviation of scores for a variation range of \(-5\leq x\leq 5\) percent. Figure 17: Variation rates of the scores for the Scenario 3, for criterion variation within \(\pm 10\%\). Figure 18: Variation rates of the scores for the Scenario 4, for criterion variation within \(\pm 10\%\). From Figure 19, it can be observed that:  
1. Scenario 1: After variations in upload speed values, the standard deviations for SD-TOPSIS, Entropy-TOPSIS and Importance-TOPSIS are, respectively, 0.1078, 0.1213 and 0.1233. 2. Scenario 2: After variations in download speed values in addition to those in upload speed, SD-TOPSIS has a standard deviation of 0.1141, Entropy-TOPSIS exhibits a standard deviation of 0.128, and Importance-TOPSIS reaches a standard deviation of 0.1284. 3. Scenario 3: After variations in ping values in addition to those in upload speed and download speed, SD-TOPSIS has a standard deviation of 0.1291, Entropy-TOPSIS exhibits a standard deviation of 0.1474, and Importance-TOPSIS reaches a standard deviation of 0.1397. 4. Scenario 4: Following the variation in packet loss values in addition to upload speed, download speed, and ping, SD-TOPSIS remains the most stable algorithm, with a standard deviation of 0.1325, whereas Entropy-TOPSIS reaches 0.1474, and Importance-TOPSIS presents a standard deviation of to 0.1408 maintaining an intermediate position. From Figure 20, it can be seen that:  
1. Scenario 1: After variations in upload speed values, the standard deviations for SD-TOPSIS, Entropy-TOPSIS and Importance-TOPSIS are, respectively, 0.1177, 0.1404 and 0.1345. 2. Scenario 2: After variations in download speed values in addition to those in upload speed, SD-TOPSIS has a standard deviation of 0.1329, Entropy-TOPSIS exhibits a standard deviation of 0.155, and Importance-TOPSIS reaches a standard deviation of 0.148. 3. Scenario 3: After variations in ping values in addition to those in upload speed, SD-TOPSIS has a standard deviation of 0.1723, Entropy-TOPSIS exhibits a standard deviation of 0.1995, and Importance-TOPSIS reaches a standard deviation of 0.1881. 4. Scenario 4: Following the variation in packet loss values in addition to upload speed, download speed, and ping, SD-TOPSIS remains the most stable algorithm, with a standard deviation of 0.1797, whereas Entropy-TOPSIS reaches 0.1971, and Importance-TOPSIS presents a standard deviation of to 0.1936 maintaining an intermediate position.