## 3 Methodology
### Sensitivity Analysis  
To perform the comparison between the three TOPSIS variants mentioned above, we use the sensitivity analysis approach [36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46]. The aim is to assess the robustness of the three TOPSIS variants in response to dynamic changes observed in a criterion value for each of the alternatives, due to satellites' mobility in LEO networks. Sensitivity analysis consists of evaluating the impact of changes in criteria values on the final score attributed by handover algorithms to each alternative. Scores should not change significantly after minor changes in criteria values, to avoid unnecessary handovers. Sensitivity \(s\) is given by:  
\[s_{i}=\left|\frac{r_{\text{modified}}-r_{\text{initial}}}{r_{\text{initial}}} \right|,\forall i=1,...,m \tag{20}\]The \(r_{\text{modified}}\) is the score obtained after modifying the value of a criterion for the alternative \(i\). We focus on the four following criteria: upload speed, download speed, ping, and packet loss. The choice of these criteria is crucial in the study of satellite handover, particularly in LEO networks. The upload speed is essential for bidirectional communication, directly impacting applications such as video calls or data uploads. The download speed determines the ability of the satellite to deliver data to the user, a key factor in ensuring a smooth user experience. The ping measures the latency between a request sent from the user terminal and the response received from the satellite network. It is a critical parameter for real-time applications such as VoIP and online gaming, where a lower latency ensures a more responsive connection. The packet loss refers to the percentage of data packets that do not reach their destination, often due to network congestion, signal degradation, or interference. High packet loss can significantly degrade service quality, leading to interruptions in video streaming, dropped calls, or reduced throughput in data transmissions. These four criteria are interdependent and directly influence the overall quality of the connection, making their optimal management essential during satellite handovers to maintain uninterrupted and high-quality service. Our analysis involves evaluating, through four scenarios, the sensitivity of each TOPSIS algorithm in response to a \(x\%\) random change in the initial criteria values for each alternative. To enhance the depth of our sensitivity analysis, we first apply variations within the range \(-5\leq x\leq 5\), followed by a broader range of \(-10\leq x\leq 10\) with \(x\in\mathbb{Z}\). This progressive approach allows us to assess the robustness of each algorithm under different levels of perturbation, providing a more comprehensive evaluation of their stability and adaptability in dynamic environments. The four scenarios analyzed in this study are as follows:  
1. First scenario: For each satellite, apply a \(x\%\) random change on the upload speed value only, while keeping other criteria values unchanged. 2. Second scenario: For each satellite, apply a \(x\%\) random change on the download speed value in addition to the previously changed upload speed value and keep the packet loss values unchanged. 3. Third scenario: For each satellite, apply a \(x\%\) random change on the ping value in addition to the previously changed upload speed and download speed values and keep the packet loss value unchanged. 4. Fourth scenario: For each satellite, apply a \(x\%\) random change on the packet loss value in addition to the previously changed upload speed, download speed, and ping. We evaluate the robustness of the three TOPSIS variants by observing the impact of these random changes on the scores of the selected alternatives. By closely examining how the score assigned to a satellite by each TOPSIS variant changes with variations in upload speed, download speed, ping, and packet loss, we assess which TOPSIS variant maintains consistent performance and ensures high service quality despite these fluctuations.