# Finding Optimal Stations Using Euclidean Distance and Adjustable Surrounding Sphere
## 4 Proposed Methods
### Euclidean Distance + Fixed Surrounding Sphere (ED + FSS)
In contrast, M2: FSS shows achieving good spatial coverage which can cover an area up to 91% in the case of four stations in Sejong city. For the spatial coverage assessment, it is possible to conclude that M2: FSS is better than M1: ED. #### 6.2.2 Performance of Coverage Percentage Versus the Number of Stations

Added Incrementally

Our previous result when establishing four stations using M2: FSS shows a high coverage percentage of about 91%, which is better than M1: ED. In this case, we compared the performance of M2: FSS and M3: ED + FSS in terms of coverage percentage versus the number of stations added incrementally. The specified number of stations is seven. In Figure 7, the plot graph shows a comparison coverage percentage (COV) as the number of stations increases. The dashed line with square symbols indicates M2: FSS that shows coverage percentage increasing sharply and degrading from stations numbered 4 to 7. In contrast, the dotted line with triangle symbols indicates M3: ED + FSS and offers a relatively stable increasing trend from stations numbered 1 to 7. We conclude that M3: ED + FSS shows a coverage increasing trend better than that of M2: FSS. Next, we investigated the additional stations of M2: FSS. As shown in Table 4 (a), light color of triangle symbols indicated the three additional stations which are located close to the border. Although the M2: FSS achieves excellent spatial coverage (98%) nonetheless, the additional stations cause loss of area coverage, which shows the transparent area inside circles. On the other hand, all seven stations from the M3: ED + FSS method are located inside the city. These stations provide both sufficient spatial coverage (94%) and right overlapping area, as clearly shown in Table 4 (b). According to the result, we can assert a performance of M3: ED + FSS in achieving spatial coverage without loss of area coverage while still preserving the overlapped areas. The nearby stations can enhance strength to neighboring stations, which makes the network more robust and its data more reliable. Figure 7: Plot of historical coverage percentage versus number of stations in Sejong. #### 6.2.3 Coverage Percentage Versus a Specified Number of Stations

In this experimental case, we compared the performance of M3: ED + FSS and M4: ED + ASS concerning coverage percentage versus a specified number of stations. The location of station results from two methods is shown in Table 5. This part of our experiment aims to consider the flexibility of finding stations when we predefine the number of stations. We will evaluate the coverage percentage and distribution of the stations in the study area. The results based on M3: ED + FSS show that the stations in similar aligned positions seem like a straight line in all four cases. On the other hand, results for M4: ED + ASS show a better balance of stations. The stations are readjusted whenever the number of stations changes. Furthermore, in four cases of a specified number of stations, the M4: ED + ASS \begin{table}
\begin{tabular}{c c c c} \hline \hline  & M2: FSS & M3: ED + FSS \\ \hline Map of Sejong city & & & \\ and & & & \\ Stations & & & \\ \hline  & C0: 49 & W1: 0.0078125 & C0: 121 & W1: 0.0078125 \\  & C1: 767 & W1: 0.0078125 & C1: 520 & W1: 0.0078125 \\  & C2: 856 & W2: 0.015625 & C2: 757 & W2: 0.015625 \\
1. Coverage Degree \& Weighted & C3: 290 & W3: 0.03125 & C3: 584 & W3: 0.03125 \\  & C4: 62 & W4: 0.0625 & C4: 42 & W4: 0.0625 \\  & C5: 0 & W5: 0.125 & C5: 0 & W5: 0.125 \\  & C6: 0 & W6: 0.25 & C6: 0 & W6: 0.25 \\  & C7: 0 & W7: 0.5 & C7: 0 & W7: 0.5 \\ \hline
2. Coverage Percentage (COV) & & 98\% & & 94\% \\ \hline
3. Weighted Coverage Degree (WCD) value & 1.61 & & 1.86 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The results of stations, coverage percentages, and weighted coverage degrees of two methods: M2: FSS and M3: ED + FSS.