# Finding Optimal Stations Using Euclidean Distance and Adjustable Surrounding Sphere
## 4 Proposed Methods
### Euclidean Distance + Fixed Surrounding Sphere (ED + FSS)
\[WCD=\ 100\times\ \frac{\sum_{i=0}^{k}W_{i}C_{i}}{N} \tag{6}\]

\(W_{i}\) is a weight value and \(\sum W_{i}=1\), \(i\in\{0,\,1,\,2,\ldots,\,k\}\), \(k\) indicates a number of stations in the network, and the weights are associated to Coverage Degree (\(C_{i}\)). ## 6 Results and Discussion

This section explains the parameters used in the experiment and compares each method's pros and cons. In scenario 1, setting up a network by considering four cases as following, (i) spatial coverage, (ii) performance of coverage percentage versus the number of the stations added incrementally, (iii) coverage percentage versus a specified number of stations, and (iv) flexibility to apply our methods to different cities. In scenario 2, finding an additional station to improve the current network is evaluated. ### Experimental Parameter Settings

The parameter settings are shown in Table 2. The area size (\(A\)) is the number of locations in study areas. The centers of the maps are located at indices 1056, 3516, and 218 for Sejong, Bangkok, and Bonn. The specified number of stations is equal to the existing stations in the cities. The diameter length of the M3: ED + FSS is a fixed value of ten kilometers and the M4: ED + ASS is predetermined. We consider the proportion of covered area from reasonable based on the number of existing stations, as shown in Figure 6. Finally, we determined that 30% is a proper value for our experiment. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Coverage Degree** & **C4** & **C3** & **C2** & **C1** & **C0** & **C4** \\ \hline Weight, \(\sum W_{i}=1\) & W4 = 0.5 & W3 = 0.25 & W2 = 0.125 & W1 = 0.0625 & W0 = 0.0625 & W4 = 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Example of weight generation. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Sejong** & **Bangkok** & **Bonn** \\ \hline Area size (\(A\)) & 2024 & 7010 & 653 \\ Index of the center of the map & 1056 & 3516 & 218 \\ Number of stations & 4 & 12 & 1 \\ Diameter length of FSS (\(dm_{s}\)) & 10 km. & 10 km. & 10 km. \\ Diameter 1 length of ASS (\(dm_{s}\)) & 14.2 km. & 25.4 km. & 8.6 km. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experiment Parameter Setting. ### Assessment of Scenario 1: Setting Up a Network

#### 6.2.1 Spatial Coverage

Table 3 shows M1: ED, M2: FSS and compares them with the existing stations in Sejong city. In Table 3, triangle symbols depict existing stations, and circles represent the spatial coverage. Let us consider a result in M1: ED, where we defined the first station at the center and used four stations as input parameters. The output from M1: ED is shown in Table 3 (b). Three stations are located near each other, but one station is located far away from its neighbors. We found significant inefficient spatial coverage in that case because almost all covered areas overlap. The COV of M1: ED is 57%, which is a 16% decrease in the current value, and WCD shows a value of 12.58, which increased 48% when compared with the current value. Next, consider the result in M2: FSS; we used the input parameters as same as M1: ED except adding a fixed diameter of ten kilometers to be used in the calculation. The result shows that most stations are located apart from the first station at the center, as shown in Table 3 (c). As a result, M2: FSS achieves the best coverage percentage up to 91% and an increase of 34% compared to the current value. On the other hand, the WCD value shows 7.44, which decreased by 13%. The M1: ED shows large overlapping areas which make a strengthened area with neighboring stations. The area of overlap can make data more reliable in case of data verification between neighboring stations and also produce a network which is fault

\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline  & & & & & & & \\ Map of Sejong city & & & & & & & \\ and &



tolerant. We denominate such overlap areas as confidence areas because they can enhance data reliability. However, this method shows spatial coverage weaknesses.