## 2 Methodology
### Dynamic Cell Optimization Method  
The core of this study, spatial optimization, assumes that each vehicle's location information within a single cell carries the same code in the same area, thus considered the same point. Vehicles within that area must have a uniformly distributed speed; if not, the cell is divided to ensure homogeneity of speed, creating small and large areas or points. As shown in Figure 2, if the first divided cell (CH1) contains different speed characteristics, the homogeneity of speed is analyzed in the subsequently divided cell (CH12), and the final cell (CH123) with ensured speed homogeneity is represented as a coordinate-based area, akin to a low-resolution point (point A). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Depth** \\ **(m)** \\ \end{tabular}  } & \multicolumn{6}{c}{**Length per Cell (km)**} \\ \cline{2-7}  & \multicolumn{3}{c}{**16 Base**} & \multicolumn{3}{c}{**4 Base**} \\ \cline{2-7}  & **Latitude** & **Longitude** & **Area (km2)** & **Latitude** & **Longitude** & **Area (km2)** \\ \hline
1 & 110.00 & 88.74 & 9761.40 & 220.00 & 177.48 & 39,045.60 \\
2 & 27.5000 & 22.1850 & 610.0875 & 110.0000 & **88.7400** & 9761.40 \\
3 &  
To determine speed homogeneity, it is necessary to assess whether the vehicles within a given area have varying speeds or if they all exhibit similar speeds. This judgment is essential to ensure that the area either consists of vehicles with diverse speed characteristics or is limited to vehicles with uniform speed behavior. This evaluation forms the basis for determining whether further spatial division is required to achieve homogeneity within that area. In Figure 3, when assuming that the speed of all vehicles within the same space is identical, the relationship between the two average speeds can be represented as Equation (1). However, when there are speed differences among individual vehicles, the relationship between the two average speeds is expressed as Equation (2). The difference between the two functions, or the space, is represented by the square of the standard deviation of the time average speed and the ratio of the time average speed. The difference between the two average speeds in the first and second spaces is represented as Equations (3) and (4), respectively. \[\overline{u_{s}}=\overline{u_{t}} \tag{1}\]  
\[\overline{u_{s}}=\overline{u_{t}}-\frac{\sigma^{2}}{\overline{u_{t}}} \tag{2}\]  
\[\sigma_{\rm{I}}^{2}/\overline{u_{t1}} \tag{3}\]  
\[\sigma_{\rm{I}2}^{2}/\overline{u_{t2}} \tag{4}\]  
Figure 3: The concept of the difference between time mean speed and space mean speed. Figure 2: Dynamic cell optimization basic concept (A, B, and C are vehicles that each travel at different speeds). As such, the difference between time mean speed and space mean speed is related to the speed variance within a cell. When the individual vehicle speeds are unevenly distributed within the cell, the difference between the two averages increases. In Figure 4, for example, when the speed of individual vehicles in cell CH1 varies between 40 kph and 90 kph, the difference between the two averages is 4.64 kph. However, in cell CH2, where the individual vehicle speeds range from 84 kph to 93 kph, the difference is only 0.06 kph, which is noticeably smaller than in cell CH1. The difference between time mean speed and space mean speed is related to the ratio of variance to average speed, meaning that as the average speed increases, this difference becomes smaller. As shown in Figure 5, when the average speeds of individual vehicle distributions in the different cells CH3, CH4, and CH5 are 31.10, 61.10, and 91.10, respectively, and have the same standard deviation, the difference in space mean speed gradually decreases. In the case of cell CH1, where speeds are mixed within the same area, the spatial division process is repeated according to the division method. As shown in Figure 6, when the TMS-SMS value for CH1 is large, the cell is divided into four smaller cells: CH10, CH11, CH12, and CH13.