## 2 Methodology
### Dynamic Cell Optimization Method
At this point, the TMS-SMS values for each of these cells are recalculated, resulting in 1.00, 0.66, 0.80, and 2.18 kph, respectively. The cell with the highest value, CH13 (2.18 kph), is further divided into CH130, CH131, CH132, and CH133. Since CH130 and CH131 have no vehicles, they are excluded, and the TMS-SMS values for CH132 and CH133 are calculated. If the values are small, further division is unnecessary, and the cell is represented by its space mean speed. Figure 4: The difference between TMS and SMS. Figure 5: Changes in TMS-SMS with increasing average speed. In the example of the spatial division process shown in Figure 6, the relationship between time mean speed and space mean speed is visualized in Figure 7. CH1 is shown in Figure 7a, and based on the TMS-SMS values, it is divided into four cells as shown in Figure 7b. Among them, CH13 is divided further as shown in Figure 7c, resulting in a final total of five cells as shown in Figure 7d: CH10, CH11, CH12, CH131, and CH133. Figure 6: The spatial division process based on TMS-SMS calculation. \[\overline{u_{s}}=\overline{u_{t}}-\frac{\sigma^{2}}{\overline{u_{t}}} \tag{2}\]0 TMS-SMS value and spatial division process. The spatial division process based on the relationship and difference between time mean speed (TMS) and space mean speed (SMS) is fundamentally about assessing the homogeneity of speeds within a given cell. To make this assessment, a clear criterion is needed. The method for spatial division using the difference between the two averages is based on the relationship between TMS and SMS, expressed by the formula. Empirically, research [18; 19; 20] has suggested that when the variance in speed within a homogeneous zone is 50, it indicates speed homogeneity. However, in this study, a threshold value of 200 has been applied to define the boundary for judging homogeneous speed cells. As shown in Figure 8, if the relationship between time mean speed and space mean speed places a given cell to the left of the boundary function used for speed homogeneity division, the cell is considered to be homogeneous and is finalized as such. If the cell is positioned to the right of the boundary, it is deemed non-homogeneous, and further spatial divisions are performed until homogeneity is achieved. This process is repeated to ensure that each cell has homogeneous speed characteristics. In this study, the focus is not on estimating the two values (time mean speed and space mean speed) but rather on determining cell division based on speed distribution. Therefore, the boundary line must be placed below and to the right of the actual trendline. To establish this boundary, a regression analysis of time mean and space mean speeds was conducted using normally distributed random numbers with intervals of 10 km/h for the mean, and standard deviations of 5, 10, and 20. For each average speed, 100 random numbers were generated, as shown in \[\overline{u_{s}}=\overline{u_{t}}-\frac{\sigma^{2}}{\overline{u_{t}}} \tag{2}\]1  
The boundary line was determined based on 85% of the speeds from a normal distribution with a standard deviation of 10 km/h, representing the reasonable maximum speed range in traffic flow. The resulting boundary function was defined as Equation (5). This boundary serves as the criterion for deciding whether further cell division is necessary based on speed homogeneity. \[\overline{u_{s}}=\overline{u_{t}}-\frac{\sigma^{2}}{\overline{u_{t}}} \tag{2}\]2  
Based on the boundary line established above, the time mean and space mean speeds were calculated for a 34 km section of Highway 1, which was divided into 1 km intervals using GPS Y-coordinates, as shown in \[\overline{u_{s}}=\overline{u_{t}}-\frac{\sigma^{2}}{\overline{u_{t}}} \tag{2}\]3 When the empirical formula for speed distribution within the sections was applied, the results were plotted as shown in Figure 10a. In Figure 10b, sections 5 and 32 exhibit uniform speed distribution, while sections 21 and 25 display non-uniform speed distribution, indicating a significant separation in speed homogeneity.