## 3 Analysis and Results
### Sensitivity of Data Aggregation Time  
In real-time time series analysis and traffic management services, the choice of data aggregation interval is crucial for accurately identifying representative attributes, such as segment speed. Shorter aggregation intervals allow for a more granular analysis, capturing rapid changes in traffic flow; however, they may yield insufficient data to establish reliable segment attributes. In contrast, longer aggregation intervals provide a larger dataset,  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Time** & **Segments** \\ \hline
10:15 & \\ \hline
10:25 & \\ \hline
10:35 & \\ \hline
10:45 & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Time series analysis of the spatial impact of accidents.  
facilitating the identification of representative segment characteristics, but risk missing sudden traffic flow variations due to events like accidents.  
This study conducted a sensitivity analysis using data aggregated at 10 min intervals to assess the impact of varying aggregation times. For a 2.4 km section near the Dongtan interchange on Expressway 1, data were also aggregated at 15 min and 3 min intervals starting from 9:30 AM. Table 4 compares these intervals: data for 15 min intervals were aggregated from 9:30 AM to 9:45 AM, while 3 min interval data were captured at 9:33, 9:36, 9:39, 9:42, and 9:45 AM. At the 3 min intervals, a reduction in upstream speed was observed at 9:33 AM, which propagated downstream by 9:36 AM. By 9:39 AM, upstream speeds began to recover, with full restoration of normal flow by 9:42 and 9:45 AM. This analysis demonstrates that the initial speed reduction caused by congestion in the upstream sorting section was alleviated by a decreased traffic volume, which in turn led to a gradual recovery in speed in the downstream merging section.  
The sensitivity analysis reveals that shorter aggregation times allow for more precise monitoring of speed distribution changes over short periods. This is particularly relevant for identifying stable flow segments. For instance, if the number of stable flow segments fluctuates significantly--from 8 to 15 in a 5 min aggregation--it may indicate the need for a shorter aggregation interval. Conversely, if the stable flow segment count remains steady, such as at 27 or 29 in a 5 min aggregation, the interval can be extended. Figure 12 illustrates the relationship between speed homogeneity space changes and data aggregation time, showing that consistent results in a 5 min aggregation support extending the interval to 10  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Aggregation Period** & **15 min** & **3 min** & **40 min** & **5 min** & **60 min** \\ \hline Number of segments & 29 & 10 & 6 & 11 & 27 & 27 \\ \cline{2-7} Time interval & 9:30-9:45 AM & 9:30-9:33 AM & 9:33-9:36 AM & 9:36-9:39 AM & 9:39-9:42 AM & 9:42-9:45 AM \\ \hline \hline \end{tabular}
\end{table}
Table 4: Analysis results of speed distribution by data aggregation time.  
or 15 min. However, if variations in speed homogeneity appear, the interval is reduced to 5 or 10 min and extended again once stability is observed.  
This adaptive approach to data aggregation intervals enhances the responsiveness of traffic flow analysis, enabling more effective real-time monitoring and decision making to accommodate dynamic traffic conditions.  
In segments where stable flow persists consistently--characterized by smooth, uniform speeds or prolonged congestion, which minimizes noticeable changes in the speed time series--it is appropriate to aggregate data at intervals longer than 10 min. Conversely, in cases where stable flow segments fluctuate, such as during the onset or easing of congestion, resulting in greater sensitivity to speed changes in the time series, data should be aggregated and applied at intervals shorter than 5 min.