## 4 Results and Discussion
### Clustering Results Analysis
#### 4.3.2 Comparative Analysis of Intercity Trip Chains from a Spatial Perspective  
This study examines the most common categories of trip chains from different years and directions to compare the characteristics of trip chains in the same year across various directions. Table 8 presents the characteristics of the predominant trip chains in different directions for 2019. The data indicate that the primary travel dates for travelers across all directions were weekdays, with male travelers dominating except in the Tianjin to Shijiazhuang direction. The departure type was consistently residential, while the arrival locations were mostly residential, except for Shijiazhuang, categorized as visiting. The main mode of travel from Beijing was the subway [67], while road travel was predominant from other cities, with road transport also used for arrivals. Travelers between Beijing and Tianjin were primarily aged 25 to 29, while those between Beijing and Shijiazhuang were mainly aged 30 to 34, and travelers between Tianjin and Shijiazhuang were mostly aged 19 to 24. The age differences reflect distinct intercity dynamics, with the commuting population dominating Beijing-Tianjin travel, business individuals prevailing in Beijing-Shijiazhuang travel, and students characterizing Tianjin-Shijiazhuang travel. For directions other than Beijing to Shijiazhuang, travel times predominantly occurred in the morning. The distinct travel times reflect its longer distance and diversified travel purposes apart from short commutes. Due to the large urban scale of Beijing, the travel distance within Beijing is typically between 5 and 10 km, while travel distances within Tianjin and Shijiazhuang are generally under 5 km. Regarding waiting \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Tianjin–Shijiazhuang** & **Shijiazhuang–Tianjin** \\ \cline{2-5}  & **May 2019** & **May 2021** & **May 2019** & **May 2021** \\ \hline Weekday & 3 & 3 & 3 & 3 \\ Gender & 2 & 1 & 1 & 1 \\ Type-O & 1 & 1 & 1 & 1 \\ Mode-O & 1 & 1 & 1 & 1 \\ Mode-D & 1 & 1 & 1 & 1 \\ Type-D & 0 & 1 & 1 & 1 \\ Age & 5 & 5 & 5 & 5 \\ MOT-O & 8 & 7 & 10 & 11 \\ Ds-O & 1 & 1 & 1 & 1 \\ Wt-O & 9 & 7 & 11 & 11 \\ Wt-D & 6 & 8 & 7 & 6 \\ Ds-D & 1 & 1 & 1 & 1 \\ Percentage & 47.6\% & 60.98\% & 67.9\% & 57.14\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Tianjin–Shijiazhuang direction in different years accounted for the most trip chain characteristics. times at departure hubs, the Beijing to Tianjin direction had the shortest waiting time, under 30 min, while the Shijiazhuang to Tianjin direction had the longest waiting time of 50-55 min. On the one hand, compared to using road transportation for travel, using the subway could more accurately control passengers' travel time [68]. This was because the schedules of subway trains were fixed, while the schedules of buses were random, depending on the possible congestion of roads [69]. Beijing had a subway system with a mileage of 699.5 km while Shijiazhuang's subway mileage was 30.3 km in 2019. Therefore, most travelers in Shijiazhuang had to choose road transportation. Travelers were more likely to allocate sufficient time for travel in order to avoid missing the train, resulting in excessively long waiting times at the station. On the other hand, there are more than 400 direct high-speed trains running every 10 min, daily between Beijing South station and Tianjin station. Therefore, it was as convenient for passengers to take the high-speed rail as to take the subway. Travelers could leave soon after arriving at the station. The waiting times at departure hubs of Tianjin to Beijing direction were 5 min more than the opposite direction. This was because Beijing had a more developed subway system than Tianjin. In 2019, the operating mileage of the Beijing subway was 699.5 km and that of the Tianjin subway was 235 km. Although Tianjin had a shorter subway mileage than Beijing, it was still better than Shijiazhuang.