## 3 Results and Analysis
### The Trip Level
#### 3.1.2 The Trip Durations  
The duration of each trip was analyzed from various perspectives. Figure 10 shows a scatter plot of all trip durations, revealing that trip durations vary significantly, with the majority falling within approximately 50 min. Long-term trips may occur under specific circumstances, and in extreme cases, trip durations can be quite long (e.g., around 1400 min). However, such instances are rare in daily human intra-urban mobility. To further explore the statistical distribution of trip durations, we plotted a histogram showing the relationship between trip durations and the corresponding number of trips. As seen in Figure 10, although extremely long trip durations exist in the datasets, they are rare in reality. To provide a more accurate statistical analysis, we considered these extremely long trip durations as outliers and excluded them when plotting the histogram. Specifically, we treated the top 0.1% of the longest trip durations as outliers after analyzing the dataset. After removing these outliers, the maximum trip duration is 190 min. The corresponding histogram is shown in Figure 11. From Figure 11, we can observe that trips lasting 7 min accounted for the largest proportion, followed closely by trips lasting 6 min and 8 min. This suggests that the peak bike-sharing travel time for intra-urban human mobility is between 6 and 8 min. Additionally, the distribution of trip durations clearly follows the \"long tail\" theory, meaning that small values make up the majority, while very large values account for only a small percentage. Figure 10: The scatter plot of all trip durations. Figure 9: The CTM diagram with the largest trip numbers during all time intervals: (**a**) origin and (**b**) destination. To clarify the results, we classified the trip durations into 5-min intervals, resulting in 38 distinct intervals. The frequency of each 5-min interval is visualized in the histogram shown in Figure 12. From Figure 12, we can observe that trip durations between 6 and 10 min accounted for the largest proportion (over 30%), followed by durations between 10 and 15 min (approximately 20%) and durations between 0 and 5 min (around 15%). This indicates that the majority of trips lasted within 15 min, suggesting that most people prefer to use bikes for intra-urban mobility when the travel time is within this range. For trips lasting longer than 15 min, many people might opt for other forms of transportation, such as cars, buses, or metros. In addition, the cumulative frequency of the 5-min interval is plotted in Figure 13. From Figure 13, we can see that trips lasting within 15 min made up about 65% of all trip durations. Approximately 90% of all trips were completed within 30 min and around 95% within 60 min. This reflects a distinctive characteristic of intra-urban human mobility facilitated by bike-sharing systems. The statistical distribution of trip durations and corresponding number of trips for each day and each hour (both origin and destination) was explored as well, which is shown in Figure 14. From Figure 14, it is evident that the distribution of trip durations and corresponding trip numbers is quite consistent across each day and each hour. Additionally, this distribution is similar to what is observed in Figure 11. This indicates that trip durations  
Figure 11: The distribution of trip durations and corresponding trip numbers. Figure 12: The histogram of all the 5 min time intervals and their corresponding frequencies. Figure 13: The histogram of the 5 min time intervals and their corresponding cumulative frequencies. generally follow the \"long tail\" theory, whether examined by hour, by day, or over the entire 28-day period, even though the number of trips varies by hour and day. This interesting finding can be considered \"common sense\" and provides valuable insights into intra-urban human mobility patterns when using bike-sharing transportation systems.