## 3 Results and Analysis
### The Bike Level  
Although analyzing bike-sharing trips at the trip level provides various insights into intra-urban human mobility characteristics, it is still insufficient for thoroughly characterizing the temporal patterns of such mobility. Hence, to gain a more detailed understanding, it is essential to conduct exploratory analysis at other levels, such as the bike level and the user level. This section focuses on the exploratory analysis of bike-sharing trips at the bike level. Based on the dataset used in this paper, 68,541 bikes are included. A key metric for assessing bikes is the number of utilizations. Therefore, this section primarily focuses on analyzing bike utilizations. First, a scatter plot showing the number of utilizations per day for each bike is presented in Figure 18. In this figure, the horizontal axis corresponds to the bike ID, and the vertical axis represents the number of utilizations. According to Figure 18, the number of utilizations generally ranges from 1 to 11. Among these, the overwhelming majority of bikes have five or fewer utilizations. To quantify this, all the number of utilizations, the occurrences of each number, the frequency of each number, and the cumulative frequency of each number are calculated, respectively. The corresponding results are listed in Table 1, which reveals that nearly 80% of the bikes had one utilization, approximately 15% had two utilizations, and nearly 99.9% had five or fewer utilizations. The histogram between the number of utilizations and the corresponding number of occurrences is shown in Figure 19, which also demonstrates a \"long tail\" distribution. These findings indicate that the majority of bikes used for intra-urban human mobility are utilized five times or fewer. This information could be valuable for bike-sharing companies in optimizing maintenance schedules and resource allocation based on bike utilization. Figure 17: The CTM diagrams of the days with the longest average trip durations in August: (**a**) origin and (**b**) destination. To further evaluate the performance of bike-sharing systems for potential maintenance and improvement, we analyzed the total service duration for each bike and made statistics for the occurrences of each total service duration among all the bikes. The results are shown in Figure 20. According to Figure 20, we can conclude that bikes with a total service duration of approximately 10 min constitute the largest proportion among all the bikes. Additionally, a significant majority of bikes had a total service duration of around 60 min or less, reflecting the temporal patterns of human mobility within urban areas. To clearly illustrate the distribution of the total service durations and the percentages of occurrences among all the bikes, we compiled statistics comparing the total service durations (in 5 min intervals) and the corresponding cumulative frequency, as listed in Table 2. According to Table 2, more than 50% of the bikes had a total service duration of 15 min or less. Approximately 80% of the bikes had a total service duration within 30 min, around 90% within 45 min, and about 95% within 60 min. Only around 5% of the bikes had a total service duration exceeding 60 min, despite a relatively large number of occurrences for durations over 60 min. The temporal patterns of intra-urban human mobility, characterized by the total service durations of the bikes, provide potentially valuable insights for related departments or companies to enhance operational strategies of bike-sharing systems. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number of Utilizations** & **Number of Occurrences** & **Frequency** & **Cumulative Frequency** \\ \hline
1 & 54,511 & 0.79530 & 0.79530 \\
2 & 10,571 & 0.15423 & 0.94953 \\
3 & 2482 & 0.03621 & 0.98575 \\
4 & 654 & 0.00954 & 0.99529 \\
5 & 233 & 0.00340 & 0.99869 \\
6 & 59 & 0.00086 & 0.99955 \\
7 & 24 & 0.00035 & 0.99990 \\
8 & 5 & 0.00007 & 0.99997 \\
9 & 1 & 0.00001 & 0.99999 \\
11 & 1 & 0.00001 & 1.00000 \\ \hline \hline \end{tabular}
\end{table}