## 4 Pre-Evaluation Based on the Spatio-Temporal Model
### Passenger Path Selection Model
#### 4.4.1 Analysis of Influencing Factors  
Analysis of Passengers' Attributes  
Passenger demographics and behavior significantly affect route selection. For example, by analyzing composition of Bus Passenger Travel in Guangzhou, as shown in Figure 5, we found that the elderly, disabled, and other passenger groups who enjoy high discounts have lower time sensitivity, and the proportion who choose transfer routes is close to or exceeds 20%. In contrast, the working group and student group prioritize timeliness, with less than 10% opting for transfer routes. In addition, the ratio of trips with transfers during off-peak periods slightly increases by two percentage points. These findings underscore the impact of passenger attributes, including travel time, on route selection. Analysis of Passenger Travel Habits  
By tracking the frequency of trips on the same OD pair over a week, the most popular route for each passenger can be identified. The proportion of the most popular bus routes in the same OD travel is shown in Figure 6. From that, one can see that bus passengers tended to take a fixed route, with stronger preferences as trip frequency decreased. When the weekly travel frequency of the same OD is three times, the proportion of passengers who choose the same route is close to 90%. As the weekly travel frequency increases, this preference gradually decreases, but overall, it exceeds 50%. This indicates that passengers generally prefer familiar paths when selecting a route. Analysis of the Impact on Travel Efficiency  
Several direct factors influence route choice, including 'travel time, walking time, and waiting time'. By integrating data on passenger's travel OD (see Section 4.2) and accessible paths (see Section 4.3), the relative importance of each factor in passengers' path selection can be analyzed. The direct efficiency function is shown in Formula (1) below:  
\[E=T_{route}+T_{wait}+T_{walk} \tag{1}\]  
Figure 5: Composition of bus passenger travel in Guangzhou. Figure 6: The proportion of the most popular bus routes in the same OD travel (Guangzhou). in this formula \(E\)--is the efficiency. \(T_{route}\)--represents the travel time, \(T_{wait}\)--represents the waiting time, and \(T_{walk}\)--represents walking time (including walking to/from the stops and during transfers). Alternative Path Impact Analysis  
Ideally, passengers would choose the optimal travel route, but given that they are often limited by incomplete access to information, differences in personal habits, and other factors, the path choices of passengers for transfer travelers, in particular, are not entirely rational and feature noticeable diversity. For example, [PERSON] [26] found that the total time difference factors have the most significant impact on passenger path selection, while [PERSON] [27] found that bus passenger path decisions are influenced by both selfishness and rationality. For all possible paths on a given OD pair, the efficiency \(E\) is calculated for each path and compared to the optimal path. The path selection distribution is shown below in Figure 7, which indicates that the majority of passengers prefer the 'optimal path', whether for direct travel or transfer travel, with proportions reaching 65% and 50%, respectively. As \(E\) increases, the likelihood of selection decreases, though the probability remains non-zero. Meanwhile, the distribution curve of different travel periods, such as peak and off-peak, basically coincides. In the case of transfers, passengers are less likely to take the 'optimal' path than they are for direct travel. This is mainly due to factors such as the integrity of information acquisition. According to the curve in Figure 7 and the relationship between the path selection probability R and the 'optimal path efficiency ratio' of direct and one-time transfer paths, Formulas (2) and (3) are developed as shown:  
\[R=\left\{ \begin{array}{ll}0.65&t^{\prime}=1\\ 0.012\times t^{\prime-3.868}&t^{\prime}>1\\ t^{\prime}=\frac{C}{c_{\min}}&\end{array} \right. \tag{2}\]  
\[R=\left\{