## 6 Numerical Example
### Results Analysis
#### 6.3.2 Solution Results Analysis  
Based on the schedule-based network, the valid path set is obtained by the \(K\)-shortest search algorithm. The passenger assignment result of each train in different sections is  
\begin{table}
\begin{tabular}{c c c} \hline
**Symbol** & **Definition** & **Value** \\ \hline \(\delta_{1}^{a}\),\(\delta_{2}^{a}\) & Coefficient of state train BPR function. & 0.1, 3.0 \\ \hline \(\delta_{1}^{s}\),\(\delta_{2}^{s}\) & Coefficient of suburban train BPR function. & 0.15, 3.0 \\ \hline \(\alpha_{1}\) & Sensitivity of passengers to transfer time. & 1.7 \\ \hline \(\alpha_{2}\) & Penalty coefficient of transfer times. & 0.2 \\ \hline \(p_{1}\) & State railway fare per kilometer. & 0.5 (CNY/km) \\ \hline \(p_{2}\) & Suburban railway fare per kilometer. & 0.25 (CNY/km) \\ \hline \(\lambda\) & Passenger hourly wage. & 60 (CNY/h) \\ \hline \(cp_{1}\) & The capacity of the state railway train. & 1000 (persons) \\ \hline \(cp_{2}\) & The capacity of the suburban railway train. & 2062 (persons) \\ \hline \(Z_{1}\) & The number of seats on the state train. & 518 (persons) \\ \hline \(Z_{2}\) & The number of seats on the suburban train. & 256 (persons) \\ \hline \(N\) & The number of state railway trains arriving at the state railway hub station in & 10 \\  & one research cycle. & 5 (min) \\ \hline \(T_{h}\) & The transfer time for passengers transfer from the state railway platform to & 5 (min) \\  & suburban railway platform at hub station. & 3 \\ \hline \(k\) & Number of valid paths between each O–D pair. & 1 \\ \hline \(\theta\) & Passenger familiarity with network information. & 1 \\ \hline \end{tabular}
\end{table}
Table 5: Parameters used in this paper.  
Figure 9: The convergence of solution approach. (**a**) PSL–SUE model. (**b**) MNL–SUE model.  
No. 3 and No. 8. The largest number of sections with different load rate distribution is 11, and the range of load rate is 40% to 50%. By analyzing the load rate of different trains, it can be seen that the load rates of train No. 1, 2, 4, 5, and 8 are relatively high. The higher load rates of train No. 1, 2, and 5 are due to the large interval from the front train, resulting in many waiting passengers. Train No. 4 is an express train with a higher speed and lower travel time cost, and the probability of waiting passengers choosing this train is higher than other trains. Train No. 8 is a state train with fewer stop stations and is more comfortable. The passengers whose destination is station No. 8, 9, 10, and 11 tend to choose this train.  
Comparing the results of PSL-SUE and MNL-SUE models, there is no obvious difference, but it can still be found that some trains are assigned more passengers in some sections than the MNL-SUE model, mainly because fewer travel paths involve these trains and sections. And the paths with a larger of the PSL-SUE model are assigned more passengers than the paths of the MNL-SUE model, and the paths with a smaller of the PSL-SUE model are assigned fewer passengers than the paths of the MNL-SUE model. Because the path selection probability of the PSL-SUE model is based on the generalized cost and considers the path length, it can be found that the PSL-SUE model can deal the path overlapping problem and can eliminate the IIA property.