## 6 Numerical Example
### Sensitivity Analysis
#### 6.4.3 Passenger Hourly Wage \(\lambda\)  
The hourly wage is equivalent to the weight of the travel path's time cost. The higher the hourly wage, the larger the proportion of time cost in the generalized cost, the greater the impact of travel time on path choice.  
1. Passengers on the state train  
Figure 15 shows the changes of passengers on the state train (No. 8) in different sections under the conditions of different hourly wages and \(\theta\) values. The passenger assignment results in Figure 15b are less than those in Figure 15a.  
Overall, passengers on the state train become progressively larger as the hourly wage increases. When the hourly wage reaches \(80\)\(\mathrm{CNY/h}\), the passengers on the state train reach the train capacity in the section between station No. 5 and No. 8 and stabilizes at \(180\) persons in the section between station No. 8 and No. 11. When \(\theta=0.1\), the polyline is flatter and does not fluctuate much because of the low passenger perception coefficient and the balanced assignment of passengers among the paths. For the other values of \(\theta\), the corresponding results do not differ much. Nevertheless, we can still find some details after observation. The larger \(\theta\) is, the more slightly passengers will be assigned.  
Figure 14: Sensitivity analysis of state railway fares to state train choice probability of suburban passengers at station No. 8 (Current train No. 8: State).  
Figure 13: Sensitivity analysis of state railway fares to state train choice probability of suburban passengers at station No. 5. (**a**) Current train No. 7 (Local). (**b**) Current train No. 8 (State).  
2. State train choice probability  
The impact on the probability that passengers choose the state train caused by hourly wage is shown in Figures 16 and 17. As can be seen from the two figures, as the hourly wage increases, the choice probability of state train increases gradually. Meanwhile, the probability of Figure 16b is higher than that of Figure 16a because the additional waiting time will be added when the current arriving train is train No. 7.  
Figure 16: Sensitivity analysis of hourly wages to state train choice probability of suburban passengers at station No. 5. (**a**) Current train No. 7 (Local). (**b**) Current train No. 8 (State).  
Figure 17: Sensitivity analysis of hourly wages to state train choice probability of suburban passengers at station No. 8 (Current train No. 8: State).  
Figure 15: Sensitivity analysis of hourly wages to state train passengers. (**a**) Section between st.5 and st.8. (**b**) Section between st.8 and st.11.  
In the schedule-based network, the state train No. 8 can overtake the local train No. 7 at station No. 7. Thus, in Figure 16a, although passengers who desire to take the state train need additional waiting time, the passengers whose destination is station No. 8 and No. 11 can arrive at their destination before passengers who take train No. 7. At this time, there is a judgment between the time cost and fare cost. When the hourly wage is greater than 50 CNY/h, the greater \(\theta\), and the greater the probability of choosing the state train and vice versa. When the hourly wage is less than 50 CNY/h, the time cost becomes immaterial. The higher \(\theta\), the more sensitive passengers are to the state railway's high fares and the lower the probability of choosing the state train.  
As also can be seen in Figures 16b and 17, when the current arriving train is the state train, there is no extra waiting time, regardless of the hourly wage, and the time cost saved by state train is higher than the fare cost increment. The choice probability of state train gradually increases with the higher hourly wage, and the larger \(\theta\) is, the greater the choice probability is.