## 5 Computational Experiments  
### Experiment Description  
As shown in Figure 7, the basic data of the two lines (Line A and Line B, for short) are from reference [38], and the lines are the planned lines of Chongqing Rail Transit in China, including the corresponding train organization scheme [38]. Line A has 15 stations numbered A1 to A15. Line B has 11 stations numbered B1 to B11. Stations A5 and B3 have the conditions for cross-line operation. We assume that at 09:40, stations A3 and A4  
Figure 6: Solution process of dynamic adjustment approach. detect a large passenger flow for Line B, the main direction of the large passenger flow on Line B is B1 to B11. To ensure the operational safety of stations A3 and A4, as well as interchange station A5 or B3, and improve the quality of passenger service, it has been decided to temporarily add a cross-line service. The initial station of the cross-line backup train is A3, and the train passes the cross-line track before station A5 (i.e., the routing of the train is A3, A4, B3, B4, \(\ldots\), and B11). For parameters, we set the values of each parameter according to the parameter values in reference [38] and the problem background. Specifically, the planned intervals for Line A and Line B are 150 s and 180 s, respectively, the minimum tracking interval is 120 s, and the minimum departure-arrival interval is 90 s. Meanwhile, the planned dwelling time and minimum dwelling time (s) for stations A1 to A15 are {35, 30, 30, 30, 30, 30, 30, 30, 30, 35, 30, 30, 30, 30, 35} and {30, 25, 25, 25, 30, 25, 25, 25, 25, 25, 25, 30, 30, 25, 25, 25, 30], respectively. The planned running time and minimum running time (s) of the sections, are {150, 180, 153, 153, 117, 162, 180, 198, 135, 240, 162, 180, 198} and {120, 144, 122, 122, 93, 93, 129, 144, 158, 108, 192, 129, 144, 158}, respectively. The planned dwelling time and minimum dwelling time (s) for stations B1 to B11 are {35, 30, 35, 30, 30, 30, 30, 35, 35, 30, 30, 35, 30, 35] and {30, 25, 30, 25, 25, 30, 25, 25, 30, 25, 25, 30, 25, 25, 30, respectively. The planned running time and minimum running time (s) for the sections are {207, 180, 162, 135, 108, 135, 162, 180, 198, 207} and {165, 144, 129, 108, 86, 108, 129, 144, 158, 165}, respectively [38]. The matrix of destination rate for the passenger flow on Line A is shown in Table 1. The data in the matrix is simulated data, which is used to verify the validity of the methods presented in this paper. In practice, the matrix can be calculated according to actual or predicted OD data in a certain direction [13]. For example, if 50 passengers get on trains in the direction at Station A13, 23 passengers go to Station A14, and 27 passengers go to Station A15 in a given period, the corresponding destination rates are 0.46 (i.e., 23/50) and 0.54 (i.e., 27/50). According to the utilization mode of the cross-line backup train, for the objective function of Model II, when analyzing the passenger flow data, it is only necessary to focus on the passenger flow on Line A. The dynamic arrival situation of the passenger  
Figure 7: Schematic of simulated lines. flow at the platforms of stations A1 to A4 is shown in Figure 8, and among passengers boarding at stations A1, A2, A3, and A4 and aligning at stations A5 (i.e., the cross-line service is not taking into account), the proportion of passengers transferring to Line B is 0.42, 0.46, 0.78 and 0.86, respectively. For simulation, Line A considers eight planned trains numbered Ta1 to Ta8, while Line B considers six planned trains numbered Tb1 to Tb8. The timetable of the first and last trains for the two lines is not adjusted, that is, the cross-line backup train is between them. The capacity of a train is set at 1320 people. The interval of the time unit for passenger flow calculation is taken as 60 s, and the larger number M is taken as 500,000. In addition, the version of the Gurobi solver is 9.1.0, and the computation termination condition is that the Gap is less than 0.1%.