## 4 Simulation Results and Discussion
### Analysis and Discussion of Simulation Results  
The scheduled waiting times according to the three types of train operation frequency are analyzed, assuming that all the intermediate stations of the considered railroad tracks (Stations 2-6) have a subsidiary track. Figures 7-9 are represented for the schduled waiting time, the frequency of overtaking station and number of train schedules for overtaking in Case 1. In Case 1, the scheduled waiting time of 10 min showed the highest frequency of 30 times in 100 simulations. In all the analyzed train schedules, the passenger train and high-speed train overtook the freight train and overtaking occurred 87 times at Intermediate Station 3, 67 times at Intermediate Station 2, and 18 times at intermediate station 5. Intermediate stations 2 and 3 required subsidiary tracks because overtaking occurred at these stations in 50 of the total 100 time schedules. Figures 10-12 are represented for the schduled waiting time, the frequency of overtaking station and number of train scheules for overtaking in Case 2. In Case 2, the scheduled waiting time of 11 min showed the highest frequency of 27 times in 100 simulations. In all the analyzed train schedules, the passenger train and high-speed train overtook the freight train as in Case 1, and the overtaking occurred 86 times at Intermediate Station 3, 73 times at Intermediate Station 2, and 40 times at Intermediate Station 5. This shows that the number of passenger and high-speed trains overtaking the freight train at Intermediate Stations 2 and 5 is larger than in Case 1. This is because the number of passenger trains is larger and the number of freight trains is smaller than those in Case 1, resulting in more passenger trains overtaking the freight trains. Intermediate Stations 2, 3, and 5 required subsidiary tracks because overtaking occurred at Intermediate Stations 2 and 3 in 38 time schedules and Intermediate Stations 2, 3, and 5 in 19 time schedules out of the 100 analyzed time schedules. The number of train schedules in which overtaking occurred only at Intermediate Station 3 was 16. Figures 13-15 are represented for the schduled waiting time, the frequency of overtaking station and number of train schedules for overtaking in Case 3. In Case 3, the scheduled waiting time of 19 min showed the highest frequency of 20 times in 100 simulations, followed by the scheduled waiting times of 21 and 22 min with 15 times. In all the analyzed train schedules, the passenger train and high-speed train overtook the freight train, as in Cases 1 and 2. Overtaking occurred in all simulations at Intermediate Station 3, and 94 times at Intermediate Station 2. The overtaking frequency increased because, even though the operation frequency of passenger trains is small in Case 3, the two trains with high-speed differences, the high-speed train, and freight train, were operated 6 and 9 times, respectively. Out of the 100 analyzed train schedules, overtaking occurred at Intermediate Stations 2, 3, and 5 in 44 time schedules and at Intermediate Stations 2 and 3 in 25 time schedules. Figure 11: Frequency of Overtaking Station for Case 2. Figure 12: Overtaking Station for Case 2. Figure 13: Analyzed Scheduled Waiting Time for Case 3. Figures 16-18 are represented for the schduled waiting time, the frequency of overtaking station and number of train scheules for overtaking in Case 4. In Case 4, the scheduled waiting time of 13 min showed the highest frequency of 38 times in 100 simulations. The passenger train and freight train were overtaken by the high-speed train in 99 time schedules, except for 1 train schedule. This is because the operation frequencies of the high-speed train and passenger train are 6 and 9, respectively, and the freight trains are overtaken by a passenger train and high-speed train. Overtaking occurred 95 times at Intermediate Station 3, and 72 times at Intermediate Station 2.