## 4 Results and Discussion  
### Peak Period Experiments  
The training dataset used was extracted from 8 October 2015 to 25 October 2015. The test dataset is from 26 October 2015 to 30 October 2015. The two lines are 685 and 56008. Line 56008 has a large passenger volume because it is a major bus line on the third ring road in Beijing. Line 685 is a normal line that has a relatively small passenger volume. If the passenger numbers of the two lines are very large, the departure frequency will be relatively high; thus, we do not need to consider the transfer situation. If the passenger numbers of both lines are small, the number of passengers who need to transfer between lines will be much smaller, so there is little need to consider the transfer coordination. Therefore, after calculation, we chose these two lines as our experimental lines. These two lines can be transferred at Fangzhuangqiaoxi bus station. With a Windows 10 operating system, a I7-8700k processor, and 32 GB memory, the PFP-XPOI model takes 20 min to finish the process of determining the station query radius totally, and the process is executed only once after the general rule is obtained. In the process of passenger flow prediction, the total time for training a single-route passenger flow prediction model is 4 min, while training a single-route CART model and a model such as SVM takes about 8 min, and the recurrent neural network (RNN) method with seven steps takes about 6 h.  
The root mean square error (RMSE) was selected to evaluate the model. The RMSE can be calculated by Equation (11). \[\text{RMSE}=\sqrt{\frac{1}{M}\sum_{m=1}^{M}\lvert y_{m}-\hat{y}_{m}\rvert^{2}} \tag{11}\]  
where \(M\) is the total number of samples. \(y_{m}\) is the true value, and \(\hat{y}_{m}\) is the predicted value. For line 56008, the optimal parameters of the predicted model are as follows. The maximum tree depth is four layers. The learning rate is 0.02. The maximum tree size is 1500, and the optimal distance is 300 m. For line 685, the optimal parameters of the model are as follows. The maximum tree depth is three layers. The learning rate is 0.01. The maximum size of the tree is 800, and the optimal distance is 300 m. The evaluation of the prediction model for lines 56008 and 685 under different distances is shown in Figure 2.  
For line 56008, the figure reflects that the RMSE value of the test set reaches the minimum at a distance of 300 m, namely where the error of the prediction model is the smallest, about 7.7. When the distance is 500 and 100 m, the RMSE is lager. Similarly, for line 685, the minimum of RSME value is also found at a distance of 300 m, about 4.9. However, the effect of different distances on the accuracy of the model in line 685 is smaller than that in line 56008. The results suggest that grouping the data by lines and training one model for each line can reduce the interference between different lines and effectively reduce the prediction error. We divided the early peak period into four sections with an interval of 30 min. Taking samples on 28 October 2015 as an example, the predicted values and true values of on-board and alighting passenger numbers of line 56008 are shown in Figures 3 and 4, respectively. Figure 2: The RMSE and distance of passenger number prediction model in lines 56008 and 685. The number of passengers boarding from 7:00 to 8:00 on line 56008 was significantly greater than that from 8:00 to 9:00. There were two main boarding stations for line 56008, namely stations 6 and 16. The peak boarding passenger flow on line 56008 was about 230. Compared with on-board passengers, the distribution of alighting passengers between 7:00 to 8:00 and 8:00 to 9:00 was more balanced, and the total number of alighting passengers was not obviously different between the two periods. However, from 7:00 to 8:00, the stations where passengers alighted were more concentrated. Stations 8 and 22 were the two main drop-off stations of line 56008. The peak alighting flow of line 56008 was about 240.