# Effective Bus Travel Time Prediction System of Multiple Routes: Introducing PMLNet Based on MDARNN
## 4 Results and Discussion
### Contrast Experiments  
To assess the effectiveness of our proposed model-PMLNet, we have selected seven alternative methods for comparison; among them, Historical Average (HA), Support Vector Regression (SVR), Partitioning and Combination Framework Linear Regression (PCF-LR) are existing methods, while PCF-unweight, PCF-LSTM, PCF-DARNN, and MDARNN are ablation experiments. HA: This method uses historical travel records as the basic data, and calculates the present travel time as the predicted value by taking the average of historical records [23]. SVR (Support Vector Regression): SVR is employed for predicting total bus travel time, following the methodology outlined in literature [29]. PCF-unweight: The current travel time is derived directly from the sum of the outputs of all four sub-modules without real-time traffic flow impact factor weighting, as shown in Equation (24)  
\[T=t_{CDSTT}+t_{TPWT}+\sum_{k=0}^{p}(t_{BSDT}(k)+t_{SSTT}(k,k+1)) \tag{24}\]  
PCF-LSTM: The method predicts all four time periods by utilizing LSTM, with four real-time traffic impact factors being employed for calibration. PCF-DARNN: Instead of MDARNN, this method employs DA-RNN to predict Stop-to-Stop Travel Time and Bus Stop Dwelling Time. The total predicted travel time is weighted and summed by four real-time traffic impact factors. Pure MDARNN: This approach utilizes the MDARNN model introduced in this work for predicting bus travel time without using the partitioning and combination framework. The model's predictions are then calibrated using traffic factors as Equation (25), where \(t^{q}\) represents the travel time of \(q\)th bus on the route predicted by the MDARNN model in the first 30 min, and \(\tilde{t^{q}}\) represents the true travel time of the \(q\)th bus on the route in the first 30 min. \[\alpha=1+\frac{1}{n}\sum_{q=1}^{n}\frac{(\tilde{t^{q}}-t^{q})}{t^{q}} \tag{25}\]  
PCF-LR: PCF-LR combines the historical average method for predicting Transfer Point Waiting Time and constructs an LSTM model for travel time prediction. The total travel time is then obtained using linear regression. This method is employed for Bus Arrival Time prediction in [9]. Figure 11: The error of various transfer points. In this study, four bus routes are considered; the results of the performance comparison are presented in Table 10. All experiments were conducted under the same environment and using the same dataset as processed in this paper as shown in Table 6.  
PMLNet outperforms other models on all routes, confirming the effectiveness of the parallel prediction framework. Notably, MAPE slightly decreases as route distance increases (Route 4 is the shortest). This is because bus travel time depends on travel status, real-time traffic congestion, stop dwelling time, and transfer waiting time. When the bus routes are shorter, the road sections are shorter, the number of bus stops is fewer, and the predicted congestion status, travel time between stops, stopping time at stops, and waiting time at transfer point will have large differences. However, the predicted values of the four sub-modules tend to stabilize as the travel distance increases, resulting in better prediction accuracy. In contrast, longer bus routes tend to have larger MAE, because the longer bus route has a greater average travel time, and the MAE accumulates as the travel time increases. In this reason, Route 4, with the shortest travel distance, has a higher MAPE value and a lower MEA value than other routes. Figure 12 shows the MAE and MAPE for the four models on different routes. The MAE and MAPE of PCF-DARNN are higher than those of PMLNet, suggesting that MDARN is more suitable than DARNN for bus travel time prediction by considering macro impact factors. Pure MDARN does not perform well in both MAE and MAPE compared to models that use division and combination framework, possibly due to the framework's design of different neural networks based on the characteristics of the four travel time parts.