# Effective Bus Travel Time Prediction System of Multiple Routes: Introducing PMLNet Based on MDARNN
## 2 Related Work
### Prediction Model Construction  
Constructing an appropriate model is crucial for ensuring a high QoS of PT. Previous studies have developed prediction models that can be roughly categorized into two types: traditional models and machine learning-based models.  
Over the last few decades, traditional models like historical average and the Kalman Filter have been extensively employed in the field. In the early years, historical average was a naive algorithm used to build bus travel time prediction models [23]. However, the historical average method heavily relies on historical data, ignores real-time traffic factors, and leads to prediction errors. Another traditional method is the Kalman Filter. One study [24] initially used the Kalman Filter to predict Bus Arrival Time by combining historical data and GPS data. Based on the historical average method, another study [25] employed the Kalman Filter to enhance the precision of predicting arrival time for each subsequent stop and construct a dynamic Bus Arrival Time prediction model. However, the Kalman Filter also has some disadvantages, as it is sensitive to anomalies, which prevents it from adapting to prediction tasks with large variability datasets, such as multi-route bus travel time prediction [26].  
Machine learning has undergone rapid advancements in recent years and has demonstrated strong performance in Bus Arrival Time prediction. Classic regressions, such as linear regression, were widely employed in the travel time prediction of vehicles [27; 28]. Nevertheless, the model is not applicable to non-linear prediction tasks. In [14], a Support Vector Regression (SVR) model was applied to predict Bus Arrival Time since the model has a greater generalization capacity. One study [29] combined a Support Vector Machine (SVM) and the GPS real-time forecast to build a hybrid Bus Arrival Time prediction model. Neural network has also been widely utilized in bus travel time prediction. Another study [30] proposed a segmentation prediction model, which employed a back propagation (BP) neural network model to predict the divided bus driving time by K-means clustering algorithm.  
The process of predicting travel time hinges on time series considerations. In order to achieve satisfactory forecasting results, RNN was incorporated to predict Bus Arrival Time as it is well-suited to address time series problems [11; 31]. In one study [31], the authors employed both the LSTM and historical average method to predict Transfer Point Waiting Time and travel time for each distinct path segment. One study [32] constructed meta-based spatiotemporal networks to model diverse dependencies for single-line Bus Arrival Time prediction. Furthermore, ref. [33] used Multi-Relational Modeling Graph Convolution (MRMGCN) as a frontend module to capture spatial relationships in multi-route areas, which combines with time series models for Bus Arrival Time prediction. In contrast, PMLNet is designed for multi-route scenarios, which incorporates bus times prediction and real-time traffic calibration. This approach, which excels in handling transfers and navigating complex urban networks, demonstrates superior performance in such contexts. However, the entire trip is roundly segmented into two parts: the travel time of bus driving and the waiting time at transfer point, without considering real-time traffic conditions. Furthermore, one study [12] proposed a dual-stage attention-based recurrent neural network (DA-RNN), which obtained a noteworthy enhancement of the time series prediction. Although attention-based mechanisms perform well, they suffer from information loss and require large resources. Therefore, in this paper, we propose a partition and combination framework PMLNet, which combines MDARNN, improved based on DA-RNN, and traditional LSTM to predict the divided bus travel time, while also incorporating four real-time traffic flow factors for correction and combination.