# A Spatio-Temporal Schedule-Based Neural Network for Urban Taxi Waiting Time Prediction
## 4 Results and Discussion
### Experiment Analysis and Discussion
#### 4.2.4 The Comparison of Prediction Results with Different Related Models  
The algorithm model proposed in this paper is compared with the original unsolved three-layer BP neural network algorithm model mentioned in a related work widely applied [39], and to an algorithm based on empirical distribution prediction waiting time [16]. Hereafter, denoted as SF1, SF2 and SF3, respectively. The SF3 algorithm predicts ride-hailing probability and waiting time based on the empirical distribution of historical data, and updates the model based on incremental learning. The initial estimate of the waiting time in a known time granularity unit is the mean value of the waiting time at the relevant time and place. For the new time granularity, the optimized waiting time prediction value is:  
\[P_{i,j,d}^{new}=\frac{\rho\times\hat{P}_{i,j,d}^{new}\times b+(1-\rho)\times P _{i,j,d}^{old}}{\rho\times b+(1-\rho)} \tag{4}\]  
where \(\hat{P}_{i,j,d}^{new}\) is the initial estimated value of the waiting time in the new time granularity unit; \(P_{i,j,d}^{old}\) is the optimized waiting time predicted value in the original data when no new data is added. \(b\) is the number of time granularities contained in the original data. The volatilization coefficient \(\rho\) is used to measure the importance of existing data and new data in the forecasting process. Figure 10: Prediction effect of different weather features. In SF3, the feature point-location set and feature-time set are selected. The feature points are used to replace the adjacent data in GPS historical data (GPS historical data is transformed into a large number of feature point historical data). The waiting time of a feature space-time point is equal to the average of the data replaced by it in the original data. Therefore, the waiting time of each feature space-time point is calculated. A mapping model composed of the feature points and its waiting time is constructed. Then, the waiting time at a certain time and place can be predicted as the average of the waiting time of its adjacent characteristic time instants and space points. When the model needs to be updated due to new data, the waiting time of the feature-time-space points of the new data is calculated through the above process. Combining with t calculated from the old data. The new model is obtained according to the formula, where B is the number of feature points. In order to enrich the feasibility of the experimental results, the experimental data is unified into 6,705,086 data with an accuracy rate added as one of the evaluation indicators. \[acc=\frac{\left|w_{t}-w_{p}\right|}{w_{t}}\times 100\% \tag{5}\]  
where \(w_{t}\) represents the true value, \(w_{p}\) denotes the model forecast value, and acc represents the accuracy of the model prediction results. The MAE value and accuracy of the respective SF1, SF2 and SFF2 algorithm models are shown in Figure 11.  
As shown in Figure 11, the experimental results exhibited by our optimized neural network SF1 give a MAE value of 58.7 and an accuracy rate of 92.4%. In contrast, the original unsolved three-layer BP neural network algorithm model, namely SF2, gives a MAE value of 112.3 and an accuracy of 58.3%, and finally, the model SF3 gives a MAE value of 76.6%, with an accuracy rate of 68.6%. Compared to the basic BP network, the approach developed in this paper considers additional time and space constraints, thus explicitly modeling taxi waiting time patterns, so the final accuracy rate is higher. As for SF3, although the trajectory of urban taxis reflects a certain trend, its randomness is still  
Figure 11: Experimental result graphs of different algorithm models. very large for some locations. The neural network that integrates multi-source data and is constrained by temporal and spatial rules and then can better model taxi waiting rules in every corner of the city.