## 4 Experiments and Results Analysis
### Performance Comparison of Different Deep Learning Models
#### 4.3.1 Establishment and Optimization of Shallow Learning Models  
The shallow learning models implemented in this study are based on the following mathematical formulations:  
Linear Regression: the objective function minimizes the sum of squared residuals:  
\[\underset{\hat{\boldsymbol{w}}}{min}\sum_{i=1}^{m}\left(y_{i}-\hat{ \boldsymbol{w}}^{T}\boldsymbol{x}_{i}\right)^{2} \tag{3}\]  
Ridge Regression: incorporates L2 regularization to prevent overfitting:  
\[\underset{\hat{\boldsymbol{w}}}{min}\sum_{i=1}^{m}\left(y_{i}-\hat{ \boldsymbol{w}}^{T}\boldsymbol{x}_{i}\right)^{2}+\lambda\|\hat{\boldsymbol{w} }\|_{2}^{2} \tag{4}\]  
LASSO Regression: employs L1 regularization for feature selection:  
\[\underset{\hat{\boldsymbol{w}}}{min}\sum_{i=1}^{m}\left(y_{i}-\hat{ \boldsymbol{w}}^{T}\boldsymbol{x}_{i}\right)^{2}+\lambda\|\hat{\boldsymbol{w} }\|_{1} \tag{5}\]  
where \(\boldsymbol{w}\) represents the model parameters, x_i and y_i are the input features and target values, respectively, m is the number of training samples, and \(\lambda>0\) is the regularization parameter.  
For linear regression models, we directly applied training data from various prediction scenarios for model training. Since linear regression models do not require hyperparameter optimization, we directly performed model calibration.  
For ridge regression and LASSO regression, we needed to determine the optimal learning rate \(\lambda\). We selected the most challenging prediction scenario (30 min sliding time window predicting 60 min future travel time) for hyperparameter optimization, testing five different values: \(\lambda=\) [0.1, 0.2, 0.5, 0.7, 1]. Results showed that models under different \(\lambda\) values were almost identical in parameters and fitting effects, so we chose \(\lambda=1\) for modeling all scenarios.  
For random forest models, we needed to optimize two hyperparameters: the number of sub-decision trees and minimum sample leaves. Based on preliminary experimental results, we determined the sub-decision tree number range as [50, 100, 200] and minimum sample leaves range as [1, 5, 10, 50], totaling 12 combinations. We determined optimal hyperparameters through a two-step grid search method:First test 4 combinations of sub-tree numbers [50; 100] with minimum sample leaves [1; 5];
2. Then test 4 combinations of sub-tree numbers [100; 200] with minimum sample leaves [10; 50].  
Finally, we determined that sub-tree number 200 and minimum sample leaves 50 was the optimal configuration, which was applied to all prediction scenarios.  
ARIMA models and support vector regression were also implemented, but practical application revealed that these two models have limitations in urban road travel time prediction. ARIMA models require data to be stationary or to achieve stationarity through differencing, while urban road travel time data often remain difficult to achieve stationarity even after multiple differencing operations. Support vector regression requires data normalization to the [0, 1] interval, while urban road travel time data contain numerous abrupt variations, making it difficult to handle potential future data fluctuations after normalization processing.