# Multi-Step Traffic Speed Prediction Based on Ensemble Learning on an Urban Road Network
## 5 Discussion
### Prediction Accuracy  
The MOE results of the proposed DDSELM and other four benchmark models are drawn in Figure 4 on southbound and northbound road links. Each subfigure shows one performance index of five prediction models under three scenarios with three kinds of prediction steps [1 h (60 min), 2 h (120 min), 3 h (180 min)] into the future. For the different \begin{table}
\begin{tabular}{c l} \hline \hline
**Representative Feature** & **Descriptions** \\ \hline \(\varepsilon_{(d,t+h)}^{\text{aff}}\) & Predicted speed difference between predicted speed and daily average value at time \(t+h\) belonging to the \(d\)th day \\ \(h\) & Prediction time step into the future, \(h\geq 1\) \\ \(\varepsilon_{(d,t)}^{\text{aff}}\) & Speed difference between measured speed and daily average value at time \(t\) belonging to the \(d\)th day \\ \(\varepsilon_{(d,t+1)}^{\text{aff}}\) & Speed difference between measured speed and daily average value at time \(t\) belonging to the \(d\)-1 th day \\ \(\varepsilon_{(d-2,t)}^{\text{aff}}\) & Speed difference between measured speed and daily average value at time \(t\) belonging to the \(d\)-2 th day \\ \(\varepsilon_{(d-3)}^{\text{aff}}\) & Speed difference between measured speed and daily average value at time \(t\) belonging to the \(d\)-3 th day \\ \(flow_{(d,t)}^{\text{aff}}\) & Flow difference between measured traffic flow and daily average value at time \(t\) belonging to the \(d\)th day \\ \(v_{(d,t)}^{\text{pref}}\) & Upstream speed difference between measured speed and daily average value at time \(t\) belonging to the \(d\)th day \\ \(v_{(d,t)}^{\text{handlef}}\) & Downstream speed difference between measured speed and daily average value at time \(t\) belonging to the \(d\)th day \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Input candidates of the proposed prediction model in this study. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Base Learner** & **Mega Learner** & **Descriptions** \\ \hline KNN & \(\surd\) & n\_neighbors = 3 \\ CATBOOST & \(\surd\) & Depth = 8, learning\_rate = 0.8, loss\_function = 'RMSE’, \\  & & random\_seed = 18 \\ SVM & \(\surd\) & C = 100, gamma = 0.01, kernel = 'rbf' \\ RIDGE REGRESSION & & \(\surd\) & Alpha = 17, random\_state = 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The key parameters of four benchmark models in Python. steps in Figure 4, one can find that the prediction accuracy of each models is decreasing with the increase of the prediction step regardless of the southbound or northbound links. This result is consistent with the results of existing studies [30; 33], which found that it is particularly difficult to conduct multi-step-ahead prediction due to the randomness and uncertainty of the travel speed. Figure 4: MOEs of five prediction models:(**a**) MAPE of five models in northbound; (**b**) MAPE of five models in southbound; (**c**) MAE of five models in northbound; (**d**) MAE of five models in southbound; (**e**) MSE of five models in northbound; (**f**) MSE of five models in southbound. As shown in Figure 4, the ensemble learning models of the proposed DDSELM can yield many more benefits than individual models (SVM, CATBOOST, and KNN) and ensemble one (BAGGING) regardless of the ahead-prediction step. In particular, the developed DDSELM in this study can outperform four kinds of benchmark models. In particular, the KNN, an individual method, performs better than SVM and CATBOOST for one-step-ahead prediction, but it also suffers many more errors than the two other individual ones for three-step-ahead prediction in Figure 4a. Compared with KNN, DDSELM always has good performance regardless of the road direction and prediction steps, among which the MAPE of northbound DDSELM is 1.16% lower (7.08% versus 8.24%) than KNN in one-step-ahead prediction, 1.58% (8.77% versus 10.35%) in two-step-ahead prediction, and 1.56% (10.34% versus 11.90%) in three-step-ahead prediction, respectively.