# Multi-Step Traffic Speed Prediction Based on Ensemble Learning on an Urban Road Network
## 4 Case Study  
The proposed model will be evaluated with traffic data collected by ITS with Internet Plus from the department of the Zhongshan Traffic Police Detachment. Zhongshan is one of the pilot cities to implement ITS applications in China, which has the ability to automatically collect city-level traffic flow data at signalized intersections. The testbed is selected on Xingzhong Rd with two-way six motorized lanes, which is the busiest and most congested south-north corridors in the Zhongshan downtown area [39]. Northbound and southbound traffic flow were collected by loop detectors located several meters before the stopline at the signalized intersection between Zhongshan Rd. and Tiyu Rd., and the two-way link travel speed was collected by floating car detection in Figure 3. In this study, the pilot dataset with the time interval of 1 h on Xingzhong Rd, was recorded over five weeks from 21 October to 24 November 2018. Referring to the correlation analysis mentioned above, this paper selected 10 representative features to calculate the Pearson correlation analysis as shown in Tables 2 and 3. Figure 3: The layout of pilot intersections in the city of Zhongshan, China. Figure 2: The framework of the proposed predictor (DDSELM) in this study. Where, \(v_{1(d,t)}(v_{2(d,t)})\) represents the \(t\)th-hour upstream(downstream) speed on the \(d\)th day. Tables 2 and 3 show the correlation between different spatial-temporal speed and flow, respectively. One can find that the correlation between current interval and the same historical interval in the past days is relatively high, regardless of the day of week. The link travel speed at time \(t\) also has a strong correlation with the upstream and downstream ones at the lowest of over 0.782. However, the correlation between the speed at interval \(t\) and \(t+1\) in the historical days decreases with the passage of time. This is because the traffic flow has a certain randomness and the current traffic state at interval \(t\) has a significant difference from the interval \(t+1\) in the historical days. In addition, the current speed has a negative correlation with the current flow, which indicates that the higher the speed is, the lower the flow is. Notably, the correlation between the variables on the northbound links is higher than the southbound, which is mainly because the northbound traffic is relatively more stable and has less fluctuation than the southbound. According to statistical analysis, those variables that have a high correlation degree of \(\geq\)0.6 [40] could be allowed for detrending. After detrending, the residual set would be inputs in this study. Input variables of the proposed DDESLM model are shown in Table 4. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline  & \(v_{(d,t)}\) & \(v_{(d-1,t)}\) & \(v_{(d-2,t)}\) & \(v_{(d-3,t)}\) & \(v_{(d-1,t+1)}\) & \(v_{(d-2,t+1)}\) & \(v_{(d-3,t+1)}\) & \(flow_{(d,t)}\) & \(v_{1(d,t)}\) & \(v_{2(d,t)}\) \\ \hline \(v_{(d,t)}\) & 1 & 0.835 & 0.813 & 0.808 & 0.687 & 0.684 & 0.675 & \(-\)0.801 & 0.782 & 0.874 \\ \(v_{(d-1,t)}\) & 0.835 & 1 & 0.835 & 0.811 & 0.732 & 0.685 & 0.687 & \(-\)0.796 & 0.775 & 0.823 \\ \(v_{(d-2,t)}\) & 0.813 & 0.835 & 1 & 0.835 & 0.695 & 0.736 & 0.685 & \(-\)0.793 & 0.751 & 0.796 \\ \(v_{(d-3,t)}\) & 0.808 & 0.811 & 0.835 & 1 & 0.690 & 0.695 & 0.734 & \(-\)0.797 & 0.734 & 0.803 \\ \(v_{(d-1,t+1)}\) & 0.687 & 0.732 & 0.695 & 0.690 & 1 & 0.835 & 0.811 & \(-\)0.750 & 0.689 & 0.692 \\ \(v_{(d-2,t+1)}\) & 0.684 & 0.685 & 0.736 & 0.695 & 0.835 & 1 & 0.835 & \(-\)0.739 & 0.668 & 0.671 \\ \(v_{(d-3,t+1)}\) & 0.675 & 0.687 & 0.685 & 0.734 & 0.811 & 0.835 & 1 & \(-\)0.737 & 0.644 & 0.680 \\ \(flow_{(d,t)}\) & \(-\)0.801 & \(-\)0.796 & \(-\)0.793 & \(-\)0.797 & \(-\)0.750 & \(-\)0.739 & \(-\)0.737 & 1 & \(-\)0.772 & \(-\)0.829 \\ \(v_{1(d,t)}\) & 0.782 & 0.775 & 0.751 & 0.734 & 0.689 & 0.668 & 0.644 & \(-\)0.772 & 1 & 0.815 \\ \(v_{2(d,t)}\) & 0.874 & 0.823 & 0.796 & 0.803 & 0.692 & 0.671 & 0.680 & \(-\)0.829 & 0.815 & 1 \\ \hline \end{tabular}
\end{table}