## 5 Model Application  
### Data Description and Preparation  
In our research, a private-sector company provided historical and real-time probe vehicle data for us to research travel time prediction. Probe vehicles collect information such as instantaneous speeds, timestamps, location, and azimuth, reflecting the running state of the urban traffic, and could play a crucial part in travel time estimation and prediction. The oracle database was acquired from ITS (Intelligent Traffic System) in Wuhan, China. We chose a partial road network in Wuhan city as a study area, as shown in Figure 1. The road network was bounded by Wuluo Road, Luoshi South Road, Xiongchu Avenue, and Dingziqiao Road, including many branches and paths. The road network was divided into links by crossing points where roads intersect. The degree of each link was obtained for the links in the entire network, except for links on the edge of the study area. Table 4 shows the selected local roads in the Wuhan road network, which includes the section number, geographic location and the length of each segment. As a result of the effect of GPS positioning error [24], probe vehicles usually deviate from its actual driving road. Therefore, we first projected GPS points to those roads according to the probe vehicle trajectory with map-matching algorithm [15; 25; 26; 27], and then, calculated link travel time using these corrected points. We calculated travel information including travel time, average speed of probe vehicles taking into consideration the probe vehicle running state at the intersections [28; 29; 30; 31]. Table 5 depicts the travel characteristics extracted from the massive quantities of statistical travel time data, including obtained link ID, exiting endpoint ID, entering endpoint ID, probe vehicle ID, the travel time for a probe vehicle traversing the link, the moment a probe vehicle entered the link and the average speed of a probe vehicle traversing the link. Existing research has shown that probe vehicle trajectories display similar traffic patterns over a weekly cycle [18; 21; 32]. According to the weekly cycle of traffic, historical characteristics between target and upstream links were extracted. Figure 2 depicts road number and traffic direction on the partial road network shown in Figure 1. We used our model to predict travel times for link 82 considering spatiotemporal correlation among link 82, link 88, and link 77. Consequently, we extracted spatiotemporal correlation characteristics from big historical data from probe vehicles from May to July 2014--about three billion records. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Section ID**} & \multicolumn{2}{c}{**Start Coordinate**} & \multicolumn{2}{c}{**End Coordinate**} & \multirow{2}{*}{**Length** **(Meter)**} \\ \cline{2-2} \cline{4-5}  & **Latitude** & **Longitude** & **Latitude** & **Longitude** & **(Meter)** \\ \hline
**88** & 30.535 & 114.329 & 30.533 & 114.334 & 475.69 \\
**82** & 30.533 & 114.334 & 30.532 & 114.338 & 489.10 \\
**77** & 30.532 & 114.338 & 30.530 & 114.342 & 411.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Selected arterial road network used in the experiment. Tables 6-8 summarize historical big data, about 299,773,570 records from probe vehicle travel time information with descriptive statistics from January to May, 2014, including: mean value; standard deviation (SD); the 25 th, 50 th and 75 th percentiles of travel time; and the minimum (Min), and maximum (Max) observations. Travel time data were recorded in the unit of seconds. From these three tables, it can be inferred that the quartile speed for the same link was similar for each day, with not much difference from day to day. In contrast, a great difference in speeds existed among different links. Figures 6-8 show the distribution of speeds among the observations from link 88, link 82 and link 77 on Mondays and Wednesdays, respectively. A histogram of the same links presents a similar pattern, with an approximately normal distribution, if outliers are excluded.