# Estimation Method for Road Link Travel Time Considering the Heterogeneity of Driving Styles
## 3 Case Study
### Supplement of Travel Time Outliers  
First, we use the box plot to filter out the outliers in the data, i.e., the discrete points in Figure 3. When supplementing, we determine its location beforehand. Then, we filtered out all the data with the same road link, cluster category, and time slot, and interpolated the missing travel time item based on Lagrange interpolation based on the travel time value of these data. The revised travel time results are shown in Figures 5 and 6. The structure of Figure 5 is similar to that of Figure 3. Figure 6 is a Hexbin diagram of the distribution of the travel estimation results in Figure 5. The shades of color on the right represent the number of scatter points within the hexagonal area. The darker the color, the more scattered points there are in the region. Compared with Figure 3, it is not arduous to recognize that the outliers have been significantly reduced. The abnormal driving time has also been reduced to a certain extent. The missing travel time items have been better corrected.  
To verify the effectiveness of the method, a method that does not consider the results of DBSCAN and directly performs interpolation is selected for comparison. Five thousand points are randomly chosen from the travel time data to estimate the travel time. The direct interpolation method and the interpolation method based on the DBSCAN results are used for comparative analysis. The results are shown in Figure 7. The abscissa is the actual value of the travel time, and the ordinate is the estimated value. The regression equations of the estimated and actual values of the two methods are, respectively:  
(1) The direct interpolation method: \(y=0.9356x+5.9443\) (Figure 7a), where R\({}^{2}\) = 0.5756. (2) The interpolation method based on the DBSCAN results: \(y=0.9695x+2.5443\) (Figure 7b), where R\({}^{2}\) = 0.7572.  
Figure 4: The output results of the number of DBSCAN algorithm clusters correspond to different input _MinPts_ values.  
Figure 5: Hourly distribution of completed travel time.  
Figure 6: Travel time estimation results of hourly density distribution.  
Figure 7: Comparison of the actual values and estimation values of two methods. (**a**) The results of the direct interpolation method. (**b**) The results of the interpolation method based on the DBSCAN results.  
The results show that the coefficient of the regression equation considering the difference in driving style of the crowd is closer to 1, with a larger R\({}^{2}\) compared with the direct interpolation method. The mean value of the deviation between the estimated value and the actual value of the method proposed in this paper is 5.7 s, with a variance of 18.2 s\({}^{2}\). In contrast, the mean value of the deviation between the estimated value of the direct interpolation method and the actual value is 9.1 s, with a variance of 44.4 s\({}^{2}\). The accuracy of the proposed method is improved by 37.4%. It shows that the estimated travel time of the algorithm proposed in this paper is closer to the actual value, and the algorithm has a higher estimation accuracy.