# Lateral Oscillation Characteristics of Vehicle Trajectories on the Straight Sections of Freeways
## 6 Conclusions  
This study sought to analyze the lateral oscillation characteristics of vehicle trajectories during the lane-keeping period on the straight sections of freeways. Two evaluation indicators of vehicle lateral motion were suggested, including the lateral amplitude (LA) and the distance traveled within the oscillation cycle (DTOC). These indicators help to provide a better explanation of trajectory oscillation and how other factors influence oscillatory behavior. To consider the lane-keeping behavior and the need for traffic safety, a new framework to determine the proper lane width by incorporating LA, lateral clearance, and vehicle width was proposed. Firstly, data reduction principles and processes were established to remove irrelevant data from the analysis. Secondly, a cluster analysis was performed to reclassify the vehicles into three groups: passenger cars, medium-large cars, and extra-large trucks. Thirdly, the speed distributions of several vehicle kinds were examined. Then, the effects of vehicle types, lane positions, and speed were analyzed independently with regard to the LA and the DTOC. Finally, the theoretical values of the lane widths under different conditions were ascertained according to the trajectory oscillation characteristics. This study was based on the dataset of naturalistic vehicle trajectories on German highways (highD), and the following conclusions could be drawn. (1) Different types of vehicles have different speed distributions on straight sections of freeways. Passenger cars have the most discrete and highest speed distribution, followed by medium-large cars and extra-large trucks. The operating speed of all vehicles obeys a Gaussian distribution. (2) The lateral amplitude (LA) and distances traveled within the oscillation cycle (DTOC) of all vehicles followed a LogNormal distribution. The LA of extra-large trucks is the smallest among the three vehicle categories, while the DTOC of passenger cars is the largest. It shows that drivers of extra-large trucks are more capable of lane-keeping. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Lane Width (m)** & \multicolumn{8}{c}{**Speed (km/h)**} \\ \hline _Passenger Cars_ & **80** & **90** & **100** & **110** & **120** & **130** & **140** & **150** \\ \hline Minimum value & 3.08 & 3.05 & 3.03 & 3.00 & 2.99 & 2.98 & 2.97 & 2.96 \\ Optimal value & 3.31 & 3.27 & 3.27 & 3.26 & 3.23 & 3.19 & 3.16 & 3.19 \\ \hline _Medium-large Cars_ & **80** & **90** & **100** & **110** & **120** & **125** & & \\ \hline Minimum value & 3.49 & 3.53 & 3.54 & 3.50 & 3.48 & 3.50 & & \\ Optimal value & 3.72 & 3.78 & 3.75 & 3.75 & 3.78 & 3.73 & & \\ \hline _Extra-large Trucks_ & **80** & **85** & **90** & **95** & & & \\ \hline Minimum value & 3.60 & 3.60 & 3.59 & 3.54 & & & \\ Optimal value & 3.80 & 3.81 & 3.82 & 3.75 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Theoretical minimum and optimum values of lane width for different speeds. Meanwhile, passenger cars are more prone to lane deviation due to their better performance and smaller size. (3) There are significant differences in the LA of the three vehicle types at different lane positions: the smallest values for the inside lane and the highest for the outside lane. The trend of DTOC is diametrically the opposite, and it can be used as a guide to determine the minimum length of straight sections of the freeway. The changing patterns of trajectory oscillation of passenger cars and medium-large cars are more complex, while those of extra-large trucks are relatively simple at different speeds. (4) In comparison to lane position, speed is the primary factor influencing trajectory oscillation. Differences in speed can also be used to explain the variations in vehicle trajectory behavior caused by lane positions. Via nonlinear regression, the fourth-order polynomial and single exponential decay models are consistent with the trends in the LA of passenger cars.