# Simulation-Oriented Analysis and Modeling of
## 3 Characteristics of Distracted Car-Following Events
### Distracted Car-Following Pattern  
Distracted car-following events have been classified into different patterns to allow for more accurate simulations for each pattern. Using the GPS information in the dataset, 593 distracted car-following events on expressways and 179 events on surface roads were distinguished. A scenario is considered to have a high traffic volume when the number of vehicles in the same direction on the lane exceeds 6 within a 5-second observation period [45]; otherwise, it is considered to have a low traffic volume. It should be noted that by \"scenario\", this study refers to the observation period under actual traffic conditions, rather than a part of a simulation. By analyzing the traffic flow on different types of roads, it can be observed that the traffic volume on surface roads consistently remains at a high level, whereas the traffic flow on expressways varies more significantly. Therefore, distracted car-following events on expressways are further divided into two groups based on traffic volume. Finally, there are 67 distracted car-following events with a high traffic volume and 526 with a low traffic volume.  
The Fuzzy C-Means clustering method was utilized to categorize distracted following behavior. This method was chosen for its flexible clustering outcomes and robustness against noise and outliers [46]. Initially, Spearman correlation analysis was employed to select critical clustering parameters from 20 common parameters of car-following behavior, including statistical indicators (mean, standard deviation, maximum, and minimum values) for distance, speed, time headway, acceleration, and deceleration. The results confirmed that the standard deviation of speed, maximum acceleration, and maximum deceleration exhibit the lowest correlation among these variables. Thus, these three parameters were selected for clustering in the Fuzzy C-Means method.  
\begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Possible Distributions**} & \multicolumn{2}{c}{**Distraction Event Duration**} & \multicolumn{2}{c}{**Distribution Diagram**} \\ \cline{2-4}  & **K-S Test** & **Chi-Squared Test** & \\  & **Statistic** & **Statistic** & \\ \hline Normal distribution & \textless{}0.001 & \textless{}0.001 & & Distraction event duration \\ Exponential distribution & 0.012 & 0.045 & & Fitted distribution \\ Extreme Value distribution & \textless{}0.001 & \textless{}0.001 & & \\
**Burr distribution** & **0.443** & **0.086** & & \\ a-Stable distribution & 0.005 & 0.017 & & \\ Gamma distribution & 0.032 & 0.057 & & \\ \hline \end{tabular}
\end{table}
Table 2: Distribution of distraction event duration.  
The clustering results revealed three patterns of distracted driving behavior, including excessive distraction driving, moderate distraction driving, and mild distraction driving. Specifically, excessive distraction driving refers to distractions that significantly impact driving safety. As seen in Figure 2, drivers in this category show considerable speed fluctuations and exhibit higher accelerations and decelerations. Moderate distraction driving refers to distractions that moderately affect driving safety, with less speed fluctuation than excessive distraction driving. Mild distraction driving refers to distractions that minimally impact driving safety, in which drivers experience minor speed fluctuations and lower accelerations/decelerations. Additionally, the clustering results under different road environments were visualized through the t-distribution Stochastic Neighbor Embedding (t-SNE) dimensionality reduction method. Figure 2 shows that the clustering results identify three distinct groups, each with its own cohesive characteristics and almost no overlap between groups. This indicates that different patterns of distraction can be effectively distinguished.  
Figure 2: Clustering results of different patterns of distracted driving.