# Measuring Collision Risk in Mixed Traffic Flow Under the Car-Following and Lane-Changing Behavior
## 3 A New Risk Measurement Method Considering Multiple Driving Behaviors
### Validation of the Effectiveness of \(R_{total}\)
#### 3.3.2 Comparison with Other SSMs  
To validate the effectiveness of the \(R_{\text{total}}\) metric and determine its threshold, we compared it with other established indicators, including TTC, MTTC, and PICUD. We also compared it with the WS2 DR metric proposed in a recent study [21]. By default, TTC assumes no risk when the relative speed (\(\Delta v\)) is less than zero. To address this, we set a maximum value of 50 s.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Car-Following** & **Lane-Changing** \\ \hline Condition 1 & \begin{tabular}{c} Consecutive rows of trajectory data \\ with a spacing smaller than 50 m. \\ \end{tabular} & Only one lane change is considered. \\ \hline Condition 2 & \begin{tabular}{c} Instances where the duration of \\ car-following exceeded 30 s. \\ \end{tabular} & \
\begin{tabular}{c} The duration before and after the \\ lane change is longer than 10 s. \\ \end{tabular} \\ \hline Condition 3 &
\begin{tabular}{c} Removed the initial and final 5 s \\ from the car-following periods. \\ \end{tabular} & - \\ \hline \hline \end{tabular}
\end{table}
Table 2: Conditions of car-following and lane-changing behaviors.  
Figure 6: Data smoothing results. (**a**) Position smoothing result of Vehicle ID56; (**b**) speed smoothing result of Vehicle ID 56; (**c**) acceleration smoothing result of Vehicle ID 56.  
To illustrate the relationship between the newly proposed SSM and existing SSMs, we present the operational result curves for four samples. These include two sets of car-following trajectories and two sets of lane-changing trajectories derived from the trajectory data described in Section 3.3.1. The results of the various indicators are presented in Figure 7. Since the trend of \(R_{\text{total}}\) is inverse to the others, we plotted \(1-R_{\text{total}}\) to better illustrate the relationships among the indicators.  
Figure 7: Cont.  
Figure 7 illustrates the variations in risk levels during car-following and lane-changing processes.  
In the car-following scenario (Figure 7a,b), SSM values decrease when the leading vehicle's speed is lower than that of the following vehicle, indicating an increase in risk levels. Notably, \(R_{\text{total}}\) captures potential risks even when \(\Delta v<0\), a situation where traditional metrics such as TTC fail to fully represent the risk.  
In the lane-changing scenario (Figure 7c,d), the risk levels exhibit significant fluctuations throughout the process. Lane changing can be divided into two phases: the  
Figure 7: Evaluation results of different vehicles. (**a**) Evaluation results of vehicle ID 63; (**b**) evaluation results of vehicle ID 361; (**c**) evaluation results of vehicle ID 1109; (**d**) evaluation results of vehicle ID 1342.  
preparation phase, where the driver transitions from the intention to change lanes to initiating the maneuver, and the execution phase, where the vehicle moves laterally to enter the target lane. To highlight the changes in risk, the time points \(t_{1}\) (5 s before the lane change) and \(t_{2}\) (5 s after the lane change) are marked in the figure. Between \(t_{1}\) and \(t_{2}\), during the execution phase, risk levels fluctuate significantly, with the highest risk occurring at points where the SSM values exhibit the greatest changes.  
A comparative analysis of the metrics reveals that the overall trend of \(1-R_{\text{total}}\) aligns with other SSMs, while TTC shows limitations under conditions where \(\Delta v<0\). In contrast, MTTC exhibits more pronounced fluctuations. PICUD and WS\({}^{2}\)DR, which both consider displacement and velocity differences, demonstrate strong correlations and consistent trends. Meanwhile, \(R_{\text{total}}\) incorporates both longitudinal and lateral risks, as well as the influences of the target vehicle's leading and following vehicles. This allows \(R_{\text{total}}\) to exhibit more sensitive fluctuations in both car-following and lane-changing scenarios, highlighting its strong applicability for dynamic risk assessment.