# Factors Affecting Rear-End Collisions in Underground Road Junctions Using VISSIM
## 3 Methodology
### Data Processing  
After data collection, TTC and density were estimated based on speed, location, and link information. The TTC was calculated using the speed and location information of the lead vehicle and the target vehicle, employing Equation (1).  
\[TTC_{i}(t)=\frac{X_{i-1}(t)-X_{i}(t)-L_{i}}{V_{i}(t)-V_{i-1}(t)}\leq 1.5 \tag{1}\]  
where X: \(V(t)\): vehicle speed;  
\(X(t)\): vehicle position;  
\(L_{i}\): subject vehicle's length;  
\(X_{i-1}(t)-X_{i}(t)\): relative distance;  
\(V_{i}(t)-V_{i-1}(t)\): relative speed.  
The Surrogate Safety Assessment Model (SSAM) (version 3.0), a road safety performance analysis software provided by the Federal Highway Administration (FHWA) of the United States, sets 1.5 s as the threshold for TTC. Thus, in this study, the threshold for TTC was set to 1.5 s to classify cases with a TTC \(\leq\) 1.5 s as conflict situations and cases with TTC > 1.5 s as non-conflict situations [35].  
The processed data were aggregated by segment and time for analysis. The analysis area was divided into 50 m segments, with a total of 116 segments. The aggregation time interval was 1 s, and the information of 250 m worth of vehicles, including the center segment (k) and the two segments before and after it, was aggregated and used for the analysis, as illustrated in Figure 5 (i.e., the information was aggregated from 116 segments every second). Table 3 shows the final variables after data processing, and Table 4 presents a sample of the collected data.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Time** & **Segment** & **Conflict** & **Acceleration** & **Speed** & **PosLat** & **Spacing** & **Density** & **Acceleration** & **Speed** & **PosLat** & **Spacing** & **Density** \\
**Frame** & **Segment** & **Conflict** & **Mean** & **Mean** & **Mean** & **Mean** & **Mean** & **Std** & **Std** & **Std** & **Std** & **Std** \\ \hline
601 & 83 & 0 & \(-0.1\) & 78.3 & 0.5 & 30.9 & 48.6 & 0.2 & 1.0 & 7.8 & 0.1 & 12.8 \\
601 & 84 & 0 & \(-0.1\) & 77.9 & 0.5 & 28.4 & 47.6 & 0.2 & 1.1 & 7.7 & 0.1 & 10.1 \\
601 & 85 & 0 & \(-0.1\) & 77.0 & 0.5 & 33.0 & 46.4 & 0.1 & 1.0 & 7.5 & 0.1 & 22.5 \\
601 & 86 & 0 & 0.3 & 79.8 & 0.5 & 35.9 & 46.6 & 0.1 & 0.6 & 4.7 & 0.2 & 26.9 \\
601 & 87 & 0 & 0.1 & 74.1 & 0.5 & 33.6 & 30.5 & 0.0 & 0.7 & 13.4 & 0.2 & 31.0 \\ : & & & & & & & & & & & & \\
4200 & 112 & 1 & \(-1.4\) & 57.0 & 0.5 & 61.8 & 34.4 & 0.0 & 3.2 & 21.7 & 0.1 & 40.9 \\
4200 & 113 & 0 & \(-1.4\) & 57.0 & 0.5 & 61.8 & 34.4 & 0.1 & 3.2 & 21.7 & 0.1 & 40.9 \\
4200 & 114 & 0 & \(-1.2\) & 58.8 & 0.5 & 64.9 & 35.7 & 0.1 & 3.4 & 22.7 & 0.1 & 43.1 \\
4200 & 115 & 0 & 0.1 & 80.7 & 0.5 & 90.3 & 29.5 & 0.1 & 0.5 & 9.1 & 0.0 & 31.7 \\
4200 & 116 & 0 & \(-0.1\) & 77.0 & 0.5 & 65.5 & 24.3 & 0.0 & 0.3 & 11.7 & 0.0 & 55.9 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Aggregated data sample.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Description** & **Variable** & **Description** \\ \hline Time frame & Simulation seconds & DensityMean & Acceleration average \\ \hline Segment & Analysis points (No.) & AccelerationStd & Standard deviation of acceleration \\ \hline Conflict & Conflict or not at segment m (conflict: 1, non-conflict: 0) & SpeedStd & Standard deviation of speed \\ \hline AccelerationMean & Average of acceleration & PosLatStd & Standard deviation of lateral \\ \hline SpeedMean & Average speed & SpacingStd &
\begin{tabular}{c} Standard deviation of distance \\ between vehicles \\ \end{tabular} \\ \hline PosLatMean & Average of lateral position & DensityStd & Standard deviation of density \\ \hline SpacingMean & Average of distance between vehicles \\ \hline \hline \end{tabular}
\end{table}
Table 3: Description of the study variables.