## 2 Materials and Methods
### Data Collection and Traffic Flow Modeling Parameter Calibration
#### 2.4.2 Parameter Calibration  
1. Car-Following Models  
* Manual Car-Following Model  
The intelligent driver model (IDM) was selected as the car-following model for manually driven vehicles [19]. A genetic algorithm was employed to optimize the parameters. The population size and the maximum number of iterations were set to 500. The calibration results of the car-following model are as follows (Table 4). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & \(\mathbf{v_{max}}(\text{m/s})\) & \(\mathbf{a_{m}}(\text{m/s}^{2})\) & \(\mathbf{b_{n}}(\text{m/s}^{2})\) & \(\mathbf{T_{s}}(\text{s})\) & \(\mathbf{s_{0}}(\text{m})\) \\ \hline value & 30 & 2.3 & 3.6 & 2.0 & 1.5 \\ \hline \hline \end{tabular}  
* Autonomous Car-Following Model  
\end{table} 
Table 4: Calibration Results of the IDM Model. Path laboratory team carried out research on car following model of autonomous vehicle traffic flow earlier, and the proposed model is widely used in the research on traffic flow characteristics of autonomous vehicle [30]. The acceleration of ACC vehicles is determined by the gap error and the difference in velocity with respect to the preceding vehicle. The ACC model is as follows [30;31]:  
\[e_{s}(t)=\Delta x(t)-t_{a}v_{s}(t)-l-s_{0} \tag{21}\]  
\[a_{s}(t)=k_{1}e_{s}(t)+k_{2}\Delta v \tag{22}\]  
where \(e_{s}(t)\) is the difference between the ACC vehicle's workshop distance at the first moment and the desired workshop distance; \(\Delta x(t)\) is the headway between the following vehicle and the leading vehicle at the moment \(t\); \(t_{a}\) is the desired workshop time distance set by the driver; \(l\) is the body length; \(s_{0}\) is the workshop distance at the time of congestion; \(a_{s}(t)\) is the acceleration of the ACC vehicle at the moment t; \(\Delta v\) is the speed difference between the following vehicle and the leading vehicle; \(k_{1}\) and \(k_{2}\) are the adjustment coefficient. See Tables 5 and 6. The CACC model expression is as follows [29]:  
\[e_{s}(t-1)=\Delta x(t-1)-t_{c}v_{s}(t-1)-l-s_{0} \tag{23}\]  
\[v_{s}(t)=v_{s}(t-1)+k_{p}e_{s}(t-1)+k_{d}e_{s}^{\prime}(t-1) \tag{24}\]  
where \(e_{s}(t-1)\) represents the gap error of the CACC vehicle at time \(t-1\); \(\Delta x(t-1)\) represents the headway between the following vehicle and the leading vehicle at time \(t-1\); \(t_{c}\) is the pre-set desired time headway; \(l\) is the vehicle length; \(s_{0}\) is the distance between vehicles in congested conditions; \(v_{s}(t)\) is the velocity of the CACC vehicle at time \(t\); \(v_{s}(t-1)\) is the velocity of the CACC vehicle at the previous time \(t-1\); \(e_{s}^{\prime}(t-1)\) represents the derivative of the gap error at time \(t-1\), i.e., the increment of the gap error per unit time; \(k_{p}\) and \(k_{d}\) are adjustment coefficients. See Tables 7 and 8. \begin{table}
\begin{tabular}{c c c c c} \hline
**Constant Time Gap \(t_{a}\) (s)** & **1.1** & **1.6** & **2.2** \\ \hline Proportion (\%) & 50.4 & 18.5 & 31.1 \\ \hline \end{tabular}
\end{table} 
Table 6: Constant Time Gaps for ACC Vehicles. \begin{table}
\begin{tabular}{c c c c c} \hline
**Constant Time Gap \(t_{c}\) (s)** & **0.6** & **0.7** & **0.9** & **1.1** \\ \hline Proportion (\%) & 57.0 & 24.0 & 7.0 & 12.0 \\ \hline \end{tabular}
\end{table} 
Table 7: Parameter Values for the CACC Car-Following Model. \begin{table}
\begin{tabular}{c c c c c} \hline
**Parameters** & \(l\) & \(s_{0}\) & \(k_{1}\) & \(k_{2}\) & \(t_{MV}\) \\ \hline Value & 5 & 2 & 0.23 & 0.07 & 1.6 \\ \hline \end{tabular}
\end{table} 
Table 5: Parameter Values for the ACC Car-Following Model. Lane Change Model  
During each lane change, vehicles must assess the presence of a lane-changing motive and allowable gap for lane changing. The probability of a vehicle changing lanes, denoted as \(P_{change lanes}\), consists of two components: the lane-changing motive generation probability \(P_{motivation}\), and the lane-changing gap acceptance probability \(P_{acceptance}\).