# Integrating Autonomous Vehicles (AVs) into Urban Traffic: Simulating Driving and Signal Control
## 3 Methodology
### Car Following Models and Lane Change Models
\begin{table}
\begin{tabular}{l c c c c c} \hline
**Wiedemann 1999 Following Model** & **AV** & **AV** & **AV** & **AV** & **Human** \\
**Parameters** & **Cautious** & **Normal** & **Aggressive** & **Platoon** & **Human** \\ \hline CC0 Standstill distance (m) & 1.50 & 1.50 & 1.00 & 1.00 & 1.50 \\ \hline CC1 Gap time distribution (s) & 1.5 & 0.9 & 0.6 & 0.5 & 0.9 \\ \hline CC2 “Following” distance oscillation (m) & 0.00 & 0.00 & 0.00 & 0.00 & 4.00 \\ \hline CC3 Threshold for entering “Following” (s) & –10.00 & –8.00 & –6.00 & –6.00 & –8.00 \\ \hline CC4 Negative speed difference (m/s) & –0.10 & –0.10 & –0.10 & –0.10 & –0.35 \\ \hline CC5 Positive speed difference (m/s) & 0.10 & 0.10 & 0.10 & 0.10 & 0.35 \\ \hline CC6 Distance dependency of oscillation (\(10^{-4}\) rad/s) & 0.00 & 0.00 & 0.00 & 0.00 & 11.44 \\ \hline CC7 Oscillation acceleration (m/s2) & 0.10 & 0.10 & 0.10 & 0.10 & 0.25 \\ \hline CC8 Acceleration from standstill (m/s2) & 3.00 & 3.50 & 4.00 & 4.00 & 3.50 \\ \hline CC9 Acceleration at 80 km/h (m/s2) & 1.20 & 1.50 & 2.00 & 2.00 & 1.50 \\ \hline \end{tabular}
\end{table} 
Table 4: Parameters influencing driving behavior in car following models within PTV VISSIM [25]. where it slows down to avoid a crash. A central aspect of the model is the desired safety distance \(\left(s_{f}\right)\), which is defined by Equation (1). \[s_{f}=s_{0}+v_{f}.T_{f}+\frac{v_{f}.\Delta v_{f}}{2\sqrt{a_{b}.b}} \tag{1}\]  
Here, \(s_{0}\) denotes the minimum standstill distance (CC0), \(v_{f}\) represents the speed of the following vehicle, and \(T_{f}\) indicates the safe time headway (CC1). The term \(\Delta v_{f}\) refers to the difference in speed between the following and leading vehicles, \(a_{b}\) is the maximum acceleration capability of the following vehicle, and \(b\) represents the comfortable deceleration rate. Equation (2) outlines how the acceleration of the following vehicle in (m/s2) \(\left(a_{follower}\right)\) is determined by evaluating the current gap between vehicles relative to the desired safety distance, as well as the speed difference between the vehicles [31]. \[a_{follower}=a\cdot\left(1-\left(\frac{v_{f}}{v_{0}}\right)^{\delta}-\left( \frac{s_{f}}{s}\right)^{2}\right) \tag{2}\]  
In this context, \(a\) stands for the maximum acceleration in (m/s2), \(v_{f}\) refers to the current speed of the following vehicle in (m/s), and \(v_{0}\) indicates the desired speed in (m/s). The exponent \(\delta\), usually set to 4 (unitless), is applied in the calculation. The desired safety distance is denoted by \(s_{f}\) in (m), while \(s\) represents the current gap to the vehicle ahead (m). Table 4 outlines the parameters related to car following model's parameters used in the PTV VISSIM model. The decision to execute a lane change is determined by the gap acceptance criterion, where a vehicle \(i\) assesses the available space \(g\) in the target lane to determine if it is adequate for a safe maneuver. This evaluation includes checking the front gap, \(g_{f}\) in (m) (Equation (3)), and the rear gap, \(g_{r}\) in (m) (Equation (4)):  
\[g_{f}=x_{lead}-x_{i}-l_{i}, \tag{3}\]  
\[g_{r}=x_{i}-x_{follower}-l_{follower}, \tag{4}\]  
where \(x_{lead}\) represents the position of the leading vehicle in the target lane in (m), while \(x_{i}\) denotes the position of the subject vehicle in (m). The length of the subject vehicle is indicated by \(l_{i}\) in (m). Additionally, \(x_{follower}\) refers to the position of the following vehicle in the target lane in (m), and \(l_{follower}\) is the length of the following vehicle in (m). A vehicle will change lanes if both the front gap (\(g_{f}\)) and the rear gap (\(g_{r}\)) are greater than the respective minimum acceptable gaps (\(g_{f,min}\) and \(g_{r,min}\)). The minimum acceptable gap \(g_{f,min}\) is influenced by safety distance, relative speeds, and deceleration.