# Integrating Autonomous Vehicles (AVs) into Urban Traffic: Simulating Driving and Signal Control
## 3 Methodology
### Car Following Models and Lane Change Models  
In the Wiedemann model, human driving behavior is recognized as naturally varying, considering that each driver possesses unique abilities in terms of perception, reaction, and assessing traffic flow [20; 25]. The model delineates four driving states: free flow, approaching, following, and critical situation, as illustrated in Figure 6. These states are defined by specific thresholds: ABX and SDX (absolute braking threshold and safe distance threshold in meters) represent the minimum and maximum gap distances during following, respectively; CLDV (closing distance in meters per second) indicates the point at which the driver becomes aware of the narrowing gap; and SDV (sensitive distance in meters) is the critical point when the driver recognizes their proximity to the vehicle ahead. OPDV (opening distance in meters per second) marks the point when the driver realizes they are traveling slower than the vehicle in front. PTV VISSIM incorporates two versions of the Wiedemann car-following model: Wiedemann 1999 and Wiedemann 1974 [22; 27; 28]. The main distinction between these versions lies in their level of customization, with Wiedemann 1999 offering a greater number of  
Figure 5: Desired speed distribution of AVs. Source: simulated data processed by authors. Figure 6: Wiedemann car-following model. Source: [26]. adjustable parameters, making it more suitable for urban and congested traffic scenarios. In contrast, Wiedemann 1974, which was originally designed for freeway conditions, utilizes more rigid, hard-coded parameters [29]. As this study aims to assess the impact of aggressive autonomous vehicles (AVs) at urban signalized intersections, the Wiedemann 1999 car-following model is utilized. The driving behavior parameters (CC) in Wiedemann 1999 are calibrated using threshold values corresponding to different driving regimes. The PTV Group (2018) outlines the definitions and default values of these CC parameters for human-driven vehicles in Table 4. Users have the flexibility to adjust these parameters based on observed vehicle behaviors, including variables such as look-ahead distance, average standstill distance, and desired safety distance components [30]. The Wiedemann 1999 model is designed for capture and includes more parameters of driving behaviors:  
* CC0: Standstill distance (the desired gap between two stationary vehicles in meters). * CC1: Following distance (the time-based component of the desired safety distance, dependent on speed in seconds). * CC2: Longitudinal oscillation (the distance a driver allows before closing in on the vehicle ahead in meters). * CC3: Perception threshold for following (the point at which the driver initiates deceleration in seconds). * CC4 and CC5: Negative and positive speed differences (sensitivity to the acceleration or deceleration of the vehicle in front in meters per second). * CC6: Speed influence on oscillation (how distance affects speed fluctuations during following in \(10^{-4}\) rad/s). * CC7: Oscillation acceleration (the minimum acceleration or deceleration applied when following another vehicle in m/s2). * CC8 and CC9: Desired acceleration from a standstill and at 80 km/h. in m/s2  
The Wiedemann 1999 model determines the acceleration of the following vehicle \(\left(a_{f}\right)\) by considering its speed relative to and the distance from the leading vehicle. This model functions across various driving regimes: free driving, where the vehicle accelerates to reach its desired speed when it is far from the vehicle ahead; approaching, where it modifies its speed to prevent a collision; following, where it keeps a safe distance; and braking,