# Traffic Simulation of Future Intelligent Vehicles in Duisburg City Inner Ring
## 2 Methodology
### Vehicle Models with Different Levels of Automation  
In this work, a driver-vehicle separate model is used for simulation. An obvious benefit of this kind of model is its flexibility. The driver model can be combined with different vehicle models (fuel, electric, hybrid, etc. ), and the vehicle model can also combine with different driver models (autonomous driver, human driver, aggressive driver, etc.). As can be seen in Figure 3, driver model and vehicle model are independent of each other and connected by data transmission. The driver model simulates the reaction of a human driver on the road. Depending on the situation of the ego vehicle, leading vehicle, and other road information, the human driver/driver model controls the vehicle with a suitable gas/brake pedal position. In the car-following models of microscopic traffic simulation, the Krauss model has fewer conflicts with the lane-changing model because of its simplicity [26]. The driver model in this work consists of two parts. The modified Krauss car-following model [27] generates the desired speed of the driver, and the fuzzy control model outputs the gas/brake pedal position depending on the desired speed of the driver and the actual speed of the vehicle. The modified [PERSON] model can be expressed as:  
\[\left\{ \begin{array}{c}v(t+t_{l})=\max(0,V_{n}-\epsilon\;a\;\eta)\\ V_{n}=\min[v_{s},\;V_{max},v_{n}(t)+a_{n}t_{l}]\\ v_{s}=-\;\tau\;b+\sqrt{\left(\tau\;b\right)^{2}+v_{n-1}(t)^{2}+2b\;g_{n}(t)} \\ x(t+1)=x(t)+v_{n}(t)\;t_{l}\end{array} \right. \tag{1}\]  
where \(v(t+\Delta t)\) represents the speed of the ego vehicle after time \(\Delta t\), \(V_{n}\) is the desired speed, \(\varphi\) is a random perturbation to allow for deviations from optimal driving, \(\epsilon\) is the imperfection factor of the driver, \(a\) is the acceleration of the ego vehicle, \(\eta\) is a random number between 0 and 1, \(v_{s}\) is the safe speed, \(V_{max}\) is the allowed speed of the road, \(v_{n}(t)\) is the speed of the ego vehicle at time \(t\), \(a_{n}\) is the maximum acceleration, \(t_{l}\) is the time step of the simulation, \(\tau\) is the reaction time of the driver, \(v_{n-1}(t)\) is the speed of the leading vehicle, \(b\) is the maximum deceleration of the ego vehicle, \(g_{n}(t)\) is the gap between the leader and the follower, \(x(t)\) is the position of the ego vehicle at time \(t\), and \(x(t+1)\) is the position of the ego vehicle at the next time step. Figure 2: Two data sources of traffic demand (**(a)** Origin–Destination (OD) matrix, where the distribution of OD areas is shown in different colors; **(b)** induction loops, where the numbers are intersections of the inner ring area). The fuzzy control model is established by a driving experiment with 34 human drivers in a driving simulator [19]. Based on the data transferred from the modified Krauss model, the desired speed of the driver \(V_{n}\) and the actual speed of the vehicle \(v_{n}(t)\), the fuzzy control model outputs gas pedal position \(p_{g}\) or brake pedal position \(p_{b}\) with human-like fuzzy rules. The vehicle model considers the characteristic of the vehicle transmission and the driving resistances and is optimized by the data from the driving experiment. Different levels of automation are reflected in the parameters of the modified Krauss model and fuzzy control model. Three degrees of automation are selected in representing the vehicle automation level of the current stage, as well as in the near future and the far-distant future. Considering the driver assistance functions of high-selling vehicles and the current automation level of vehicles on the road, Level 0 (no automation) is selected for the current stage. Level 2 (partial automation level) and Level 5 (fully autonomous vehicle) are selected for the automation levels in the near future and far-distant future, respectively. In order to effectively distinguish the difference between Level 0 and Level 2, it is assumed that, in the simulation, Level 2 vehicles are in the driving assisted mode.