## 3 Driver Model
### Vehicle Guidance Model with Different Degrees of Automation  
According to the classification of automation levels in vehicles, six different levels of automation have been defined based on the extent of driver intervention and required attentiveness. This classification has been modified several times and is now widely accepted by researchers and the automotive industry. In this classification system, Level 0 represents no automation at all, and Level 5 represents full automation. Today, most car owners still have level 0 or 1 vehicles due to the additional price of higher equipped vehicles. However, due to government regulations, more and more assistance systems in vehicles are becoming standard, which promotes the penetration of the vehicle population with driver assistance systems. Level 2 is also called the partial automation level, which has both longitudinal control (acceleration/deceleration assistance) and lateral control (steering control assistance). In the near future, there is good reason to believe that these assistance systems will be widely used on most cars on the road. Additionally, there will be a day that fully autonomous cars become a common choice. Based on these assumptions, the automation levels to be simulated were set at Level 0, Level 2 and Level 5 to represent the automation level of the current stage, that in the near future and that in the far future. There are many differences in driving behavior between human drivers and machines. The parameters that make the biggest differences are reaction time, action points and time headway [19]. In this paper, the reaction time \(\tau\) and the imperfection factor \(\epsilon\) were used to distinguish different levels of automation. The reaction time \(\tau\) is affected by factors such as age, gender of the drivers, temperature, altitude of the environment [20] and unexpected situations [21]. However, human drivers' reaction times fluctuate in a relatively small range, from 0.9 to 1.2 s [21] or 0.5 to 2 s [22]. Consequently, \(\tau=1\) was set as the average reaction time for human drivers. For an autonomous car (Level 5), the reaction time was set to \(\tau=0.5\)[19]. The partially automated vehicles with automation Level 2 still need the driver's supervision all the time. In other words, the reaction activity is still made by the driver. Thus, the reaction time of vehicle in Level 2 should be same as Level 0. The imperfection factor of the driver will not be parameterized in this work. Instead, different models were used to represent imperfect driving behaviors. As in Figure 4, the driver model receives traffic data and uses Model K (modified Krauss model) to generate the desired speed V\({}_{n}\). Then, Model F (fuzzy control model) generates the pedal position imitating real human drivers' behaviors. Model VM (Vehicle Model) then generates the vehicle speed based on vehicle parameters and inputs it back into the simulation. Besides reaction time, another difference between human and machine driving is the action points. In order to better imitate unstable action points, the fuzzy control model was extended by a randomness factor \(r\). Based on the analysis of real data from different drivers of the driving experiment in the simulator, \(r=0.5\) was set for human drivers. That means that plus and minus 50% randomness of pedal position has been added into the fuzzy control system representing Level 0 (no automation level driving). Unlike human drivers, the driver assistance system and the completely autonomous system have stable action points with no randomness. Therefore, \(r=0\) is set for Level 2 and Level 5.