## 3 Simulation Experimental Design
### Vehicle Operating Rules  
#### 3.1.1 Car-Following Rules  
Firstly, the car-following model is introduced. The car-following model of HVs of the simulation in this paper is based on the intelligent driver model (IDM). The IDM model was used in the simulation experiments to simulate HVs. The IDM model is based on vehicle speed, inter-vehicle spacing, and the velocity difference between the preceding and following vehicles, while also considering human factors such as reaction time and estimation errors. It is easy to calibrate and has good empirical conformity [38]. Currently, it is widely applied in traffic simulation. According to [PERSON] et al. 's comparative study of several commonly used car-following models in the SUMO software, in a single-lane, signal-free environment, IDM exhibits higher traffic efficiency compared to CarFollowing-Wiedemann and CarFollowing-Pwagner. The default car-following model in SUMO, CarFollowing-Krauss, has a similar control performance to IDM and performs better at signalized intersections [39]. Considering that the research scenario in this paper does not involve signalized intersections and IDM is more widely used in traffic simulation studies, we have chosen IDM as the simulation model for HVs. The basic rules of IDM [40] are as follows:  
1. Acceleration  
The acceleration model of the ego vehicle is as follows:  
\[\dot{v}=a\left[1-\left(\frac{v}{v_{0}}\right)^{\delta}-\left(\frac{s^{*}(v, \triangle v)}{s}\right)^{2}\right] \tag{3}\]  
where \(a\) is the maximum acceleration of the ego vehicle, \(v\) is the current speed of the ego vehicle, \(v_{0}\) is the desired speed, \(\delta\) is the acceleration index, \(\Delta v\) is the difference in speed between ego vehicle and the front vehicle, \(s\) is the current distance between ego vehicle and the front vehicle, and \(s^{*}(v,\Delta v)\) is the desired car-following distance. The desired car-following distance is given by:  
\[s^{*}(v,\triangle v)=s_{0}+max\left(0,vT+\frac{v\triangle v}{2\sqrt{ab}}\right) \tag{4}\]  
where \(b\) is the comfortable deceleration. 2. Equilibrium flow state  
In this state, the ego vehicle maintains a balanced car-following distance \(s\) from the front vehicle, \(\dot{v}\approx\Delta v\approx 0\). As \(\dot{v}\approx 0\), Equation (3) can be transformed as follows:  
\[s^{*}(v,\Delta v)=s\left[1-\left(\frac{v}{v_{0}}\right)^{\delta}\right]^{\frac{1} {2}} \tag{5}\]  
Since \(\Delta v\approx 0\), Equation (4) can be transformed as follows:  
\[s^{*}(v,\Delta v)=s_{0}+vT \tag{6}\]  
Combining Equations (3) and (4), the actual car distance \(s\) is:  
\[s=s_{e}(v)=\frac{s_{0}+vT}{\sqrt{1-\left(\frac{v}{v_{0}}\right)^{\delta}}} \tag{7}\]  
Equation (7) is the equation for the equilibrium car-following distance \(s_{e}(v)\) in the equilibrium flow state. 3. Braking strategy  
When studying the braking strategy itself, set the term \(v\Delta v/\left(2\sqrt{ab}\right)\) and \(s_{0}+vT\) in \(s^{*}\) to zero, together with the free acceleration term \(a\Big{[}1-\left(v/v_{0}\right)^{\delta}\Big{]}\). When approaching a standing vehicle or a red traffic light \((\Delta v=v)\), then:  
\[\dot{v}=-a\bigg{(}\frac{s^{*}}{s}\bigg{)}^{2}=-\frac{av^{2}(\Delta v)^{2}}{4 abs^{2}}=-\bigg{(}\frac{v^{2}}{2s}\bigg{)}^{2}\frac{1}{b} \tag{8}\]  
With the kinematic deceleration defined as:  
\[b_{kin}=\frac{v^{2}}{2s} \tag{9}\]  
This part of the acceleration can be written as:  
\[\dot{v}=-\frac{b_{kin}^{2}}{b} \tag{10}\]  
With Equation (10), when decelerating at a deceleration \(b_{kin}\), the braking distance of ego vehicle equals to the distance from ego vehicle to the stationary vehicle ahead. In this case, two possible situations are as follows. 1. When \(b_{kin}>b\), which is defined as a critical situation, the actual deceleration is even stronger than necessary, \(\left|\dot{v}\right|=b_{kin}^{2}/b>b_{kin}\). This overcompensation decreases \(b_{kin}\) and thus helps to turn back to normal situation;
2. When \(b_{kin}<b\), \(b_{kin}^{2}/b<b_{kin}\).