# The Impact of Automated Vehicles on Road and Intersection Capacity
## 2 Methods
### Following Model and Parameter Calibration
#### 2.5.2 The ACC Following Model  
At present, autonomous vehicles are mainly divided into two categories. The first category is autonomous vehicles based on adaptive cruise control [32]. By means of the vehicle's own sensors, such as the vehicle camera, microwave radar, millimeter-wave radar, etc., it can sense other vehicles, non-motor vehicles, pedestrians, and transportation infrastructure around the vehicle, and then calculate through the vehicle processor, and finally control the vehicle, to make it behave appropriately. It is also the research direction of many enterprises, both at home and abroad.  
Since ACC autonomous vehicles are rarely, or even never, operated on a road in real road traffic, so research related to this driving model remains mostly theoretical. Parameters of traditional human-driven vehicle-following models (such as IDM, LCM, FVD, etc.), are changed, to simulate the man-machine mixed environment, and then the characteristics of heterogeneous traffic flow are studied. Since it is based on the following model of artificial vehicles, it is difficult to objectively reflect the behavior characteristics of autonomous vehicles on the actual road through the assumption of the operating characteristics of autonomous vehicles, such as the fact that autonomous vehicles can maintain a smaller headspace, and a shorter starting and accelerating time. Among the existing self-driving vehicle-following models, the ACC automatic driving following model proposed by the PATH Laboratory of the University of California, Berkeley, is the most widely used. This model is determined by real vehicle data, and a large number of experiments are conducted in order to calibrate model parameters, which has a certain authenticity. Therefore, the ACC autonomous vehicle-following model proposed by the PATH laboratory is selected in this paper [32], and its specific form is shown in Formulas (12) and (13).  
\[a_{n}(t)=k_{1}e_{n}(t)+k_{2}\Delta v_{n}(t), \tag{12}\]  
\[e_{n}(t)=h_{n}(t)-l-s_{0}-t_{a}v_{n}(t), \tag{13}\]  
where \(a_{n}(t)\) represents the acceleration of the vehicle, \(e_{n}(t)\) represents the error between actual vehicle spacing and expected vehicle spacing at the time, \(\Delta v_{n}(t)\) represents the  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(a\) & 1 \\ \(v_{0}\) & 34 \\ \(s_{0}\) & 1.5 \\ \(b\) & 2 \\ \(l\) & 5 \\ \(T\) & 1.5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The IDM following model, where parameter specifies the value.  
difference in vehicle speed before and after the time, \(k_{1}\) represents the control coefficient of workshop distance error, \(k_{2}\) represents the speed difference control coefficient; \(h_{n}(t)\) represents the space headway of the vehicle at the moment, \(l\) represents vehicle length, \(s_{0}\) represents minimum expected (safety) workshop distance, \(t_{a}\) represents the expected time headway, and \(v_{n}(t)\) represents speed of the vehicle at the time.  
With reference to the recommended values of model parameters from the PATH laboratory, and in order to maintain the consistency of the performance of human-driven vehicles and self-driving vehicles, the values of the ACC self-driving vehicle-following model parameters, are shown in Table 2.