## 4 Numerical Simulation Analysis and Results
### Macroscopic Numerical Analysis
#### 4.2.1 Macroscopic Numerical Analysis in the Vehicle Starting Scenario  
In the initial state, 21 vehicles were lined up with a headway of 7.5 m and an initial speed of 0. At time \(t=0\), the leading vehicle (Car 1) started to speed up with a initial acceleration 3m/s^2 that decreases in magnitude to 0 until traveling at a constant speed. The remaining 20 test vehicles accelerated in response to the speed change of Car 1 by the extended IDM model proposed in this paper. Finally, all vehicles reached a uniform speed of 12 m/ s. Calculate and record the average acceleration of 20 test vehicles at 0.1 s intervals, as shown in Figure 7.  
Comparing Figure 7a\(-\)d, the averages of acceleration differences of the fleet in the four cases follow similar trends. Take the standard driver (Figure 7c) as an example. When the penetration rate of CAVs is below 50%, compared with the centralized arrangement of CAVs, the average acceleration differences of the fleet decrease more slowly under the decentralized arrangement of CAVs. This indicates that the distribution degree of CAVs has a great impact on the stability of the fleet, because some CAVs running in the ACC mode cannot give full play to their intelligence level. When the penetration rate of CAVs is 50%, the average acceleration of CAVs under the centralized arrangement is 7.68% lower than that under the decentralized arrangement. This coincides with the greatest influence of the distribution degree of CAVs on the stability of traffic flow. When the penetration rate of CAVs is above 50%, the average of acceleration differences of the fleet decreases faster  
Figure 7: The averages of acceleration differences of the fleet at distinct penetration rates and different distribution degrees of CAVs in the starting scenario.  
with the increase of penetration rate under the decentralized arrangement of CAVs. When the penetration rate of CAVs increases to 70%, the average of acceleration differences of the fleet shows a similar trend under both arrangements, suggesting that the distribution degree of CAVs has little impact on the stability of the fleet at this time.  
It can be summarized from Figure 7a-d that the average of acceleration differences of the fleet increases slightly with the increase of penetration rate for RV drivers with Type I and Type IV response characteristics and under the decentralized arrangement of CAVs. The curve reaches the inflection point where the penetration rate is 50%, namely, where the acceleration difference begins to decrease significantly. This means that mixing a small number of CAVs with the RVs driven by these two types of drivers is of no help in improving the stability of the traffic flow. Only when the proportion of CAVs is more than half can some of them give full play to their intelligent features, hence alleviating the interference to a great extent. From the perspective of the whole fleet, the average of acceleration differences of the fleet is slightly lower for RV drivers with Type I and Type IV response characteristics than for the standard RV drivers. The reason is that Type I and Type IV drivers tend to be insensitive and conservative and maintain a low speed, so the overall acceleration fluctuation of the fleet is small during the starting process. For RV drivers with Type II response characteristics, the curve of the average of acceleration differences of the fleet with respect to the penetration rate of CAVs shows a similar trend to that for RV drivers with the standard type of response characteristics. In addition, the range of acceleration difference variation is wide, mainly because the Type II drivers tend to be more perceptive and pursue higher speeds. To sum up, for RV drivers with Type IV response characteristics, the whole fleet started more smoothly, which is consistent with the results of the stability analysis in Section 2.