## 4 Experiment and Results
### Analysis of Results Considering Different Autonomous Vehicle Penetration Rates  
With the rapid development of autonomous driving technology, the proportion of autonomous vehicles in future transportation systems is expected to gradually increase. This trend will impact traffic flow characteristics, carbon emissions, and traffic efficiency. Therefore, it is necessary to analyze and compare the optimization effects of signal control schemes under different autonomous vehicle penetration rates. Table 11 presents global autonomous vehicle penetration rate data for 2023, and the market penetration rate of autonomous vehicles is expected to continue to rise in the future [54]. Based on this, this study assumes that the growth in autonomous vehicle market penetration will come primarily from autonomous electric vehicles, while the share of other vehicle types will decrease. A traffic flow of 4576 pcu/h is set, with manually driven vehicles modeled using the IDM model and autonomous vehicles modeled using the CACC model. Mixed traffic flows with 75%, 50%, and 25% connected vehicle penetration rates are randomly generated for testing. Additionally, the optimization effects of various signal control schemes are compared under two non-mixed traffic flow conditions: 100% and 0% penetration rates.  
To accurately illustrate the performance differences of signal control schemes under varying penetration rates, Figure 12 shows that traditional signal control schemes, such as  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Control Method**} & \multicolumn{3}{c}{**Average CO2 Emissions (g)**} \\ \cline{2-4}  & **2400 pcu/h** & **3600 pcu/h** & **4800 pcu/h** \\ \hline Webster signal timing & 190.55 & 200.30 & 218.26 \\ Actuated signal timing & 188.18 & 198.14 & 221.13 \\ DQN-CO2 Reduction & 182.78 & 190.12 & 213.93 \\ D3 QN-CO2 Reduction & 178.28 & 183.12 & 212.01 \\ Rainbow DQN_AM-Time & 178.65 & 186.26 & 204.85 \\ Rainbow DQN_AM-CO2 Reduction & 175.18 & 180.53 & 192.02 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Average vehicle CO2 emissions at different traffic intensities.  
Webster and actuated signal control, perform less effectively in terms of average vehicle waiting time optimization in mixed traffic environments compared with non-mixed traffic environments. This is because, in mixed traffic conditions, especially under low penetration rates, connected autonomous vehicles cannot form an effective collaborative driving environment. In contrast, the proposed scheme in this study demonstrates more stable control strategies in mixed traffic environments. As the penetration rate increases, the average vehicle waiting time decreases. Specifically, at a 50% penetration rate, the average waiting time is 19.63 s, which is 6.35% lower compared with the scheme with the same algorithm but a different reward function, 14.20% lower compared with the scheme with the same reward function but a different algorithm, and 25.78% lower compared with the actuated signal control scheme.  
Figure 13 shows the trend of average vehicle CO\({}_{2}\) emissions under different penetration rates. Similar to Figure 12, the proposed optimization scheme performs best at a 50% penetration rate, where the average vehicle CO\({}_{2}\) emissions are 167 g. Compared to the Rainbow DQN_AM-Time scheme, D3 QN-CO2 Reduction, and the actuated signal timing scheme, emissions are reduced by 4.58%, 6.60%, and 6.97%, respectively. This is because, in a mixed-traffic environment, connected autonomous vehicles require frequent acceleration and deceleration, and other control schemes fail to learn the correct strategies effectively. It is noteworthy that at a 100% penetration rate, the CO\({}_{2}\) emissions component in the reward function is smaller, and thus, the performance difference between the proposed scheme and the Rainbow DQN_AM-Time scheme is not significant.