## 5 Conclusions  
This paper developed a distributed cooperation scheme for coordinating vehicles at signal-free intersections in a mixed traffic environment of AVs and MVs. The traffic conflict graph was constructed to recognize the communication topologies of the vehicles in conflict relationships, assuming that all AVs and MVs were connected and shared information in the CZ. We formulated the coordination issue into a multi-objective optimization problem, which was solved by optimizing the sum of weighted indexes of the conflict elimination, traffic mobility, and fuel economy in a prediction horizon synchronously. The future trajectories of AVs and MVs, as the inputs of the optimization model, were predicted by using the \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Demand 1**} & \multicolumn{2}{c}{**Demand 2**} \\ \cline{2-5}
**PRA** & **This Study** & **[PERSON] et al. [24]** & **This Study** & **[PERSON] et al. [24]** \\ \hline
100\% & 69.1 & 78.2 & 157.8 & 173.2 \\
70\% & 164.2 & 191.6 & 1062.3 & 1057.0 \\
50\% & 211.7 & 204.3 & 1552.1 & 1363.2 \\
30\% & 265.6 & 228.3 & 2521.6 & 2000.1 \\
0\% & 318.4 & 270.9 & 3256.2 & 2468.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of total delays (s) between the scheme of this paper and [PERSON] et al. [24] for the two demands under different penetration rates of AVs. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**\# Var.**} & \multicolumn{2}{c}{**\# Con.**} & \multicolumn{2}{c}{**\# Com.**} \\ \cline{2-7}
**PRA** & **This Study** & **[PERSON] et al. [24]** & **This Study** & **[PERSON] et al. [24]** & **This Study** & **[PERSON] et al. [24]** \\ \hline
100\% & 25.5 & 150.9 & 20.4 & 92.8 & 26.5 & 38.8 \\
70\% & 20.3 & 130.3 & 16.2 & 88.5 & 21.6 & 33.0 \\
50\% & 15.5 & 72.7 & 12.4 & 84.4 & 18.4 & 29.1 \\
30\% & 10.4 & 51.3 & 5.2 & 82.0 & 15.1 & 25.3 \\
0\% & 0 & 15.9 & 0 & 75.0 & 10.2 & 19.4 \\ \hline \hline \end{tabular} \# Var.: Mean number of variables per second. # Con.: Mean number of constraints per second. # Com.: Mean number of communications per second.  
\end{table} 
Table 7: Comparison of complexity parameters between the scheme of this paper and [PERSON] et al. [24] for demand 2 under different penetration rates of AVs. -vehicular longitudinal dynamic model and Krauss car-following model, respectively. To obtain the local optimal solutions, we presented a distributed receding horizon algorithm to calculate the optimal control inputs for each AV in the CZ. The simulations evaluated the effectiveness and superiority of the proposed scheme. The results showed that the proposed scheme outperformed the no-control operation by decreasing travel time by 29.7-45.5%, and reducing fuel consumption by 27.6-35.3% under 70-100% PRA. Compared to the fixed-time signal control strategy, the proposed scheme decreased travel time by 34.5-49.2% and reduced fuel consumption by 21.6-29.9% under 70-100% PRA. Additionally, according to the comparison results with the strategy of jointly optimizing the vehicle trajectory and signal timing, the proposed scheme performs better at high penetration rates of AVs and under not very dense traffic demand, and suffers less computational burden. Though this study considers a typical dual-lane intersection with four approaches, it can be easily extended to on-ramps of expressways or other types of intersections according to the conflict relationships. In addition, advanced driver guidance systems for MVs are expected to be integrated into the intersection coordination framework in future studies. Based on the prompt information of the system, the drivers of MVs can actively manipulate the vehicles to cross the intersection safely and smoothly. In addition, the combination of artificial intelligence methods and other types of optimization methods with the proposed strategy of this paper will be further considered in the future.