## 5 Conclusions and Future Work  
In this study, a Conflict Duration Graph-based (CDG-based) coordination method for CAVs at signal-free intersections was proposed. The major contributions of this study can be summarized as follows:  
1. We employed a CDG inspired by a Gantt chart to represent the crucial factors for scheduling in CAVs trajectories. After that, we established a CDG-based framework of conflict detection and resolution, which can show the occupation state of the conflict points and identify the existence of collision accidents in a visualization manner. 2. Considering that the number of vehicles entering the intersection at the same time will increase along with the traffic flow, we proposed a conflict resolution method for the multi-vehicle collision to ensure traffic safety and efficiency, which consists of a Speed Control-based Intersection Coordination Model (SICM) model and a Geometric Translation-based Intersection Coordination Algorithm (TICA). The SICM model takes the design speed as a decision variable to reduce the difficulty of controlling vehicle speed throughout and identifies constraints among multi-vehicle collision scenarios. The TICA algorithm allocates the spatial and temporal resources of intersections by translating time blocks into the form of combinatorial optimization in order to pursue higher computing efficiency and shorter computing time. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**ID**} & **Arrival** & **Initial** & **Modified** & **Driving** & **Length** & **Arrival** & \multicolumn{3}{c}{**Serial Number**} \\  & **Time** & **Speed** & **Speed** & **Strategy** & **Lane** & & **of Conflict Points** & \\ \hline
61 & 122.50 & 11.97 & 25.09 & Slow down & 5 & S2 & 4 & 5 & 6 & 7 \\
62 & 123.37 & 44.89 & default (30) & Stay constant & 5 & W2 & 1 & 2 & 3 & 4 \\
63 & 123.60 & 44.40 & default (30) & Stay constant & 5 & E2 & 7 & 8 & 9 & 10 \\
64 & 126.94 & 23.53 & 25.02 & Slow down & 5 & W1 & 12 & 16 & 15 & 8 \\
65 & 126.97 & 48.96 & 25.38 & Slow down & 5 & N2 & 10 & 11 & 12 & 1 \\
66 & 133.43 & 48.19 & 26.35 & Slow down & 3 & N1 & 9 & 15 & 14 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Motion information in multi-vehicle collisions. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Test** & **Amount of** & **Average** & **Maximum** & **Average** & **Maximum** & **Total Delay** \\
**Scenario** & **Collisions** & **Speed (km/h)** & **Transit Time (s)** & **Transit Time (s)** & **Delay Time (s)** & **Time (s)** \\ \hline
90A & 2\(\rightarrow\)0 & 34.14\(\rightarrow\)33.84 & 26.45\(\rightarrow\)33.69\(\uparrow\) & 24.19\(\rightarrow\)24.50\(\uparrow\) & 8.90 & 25.31 \\
90B & 6\(\rightarrow\)0 & 34.54\(\rightarrow\)34.22 & 26.45\(\rightarrow\)32.06\(\uparrow\) & 24.0  
* We developed a MATLAB-based simulation platform and designed 12 test scenarios to validate the proposed method. This platform provided a more flexible choice for integrated development than commercial traffic simulation software. The comparison results before and after speed control showed that the proposed algorithm can resolve all the collisions at some expense to traffic efficiency. On the whole, the signal-free traffic mode is superior to the traditional signal-controlled mode with significant growth in the road capacity and a decline in transit delay per vehicle. Further, vehicles can cross signal-free intersection areas without stopping in low to medium traffic flows. However, some limitations were observed in the present work:  
* The study could not address the coordination problem in mixed traffic flow and a partial CAV environment, which consists of CAVs, human-driven vehicles, pedestrians, etc. In more realistic situations, the other road users will also occupy the temporal-spatial resource and their trajectories will form some new overlapping points with the vehicle routes. Thus, we need to add some dynamic conflict points to the conflict-duration graph.