# Virtual Belt Algorithm for the Management of Isolated Autonomous Intersection
## 7 Numerical Simulation
### Simulation B  
In this simulation, several scenarios are constructed to show the performance of the VB algorithm on high traffic load. The MA algorithm and traffic lights are used as comparison. The mean traffic load of each road varies from 500 vehicle/h to 3000 vehicle/h in the simulation.  
Figure 25 shows the maximum travel times of the intersections managed by VB, MA, TLA, TLB and TLC in 1800 s. The maximum travel times of the scenarios using VB algorithm are further plotted in Figure 26. Figure 25 suggests that with the growing of traffic load, the maximum travel times of the intersection controlled by TLA, TLB and TLC increase remarkably. The maximum travel times exceed 500 s on the traffic load of 2000 vehicle/h. The MA algorithm shows better than the TL algorithm just on the traffic load of 500 vehicle/h and 1000 vehicle/h. The maximum travel time shows a notable increase on the  
before real-time application, the complexity of the intersection will not affect the real-time performance of the VB algorithm. When an intersection is modeled as several VBs, the online algorithm can be utilized to plan the trajectories of waiting vehicle to pass the intersection. The core of the online algorithm is that, based on the constructed VBs, several candidate trajectories can be selected for each approaching CAV. Thus, there are more opportunities can be provided by the VB algorithm for an approaching CAV through the intersection. Since the constraints of the speed and acceleration of CAVs are considered, the online algorithm can be used for different kinds of vehicles on road, which guarantees the flexible of the VB algorithm to common vehicles. In the simulation, instead of a homogeneous intersection with a symmetrical structure, an inhomogeneous intersection with a general structure is considered to represent a general case. The counts of VBs in different roads are not the same and there are overlaps among these VBs. Moreover, the considered CAVs are of different dynamic performances, such as maximum speed and maximum acceleration. The successful application of the proposed VB algorithm indicates that this algorithm is effective to manage such a general intersection.  
There are three research directions for the future investigation: The first one is to apply the VB algorithm to other types of intersection, such as roundabout and 3-way intersection. The second one is to extend the VB algorithm to the management of multi-intersection. The third one is to investigate the VB algorithm with the fuel economy performance.  
Conceptualization, C.B. and G.Y.; methodology, C.B.; validation, C.B., G.Y. and L.X.; writing--original draft preparation, C.B.; writing--review and editing, N.Z.; supervision, G.Y.  
This research was funded by National Natural Science Foundation of China, grant number 51575103, U1664258, National Key R&D Program in China, grant number 2016 YFB0100906, 2016 YFD0700905, Foundation of State Key Laboratory of Automotive Simulation and Control, grant number 20160112, Scientific Research Foundation of Graduate School of Southeast University and Southeast University Excellent Doctor Degree Thesis Training Fund, grant number YBJJ1703, YBJJ1704.  
The authors wish to express their gratitude to the anonymous reviewers and the associate editor for their rigorous comments during the review process.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} CAV & Connected and Autonomous Vehicle \\ CVG & Collided Virtual Grid \\ CVGR & Collided Virtual Grid Record \\ DSRC & Dedicated Short Range Communication \\ MA & Multi-Agent \\ IMU & Intersection Management Unit \\ RCAV & Request of a CAV \\ TLA & Traffic Light with the green time of 17 s \\ TLB & Traffic Light with the green time of 22 s \\ TLC & Traffic Light with the green time of 27 s \\ VB & Virtual Belt \\ VG & Virtual Grid \\ VP & Virtual Path \\ \end{tabular}