# The Impact of Automated Vehicles on Road and Intersection Capacity
## 3 The Homogeneous Road Traffic Flow-Density Relationship
### Experimental Verification  
In order to verify the correctness of the derivation of homogeneous traffic flow on a road in a single environment, SUMO was used, to build a single-lane road environment under ideal conditions, and set a balanced traffic flow for simulation. The simulation effect is shown in Figure 2. The length of the road network is 1 km, and the simulation time is 3600 s. The number of vehicles loaded is set as the maximum (10,000 in this experiment). The vehicle speed is set from 0 to \(v_{0}\) and simulated successively. Since the SUMO simulation step size has a certain impact on the results, but the increase of the simulation step size will cause the exponential increase of the simulation time, this paper selected two simulation step sizes: 1 s, and 0.1 s. Table 4 shows the specific parameters of a manual vehicle, an ACC autonomous vehicle, and a CACC autonomous vehicle.  
The data are acquired by the detector, and then processed. The flow-density relationship of three kinds of vehicles, under different simulation steps, is shown in Figure 3.  
As can be seen from the figure above, as the simulation step length of SUMO becomes shorter, the simulation traffic volume keeps approaching the theoretical traffic volume. This is because the shorter the simulation step size is, the higher the simulation accuracy will be. Therefore, when the simulation step size is 1 s, there is a large error, and the average error is shown in Table 5. However, as the SUMO simulation step length becomes shorter, its simulation time increases exponentially. In order to balance the relationship between simulation error and simulation time, the simulation step size of 0.1 s is used for subsequent experiments.  
Figure 1: Flow-density diagram for a single vehicle composition.  
Figure 2: SUMO simulation diagram: single road traffic flow.  
Figure 3: Flow-density graphs of different types of vehicles, based on SUMO simulation.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Vehicle Type** & **Parameter Name** & **Parameter Value** \\ \hline  & color & green \\  & carFollowModel & lDM \\  & length & 5 \\  & accel & 1 \\ manual vehicle & decel & 2 \\  & minGap & 1.5 \\  & tau & 1.5 \\  & maxSpeed & \([1,v_{0})\) \\  & delat & 0 \\ \hline  & color & red \\  & carFollowModel & ACC \\  & length & 5 \\  & accel & 1 \\ ACC autonomous vehicle & decel & 2 \\  & minGap & 1.5 \\  & tau & 1.1 \\  & maxSpeed & \([1,v_{0})\) \\  & speedDev & 0 \\ \hline  & color & red \\  & carFollowModel & CACC \\  & length & 5 \\  & accel & 1 \\  & decel & 2 \\  & minGap & 1.5 \\  & tau & 0.6 \\  & maxSpeed & \([1,v_{0})\) \\  & speedDev & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Vehicle parameter settings in SUMO.  
By comparing fully human-driven vehicles, fully ACC autonomous vehicles, and fully CACC autonomous vehicles, it can be found that road traffic capacity is constantly increasing in theory and simulation experiments. In the simulation experiment, the maximum flow of a fully ACC autonomous driving vehicle, is 1.48 times that of a fully manual driving vehicle. The maximum flow rate of a fully CACC autonomous vehicle is 2.14 times that of a fully manual vehicle, which is close to the theoretical value. This proves that the model is correct.