# Steady-Speed Traffic Capacity Analysis for Autonomous and Human-Driven Vehicles
## 4 Results
### Space Headway, Time Headway, Density, and Capacity Analysis  
The average space headways are calculated using Equation (1), as explained in the methodology section. The length of each vehicle presented in Table 1 is summed to the average clearance of the corresponding vehicle to obtain the average space headway. However, the human-driven data are collected from randomly selected vehicles detected by the lidar device while driving on roads. Therefore, it is assumed that the length of these vehicles equals the average of the selected ACC vehicles to ensure a fair comparison. One important reason behind this is that the detected human-driven vehicles were either sedans or SUVs, which are in the same category as the vehicles used in our experiment. Furthermore, the average time headways are calculated using Equation (2). In this equation, each average space headway is divided by the corresponding constant driving speed employed during the experiment. This derived parameter holds significant importance in our study, serving as a crucial metric for comparison with results documented in the existing literature. The incorporation of this normalized time headway allows us to contextualize and benchmark our findings against established research, providing a comprehensive understanding of how our experiment aligns with and contributes to the broader body of knowledge in the field. An example calculation of the average space headway and average time headway for Subaru at a speed of 30 km/h is illustrated below. The other experiment results are provided in Table 3.  
\[\text{Avg.Space headway}=10,537+4690=15,227\text{ mm}=15.227\text{ m}, \tag{5}\]  
\[\text{Avg.Time headway}=\frac{15.227}{30/3.6}=1.827\text{ s}, \tag{6}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Speed [km/h]** & **Human-Driven Clearance [mm]** & **Subaru Clearance [mm]** & **Volvo Clearance [mm]** & **VW Clearance [mm]** \\ \hline
30 & 7514 & 10,537 & 7985 & 12,410 \\
40 & 9846 & 11,732 & 12,124 & 14,586 \\
50 & 12,420 & 14,000 & 14,076 & 16,951 \\
60 & 15,156 & 15,607 & 16,660 & 19,174 \\
70 & 17,031 & 18,487 & 20,015 & 21,687 \\
80 & 19,960 & 20,547 & 22,557 & 24,135 \\
90 & 23,552 & 25,480 & 24,708 & 26,464 \\
100 & 25,909 & 26,503 & 29,826 & 28,452 \\
110 & 27,211 & 27,247 & 32,538 & 28,876 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of average clearance for all tested vehicles. Figure 14: Summary of average clearance of tested vehicles. The final phase of this study involves the calculation of traffic density and traffic capacity achieved by the tested vehicles by using Equations (3) and (4). The two indicators play a crucial role in understanding and managing traffic flow on roads and highways. The distribution of these indicators through multiple constant driving speeds performed by humans and AVs will certainly clarify the advantages of one driving method over the other. Additionally, it will differentiate the performance of ACC sensors used during the empirical test. The results presented in Table 4 indicate that ACC-equipped vehicles achieved lower percentages of densities and capacities than human-driven vehicles. Although, in a few cases, the ACC sensors might yield similar capacity values, they never fall below the capacities obtained by humans. The range between the minimum decrease and maximum decrease in capacity caused by using ACC systems is 0.8-28.2%, in which the minimum percentage is obtained at the highest driving speed, while the maximum percentage is obtained at the lowest speed. Sample calculations of traffic density and capacity for Subaru at 30 km/h are shown as follows:  
\[\text{Avg.Density}=\frac{1000}{15.227}=65.67\ \text{veh/km}, \tag{7}\]  
\[\text{Avg.Flow (Capacity)}=65.67\times 30=\ \text{veh/h}, \tag{8}\]