# Integrating Autonomous Vehicles (AVs) into Urban Traffic: Simulating Driving and Signal Control
## 3 Methodology
### Model Calibrations and Validation
#### 3.8.1 Average Queue Length Validation  
To validate the accuracy of the simulated average queue in this study, real-world data were collected during the red signal phase at different cycle times. Queue measurements were taken simultaneously across all lanes for each direction. The average queue length was calculated by summing the total number of vehicles across the three lanes, multiplying by the standard vehicle length of 4.481 m, and dividing by 3 to account for the three lanes, as presented in Tables 7-10.  
The calculated estimated average queue length was then compared with the simulated average queue from the PTV VISSIM microsimulation platform, as shown in Figure 11. This validation process ensured that the simulation accurately represented real-world conditions, enhancing the reliability of the study's findings and the subsequent analysis of the impact of AVs on traffic dynamics at the signalized intersection. The accuracy difference was calculated using the following formula:  
\[\textit{Accuracy Difference}(\%)=\left(\frac{\textit{Simulated Average Queue }-\textit{Estimated Average Queue}}{\textit{Estimated Average Queue}}\right)\times 100. \tag{10}\]  
The accuracy difference for the north-bound direction was around 6.30%. For the east-bound direction, the simulated average queue had an accuracy difference of 10.24%. In the south-bound direction, the accuracy difference was about 3.60%, while the west-bound direction showed an accuracy difference of 3.54%.  
Figure 10: Intersection design calibrated for no lane changes: each lane as a separate link. Source: PTV VISSIM model.  
Figure 9: Treating the east-bound and west-bound directions as three-lane roads. Source: PTV VISSIM model.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Bound** & \begin{tabular}{c} **Num. of** \\ **Lane** \\ \end{tabular} & \begin{tabular}{c} **Num. of Vehicles** \\ **at First Lane** \\ \end{tabular} & \begin{tabular}{c} **Num. of Vehicles** \\ **at Second Lane** \\ \end{tabular} & \
\begin{tabular}{c} **Num. of Vehicles** \\ **at Third Lane** \\ \end{tabular} &
\begin{tabular}{c} **Estimated Average** \\ **Queue (m)** \\ \end{tabular} \\ \hline North & 3 & 12 & 11 & 8 & 46.303 \\ North & 3 & 11 & 14 & 7 & 47.797 \\ North & 3 & 13 & 12 & 6 & 4  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Bound**} & **Num. of** & **Num. of Vehicles** & **Num. of Vehicles** & **Num. of Vehicles** & **Estimated Average** \\  & **Lane** & **at First Lane** & **at Second Lane** & **at Third Lane** & **Queue (m)** \\ \hline West & 3 & 14 & 13 & 11 & 56.759 \\ West & 3 & 13 & 12 & 12 & 55.265 \\ West & 3 & 15 & 12 & 9 & 53.772 \\ West & 3 & 13 & 15 & 6 & 50.784 \\ West & 3 & 12 & 13 & 11 & 53.772 \\ West & 3 & 14 & 15 & 8 & 55.265 \\ West & 3 & 17 & 13 & 6 & 53.772 \\ West & 3 & 15 & 14 & 8 & 55.265 \\ West & 3 & 14 & 13 & 9 & 53.772 \\ West & 3 & 13 & 11 & 12 & 53.772 \\ West & 3 & 12 & 13 & 9 & 50.784 \\ West & 3 & 14 & 15 & 6 & 52.278 \\ West & 3 & 13 & 12 & 12 & 55.265 \\ West & 3 & 14 & 13 & 11 & 56.759 \\ West & 3 & 13 & 11 & 9 & 49.291 \\ West & 3 & 12 & 13 & 13 & 56.759 \\ West & 3 & 11 & 10 & 9 & 44.81 \\ West & 3 & 13 & 11 & 8 & 47.797 \\ West & 3 & 12 & 11 & 13 & 53.772 \\ \hline \hline \end{tabular}
\end{table}
Table 10: West-bound average queue length real-world data.  
Figure 11: Comparison of estimated and simulated average queue length for all directions. Source: processed by authors.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Bound**} & **Num. of** & **Num. of Vehicles** & **Num. of Vehicles** & **Num. of Vehicles** & **Estimated Average** \\  & **Lane** & **at First Lane** & **at Second Lane** & **at Third Lane** & **Queue (m)** \\ \hline South & 3 & 13 & 13 & 7 & 49.291 \\ South & 3 & 15 & 11 & 8 & 50.784 \\ South & 3 & 11 & 14 & 9 & 50.784 \\ South & 3 & 17 & 14 & 4 & 52.278 \\ South & 3 & 13 & 11 & 9 & 49.291 \\ South & 3 & 14 & 12 & 7 & 49.291 \\ South & 3 & 13 & 14 & 7 & 50.784 \\ South & 3 & 14 &