## 5 Simulation and Results
### Simulation
#### 5.3.2 Scenario 2: Emergency Vehicle Priority  
In scenario 2, emergency vehicles (EVs), such as ambulances or fire trucks, must be prioritized so that they can pass directly through the traffic network. As in a real-life emergency, the Traffic Management Center (TMC) must adjust the traffic signal time dynamically to prioritize EV traffic while minimizing disruptions to normal traffic flow. The objective is to identify whether the system reduces EV travel and waiting times and maintains a reasonable flow of regular vehicles (RVs) while managing to reduce EV travel and waiting times.  
Based on Table 2, the hierarchical Stackelberg model significantly reduced the average travel time of emergency vehicles (EVs) to 150 s, a 50% reduction compared with the basic model. In the case of regular vehicles, the average number of queues is significantly shorter, with 11 hierarchical models and 25 base models, reflecting a 56 percent improvement in congestion management. Even though the standard Stackelberg model improves the performance of emergency vehicles, it leads to longer waiting times and queues for regular vehicles due to the absence of hierarchical priority. Using a hierarchical model, emergency vehicles receive priority without exacerbating the flow of normal vehicles, which is critical in real emergency situations.  
\begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Model** & \begin{tabular}{c} **EV Average Travel Time** \\ **(s)** \\ \end{tabular} & \begin{tabular}{c} **EV Average Waiting Time** \\ **(s)** \\ \end{tabular} & \begin{tabular}{c} **RV Average** \\ **Travel Time** \\ **(s)** \\ \end{tabular} & \begin{tabular}{c} **RV Average** \\ **Waiting Time** \\ **(s)** \\ \end{tabular} & \begin{tabular}{c} **Average Queue** \\ **Length** \\ **(Vehicles)** \\ \end{tabular} \\ \hline \begin{tabular}{c} Hierarchical \\ Stackelberg \\ Model \\ \end{tabular} & 280 & 60 & 320 & 80 & 10 \\ \hline \
\begin{tabular}{c} Standard \\ Stackelberg \\ Model \\ \end{tabular} & 300 & 65 & 340 & 90 & 12 \\ \hline
\begin{tabular}{c} Baseline Model \\ \end{tabular} & 350 & 80 & 380 & 110 & 15 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of EV and RV performance metrics under normal traffic conditions for three traffic management models.  
\begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Model** & \begin{tabular}{c} **EV Average Travel Time** \\ **(s)** \\ \end{tabular} & \begin{tabular}{c} **EV Average** \\ **Waiting Time** \\ **(s)** \\ \end{tabular} & \begin{tabular}{c} **RV Average** \\ **Travel Time** \\ **(s)** \\ \end{tabular} & \begin{tabular}{c} **Average Queue** \\ **Waiting Time** \\ **(s)** \\ \end{tabular} & \begin{tabular}{c} **Length** \\ **(Vehicles)** \\ \end{tabular} \\ \hline \begin{tabular}{c} Hierarchical \\ Stackelberg \\ Model \\ \end{tabular} & 150 & 20 & 350 & 100 & 11 \\ \hline \
\begin{tabular}{c} Standard \\ Stackelberg \\ Model \\ \end{tabular} & 200 & 40 & 380 & 120 & 14 \\ \hline
\begin{tabular}{c} Baseline \\ Model \\ \end{tabular} & 300 & 80 & 450 & 150 & 25 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparative performance of traffic control models under emergency vehicle priority conditions.