## 5 Simulation and Results
### Interpretation  
1. Explicit priority and separation of objectives: the hierarchical structure allows a clear priority for the emergency vehicle (EV) while at the same time optimizing the route for the regular vehicle (RV). This decoupling ensures that the priority of EVs is not at the expense of excessive RV delays, as the Traffic Management Centre (TMC) dynamically balances the two objectives through utility functions (Equations (1)-(3)). Tables 1-3 show this balance, showing that the EV travel time has been significantly reduced (e.g., 50% of the improvement in Scenario 2) and that there has been no disproportionate  
\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} & 150 & 20 & 350 & 100 & 21 \\ \hline \
\begin{tabular}{c} Standard \\ Stackelberg \\ Model \\ \end{tabular} & 200 & 40 & 380 & 120 & 25 \\ \hline
\begin{tabular}{c} Baseline \\ Model \\ \end{tabular} & 300 & 80 & 450 & 150 & 33 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Evaluation of traffic control strategies under peak congestion: Impact on emergency and regular vehicle performance.  
increase in RV delays (e.g., only 33% of the RV wait time in Scenario 2 has been extended compared to 67% of baseline).
2. Real-time adaptability: Hierarchy allows real-time adjustments by distributing decision-making between levels. For example, TMC acts as a global coordinator (upper level), and EVs and RVs react locally (lower level). This avoids the rigidity of single-level models where centralized control struggles to adapt to local emergency or congestion.
3. Fairness through hierarchical feedback: The inclusion of fairness indicators (Gini coefficients, skewness) in the algorithm ensures that resource allocation is monitored and iteratively adjusted. The hierarchical structure fundamentally supports this, allowing the TMC to penalize unfair results (e.g., through the Fairness Penalty in Equation (1) and to redistribute signal timing or lane priority. This explains why all scenarios achieve the Gini values below (approximately 0) in the model compared to a non-hierarchical approach.
4. Mitigation of conflict propagation: In the traditional Stackelberg or Nash model, conflicts between EVs and RVs often spread uncontrollably, leading to congestion. Hierarchical models mitigate this by limiting EV decisions to priority only critical routes, while RVs maximize the remaining resources. This is demonstrated in scenario 3 (peak congestion), where hierarchical models reduce queue length by 44% compared to baseline models, whereas standard Stackelberg models (lack of hierarchy) do not manage spillover effects as effectively.