## 6 Conclusions and Future Work  
This study proposes a hierarchical Stackelberg model for traffic management to address the complex challenges of prioritizing emergency vehicles (EVs) while maintaining fairness and minimizing delays for ordinary vehicles (RVs). This approach extends the traditional Stackelberg framework by introducing a multilevel decision-making structure in which the Traffic Management Center (TMC) is the leader, followed by emergency vehicles as the first and regular vehicles as the second. A hierarchical traffic control structure is more effective in situations involving emergency vehicles. Based on the simulation results, the hierarchical Stackelberg model is superior to the traditional one. Across all traffic scenarios, including normal conditions, emergency vehicle priority, and peak traffic congestion, the model consistently reduces the average travel time and waiting time for emergency vehicles. By including fairness metrics like Gini and Skewness coefficients, regular vehicle delays remained within acceptable bounds, as reflected in fairness metrics if emergency vehicles were prioritized. This model improves overall traffic flow, reduces congestion, and addresses the often overlooked issue of distributing resources equally among different types of vehicles.  
Critical direction for future research includes the inclusion of unexpected infrastructure disturbances such as bridge failures, accidents, and scheduled road closures [29, 30]. These disturbances can have a significant impact on travel behavior and system reliability, thereby reducing network resilience. Included in this dynamic, the model would better capture the uncertainties of the real world and improve its operational application. Another promising extension is the explicit integration of road safety into the objective function of the model [31, 32], in addition to efficiency and fairness. Safety has economic, social and ethical dimensions, and ignoring it can ignore critical aspects of system performance. The inclusion of penalties for crash risk could provide a more comprehensive assessment of traffic management strategies.  
**Author Contributions:** Conceptualization, A.G. and N.B.H.; methodology, M.A. and A.G.; software, M.A.; validation, A.G., M.A. and A.E.; formal analysis, A.G.; resources, Z.K.; writing--original draft preparation, A.G.; writing--review and editing, A.E. and Z.K.; visualization, M.A.; supervision, N.B.H. All authors have read and agreed to the published version of the manuscript.  
**Funding:** The authors extend their appreciation to the Deanship of Scientific Research at Northern Border University, Arar, KSA, for funding this research work through the project number \"NBU-FFR-2025-2441-01\".  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
**Acknowledgments:** Open Access funding provided by the Qatar National Library.  
**Conflicts of Interest:** The authors declare no conflicts of interest.