## 5 Simulation and Results
Initially, \(\alpha\) (delay minimization) decreased rapidly from 0.9 to 0.25, while \(\beta\) (EV priority) increased from 0.1 to 0.75 by the 30 th epoch, highlighting the shift to priority for emergency vehicles. The fairness weight \(\gamma\) gradually decreased from 0.8 to about 0.15, reflecting a reduction in the emphasis on fairness, as other objectives are at the forefront. Stabilization points are marked with vertical lines, and all weights converge within 30 epochs. The initial dynamics highlight a sharp increase in \(\alpha\) and \(\beta\), and a steady decline in \(\gamma\). These convergence models show that the optimization process has succeeded in navigating the differences between competing objectives. The final weight distribution (moderate \(\alpha\), high \(\beta\), low \(\gamma\)) implies that the system prioritizes emergency vehicles while accepting some delays for regular traffic, with relatively relaxed fairness constraints. All parameters are stable within 30 epochs, showing efficient convergence. The practical values of parameters \(\alpha\) (delay reduction), \(\beta\) (emergency vehicle priority), and \(\gamma\) (fairness penalty) must be determined in relation to specific operational contexts, policy priorities, and dominant traffic dynamics. In the case of delay minimization parameter \(\alpha\), a value between 0.5 and 0.7 is generally recommended. This emphasizes the overall efficiency of the network and is particularly suitable in situations where congestion management is important, but there is no immediate need for emergency vehicles (EVs). When the efficiency of the entire system is a priority, \(\alpha\) should be relatively high. The parameter \(\beta\), which controls the priority of emergency vehicles, is best kept between 0.2 and 0.5 in normal traffic operations. In emergency situations, however, \(\beta\) should be increased considerably and could reach values between 0.6 and 0.9. This ensures that EVs receive sufficient priority without unnecessarily disrupting regular traffic in emergency  
Figure 4: Convergence dynamics of multi-objective weights in optimization process. Figure 3: Evaluation of trade-offs between emergency vehicle prioritization and fairness in traffic management systems. situations. The fairness penalty parameter \(\gamma\) is usually selected between 0.1 and 0.4. A higher \(\gamma\) reflects a stronger emphasis on an equitable distribution of resources, minimizing the differences in travel time between different types of vehicles. This is especially relevant in urban environments where social equity or public transport vehicles (such as buses) are part of the traffic ecosystem. However, in emergency situations where the priority routing is more important, \(\gamma\) should be reduced to prevent it from reversing the priority expected. Under regular traffic conditions, parameters such as \(\alpha=0.6\), \(\beta=0.3\), and \(\gamma=0.2\) can be effective in maintaining a balanced balance between network efficiency, emergency preparedness, and fairness. On the other hand, in emergency scenarios where emergency vehicles (EVs) need priority routing, weights are adjusted to emphasize response by adjusting \(\beta\) to 0.8, reducing \(\gamma\) to 0.1, and moderate \(\alpha\) to about 0.4. In cases of severe congestion, when the stabilization of the overall network flow becomes important, higher priority is placed on the minimization of delay by setting \(\alpha\) to 0.7, \(\beta\) to 0.2, and \(\gamma\) to 0.3. In contexts where equity considerations are of paramount importance, the Fairness component ( \(\gamma=0.4\)) is given more weight, and \(\alpha\) and \(\beta\) are properly adjusted to maintain system balance. These configurations reflect the adaptability of the model to various operational objectives and traffic environments. In adaptive systems, these parameters can be continuously adjusted with real-time feedback or reinforcement learning.