## 3 Proposed Approach and Methodology
### Role of Rewards in Standard and Rerouting Scenarios
In the standard scenario, most vehicles go straight; in the symmetric rerouting scenario, traffic is redistributed via turns; and in the asymmetric routing scenario, a priority direction is given precedence. We began with a typical arterial scenario, the \"standard\" where 75% of vehicles travel straight and 25% turn. However, when traffic demand exceeds capacity, the system activates the rerouting \"symmetrical\" scenario,\" where 75% of vehicles are redirected to turn, helping balance traffic load. An \"asymmetrical\" rerouting scenario was also explored, where one direction is prioritized over the other, allowing for greater flow in one direction and reducing traffic in the opposite direction. Rerouting is applied exclusively to the prioritized direction. To further optimize traffic in rerouting scenarios, upstream anti-bottlenecking and smart rerouting techniques are employed, adjusting intersection control in real time based on congestion levels and dynamically assigning priority to alternative routes. To integrate the three traffic scenarios (\"standard\", \"symmetrical rerouting\", and \"asymmetrical rerouting\") into the reward equation (Equation (2)), the reward was adjusted dynamically to account for the specific goals and constraints of each scenario. This was achieved by introducing scenario-specific weights, \(\omega\), that adjusts the priority of the reward based on the current traffic scenario or parameters into the reward function, ensuring that the policy aligns with the objectives of each traffic condition. Below is a modified version of the reward equation:  
\[\mathrm{r_{t}}=\omega p_{vch}(\mathrm{atwt}_{vch,t-1}-\mathrm{atwt}_{vch,t})+ \omega p_{ped}\Big{(}\mathrm{atwt}_{ped,\ t-1}-\mathrm{atwt}_{ped,t}\Big{)} \tag{5}\]  
To accommodate varying traffic conditions, the reward function incorporates scenario-specific weights (\(\omega\)) and parameters (\(p_{vch}\) and \(p_{ped}\) ). The weights are dynamically adjusted based on the current traffic scenario:  
_Standard Scenario:_\(\omega=1\) serves as the baseline, ensuring a balanced prioritization of vehicles (\(p_{vch}\)) and pedestrians (\(p_{ped}\)). _Symmetrical Rerouting:_\(\omega>1\) increases responsiveness to congestion, with \(p_{vch}\) adjusted to prioritize turning movements, reducing oversaturation of straight-through lanes. _Asymmetrical Rerouting:_\(\omega\) varies across directions to reflect priorities, e.g., \(\omega=1.5\) for the prioritized direction and \(\omega=0.8\) for the less-prioritized direction. In this scenario, \(p_{vch}\) is weighted more heavily in the prioritized direction. These weights and parameters are selected using a combination of empirical testing and domain-specific traffic management knowledge, ensuring the system's adaptability to real-world traffic challenges and referring to our previous work [22; 24]. The inclusion of \(\omega\) allows the reward function to adapt to the needs of the traffic scenario dynamically. By varying \(p_{vch}\) and \(p_{ped}\), the system can optimize for different priorities, such as faster vehicle movement in high-demand scenarios or equitable pedestrian crossings in normal conditions. This approach ensures that the reinforcement learning agent learns policies tailored to the specific challenges and goals of each traffic scenario, improving overall system performance.