## Materials and Methods
### Dynamic Signal Timing Method for Intersections  
The signal operating modes used in signalized intersections are the most important parameters affecting the performance of the intersections. As mentioned in Section 2.1.1, signal models can have fixed, semi-constant, or fully actuated (dynamic) modes. These modes are extremely important in the efficiency of intersections and in managing traffic.  
In this study, the intersections chosen for the model study are the intersections that can provide data, thanks to the sensors that they have. Therefore, values such as time between phases or currents, circuit duration, saturated flow, red, green, and protection times are quite sufficient to propose a new model. Green times are critical values that affect queuing in the junction arms or the discharge of the queue lengths. As a result of the analysis and the gained outputs, a calculation method for effective green periods is proposed in this study. It is aimed to calculate the effective green times and to give more time to the  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Unit** & **Description** \\ \hline \(k\) & - & Number of incoming vehicles \\ \(t_{i},t_{i+1}\) & Entry times of the vehicles to & Arrival times of the vehicles \\ \(l_{i}\) & the intersection & Phases of intersections \\ \(N_{t}\) & s & Difference between arrival times \\ \(S_{t}\) & s & Difference between service times \\ \(Q_{kl}\) & - & Number of vehicles arriving per unit time \\ \(Q_{sl}\) & - & This parameter is also shown with \(\lambda\) on queuing models. \\ \(Q_{sl}\) & - & Number of vehicles serviced per unit time \\ \(\varphi_{l}\) & - & This parameter is also shown with \(\mu\) on queuing models. \\ \(\gamma\) & - & Saturation flow rate (maximum flow rate highest traffic intensity) \\ \(\varphi_{d}\) & - & The highest current density is seen during the day. \\ \hline \hline \end{tabular}
\end{table}
Table 4: Description of relevant variables.  
Figure 7: Flow diagram of dynamic phase sequences model for a signalized intersection.  
busy branches by using the critical current values calculated over the number of vehicles taken from the intersection connecting arms with the proposed signal durations calculation method. Therefore, it is aimed to use proportionally more regular green time in the periods when the connected arms are intense and to prevent unbalanced waiting losses.  
In the effective green time calculation method, the critical current value calculated in the dynamic phase sequence model suggested in Section 2.5.2 and the time created by the intersection at the end of each cycle were taken as the main input.  
The number of vehicles arriving per unit time:  
\[Q_{kl}=\frac{Vehicle_{n}\times 60}{N_{t}} \tag{5}\]  
The number of vehicles passing through the traffic light point per unit time:  
\[Q_{sl}=\frac{Vehicle_{s}\times 60}{S_{t}} \tag{6}\]  
By finding the ratio of these values to the saturated critical flow, it is aimed to distribute the green times proportionally to all four arms. The flow of the method is given in Table 5. As can be seen from the table below, the new critical value is determined by comparing the flow intensities with the highest saturated flow value at the end of the day.