## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Flow**} & \multirow{2}{*}{**Period** **(Hours)**} & \multirow{2}{*}{**Arrival Rate**} & \multirow{2}{*}{**Service Rate**} & \multirow{2}{*}{**Intensity (Flow Ratio)**} & \multirow{2}{*}{**Vehicle in the System**} & \multirow{2}{*}{**Spent in the System in**} \\  & & & & & **the System** & & **System (min)** \\ \hline
1. flow & 07–10 & 7.23 & 7.42 & 0.97 & 38.05 & 5.26 & 5.13 \\
2. flow & 07–10 & 7.03 & 8.21 & 0.86 & 5.96 & 0.85 & 0.73 \\
3. flow & 07–10 & 6.89 & 8.56 & 0.80 & 4.13 & 0.60 & 0.48 \\
1. flow & 11–14 & 6.32 & 7.02 & 0.90 & 9.03 & 1.43 & 1.29 \\
2. flow & 11–14 & 6.27 & 9.23 & 0.68 & 2.12 & 0.34 & 0.23 \\
3. flow & 11–14 & 6.15 & 12.32 & 0.50 & 1.00 & 0.16 & 0.08 \\
1. flow & 15–18 & 7.52 & 8.15 & 0.92 & 11.94 & 1.59 & 1.46 \\
2. flow & 15–18 & 7.45 & 14.23 & 0.52 & 1.10 & 0.15 & 0.08 \\
3. flow & 15–18 & 7.03 & 7.42 & 0.95 & 18.03 & 2.56 & 2.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The 1 day performance values at Kartal Sahilyolu Junction. Figure 10: Number of vehicles comes from all directions to the intersection. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Phase**} & \multirow{2}{*}{**Period** **(Hours)**} & \multirow{2}{*}{**Arrival Rate**} & \multirow{2}{*}{**Service Rate**} & \multirow{2}{*}{**Intensity (Flow Ratio)**} & \multirow{2}{*}{**Vehicle in the System**} & \multirow{2}{*}{**Spent in the System in**} \\  & & & & & **the System** & & **System (min)** \\ \hline
1. Phase & 07–10 & 5.32 & 5.45 & 0.98 & 40.92 & 7.69 & 7.51 \\
2. Phase & 07–10 & 2.29 & 2.65 & 0.86 & 6.36 & 2.78 & 2.40 \\
3. Phase & 07–10 & 2.98 & 4.52 & 0.66 & 1.94 & 0.65 & 0.43 \\
4. Phase & 07–10 & 3.52 & 6.3 & 0.56 & 1.27 & 0.36 & 0.20 \\
1. Phase & 11–14 & 4.72 & 5.63 & 0.84 & 5.19 & 1.10 & 0.92 \\
2. Phase & 11–14 & 0.75 & 1.2 & 0.63 & 1.67 & 2.22 & 1.39 \\
3. Phase & 11–14 & 2.74 & 2.96 & 0.93 & 12.45 & 4.55 & 4.21 \\
4. Phase & 11–14 & 4.23 & 5.52 & 0.77 & 3.28 & 0.78 & 0.59 \\
1. Phase & 15–18 & 8.69 & 10.35 & 0.84 & 5.23 & 0.60 & 0.51 \\
2. Phase & 15–18 & 1.17 & 2.1 & 0.56 & 1.26 & 1.08 & 0.60 \\
3. Phase & 15–18 & 3.52 & 3.68 & 0.96 & 22.00 & 6.25 & 5.98 \\
4. Phase & 15–18 & 4.56 & 6.85 & 0.67 & 1.99 & 0.44 & 0.29 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: The 10-day performance values of phases at Kartal–Sahilyolu intersection. We can calculate the results below for the 1 st phase according to the formulas given in Table 3. The number of vehicles obtained from the entrance sensors was 957 in a 3 h period for the 1 st phase, and the number of vehicles obtained from the output sensors in approximately 79 minutes of green time was 431. For the number of vehicles arriving per unit time, the arrival rate is as follows:  
\[\lambda=\frac{957}{180}=5.32 \tag{7}\]  
For the number of vehicles serviced per unit time, the service rate is as follows:  
\[\mu=\frac{430}{79}=5.45 \tag{8}\]  
For the intensity, the flow ratio is as follows:  
\[\rho=\frac{5.32}{5.45}=0.98 \tag{9}\]  
The number of the vehicles in the system is as follows:  
\[L_{s}=\frac{\lambda}{\mu-\lambda}=40.92 \tag{10}\]  
The mean time spent in the system and queue is as follows:  
\[W_{s}=\frac{\rho}{(1-\rho)\lambda}=7.69 \tag{11}\]  
\[W_{q}=\frac{\rho}{(\mu-\lambda)}=7.51 \tag{12}\]  
In the following Figure 11, the variation of the average vehicle durations obtained from the phases during three different periods of the day can be seen. The figure below demonstrates the average vehicle delays experienced in four different phases during three different periods of the day. The fluctuation of each phase in separate time zones indicates that the operating principles of the phases need improvement. In a well-planned intersection, the time differences between vehicle delays should not be too long due to the phase duration. For example, the average time spent by vehicles in the 1 st phase between 15:00-18:00 is 0.6 min, while in the 3 rd phase it goes up to 6.25 min.