## 6 Case Study  
The trained models (that use INF and SIG waveforms) can be used to evaluate the efficacy of different signal timing plans for an intersection. This can then provide trade-offs for choosing a variety of signal timing parameters, including different green phase splits.  
The 75 th percentile of wait times as MOE is used for the rest of this discussion. In general, adding more time to the major street results in increased wait time on the minor street. The tradeoff can be clearly seen in Figure 7. It shows a scatter plot of 75 th percentile of wait times for major vs. minor movements for different barrier-1 times (Figure 1). Based on this plot, a value of 60-70 s of green time may be appropriate as it minimizes the wait time on major street while not significantly impacting the wait time on the minor street. Of course a traffic engineer can look at these plots and other constraints to derive the optimal values. Given that our approach is computationally very inexpensive, optimal values can be derived separately for various hours of the day and day of the week combinations.  
Table 4 shows a case study on a real intersection in Seminole County, Florida. We varied the barrier-1 time (keeping the cycle length fixed) to understand its impact on the wait time for traffic on major streets (NBT and SBT). These results show that changing the barrier time from 80 s to 60 s can lead to a 25% improvement in wait time for the major direction without significantly affecting the wait times on the minor street.  
Rather than to provide one optimal signal timing plan, this framework can be extremely useful to practitioners to set green time splits for an intersection by understanding the trade offs for different hours of the day and days of the week.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Model** & **MSE** & **RMSE** & **MAE** \\ \hline FCN & \(1.5\times 10^{-4}\) & 0.0084 & 0.003 \\ RNN-FCN & \(2.2\times 10^{-4}\) & 0.0091 & 0.0032 \\ T-GCN [14] & \(1.2\times 10^{-4}\) & 0.008 & 0.0026 \\ STGCN [21] & \(1.5\times 10^{-4}\) & 0.0085 & 0.0031 \\ ST-RGAN [15] & \(5.4\times 10^{-3}\) & 0.0165 & 0.0095 \\ InterTwin (ours) & \(0.9\times 10^{-4}\) & 0.0076 & 0.0023 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Table comparing performance of different models. The input to the models are ADV, STP, and SIG. This suggests that our InterTwin model has better accuracy compared to other model architectures. MSE: Mean Square Error, RMSE: Root Mean Square Error, and MAE: Mean Absolute Error.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Model** & **Inputs** & **Train Error (MSE)** & **Test Error (MSE)** \\ \hline InterTwin & STP ADV SIG & \(0.9\times 10^{-4}\) & \(0.9\times 10^{-4}\) \\ InterTwin & INF SIG & \(2.0\times 10^{-4}\) & \(2.1\times 10^{-4}\) \\ FCN & STP ADV SIG & \(1.3\times 10^{-4}\) & \(1.5\times 10^{-4}\) \\ FCN & INF SIG & \(3.0\times 10^{-4}\) & \(3\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of model performance for different input parameters. This suggests that using STP, ADV has better accuracy compared to using INF waveform. The InterTwin model also has better accuracy. It is more practical to use INF along with SIG as INF waveforms are not affected by SIG and multiple signal timing parameters can be evaluated in parallel. Whereas, the other model (STP ADV SIG) can be useful to understand performance measures on recorded historical data.