# Integrated Spatio-Temporal Graph Neural Network for Traffic Forecasting
## 4 Experimental Analysis
### Dataset Description
The Figure 4 bar chart illustrates the percentage improvement of the ISTGCN (proposed) model over other models (USTGCN, LSGCN, Graph WaveNet, ASTGCN, and DCRNN) across three evaluation metrics--RMSE, MAE, and MAPE--over prediction intervals of 15, 30, and 45 min. ISTGCN consistently outperforms its competitors, demonstrating substantial improvements in reducing RMSE and MAE, which measure numerical accuracy and error magnitude, respectively. MAPE improvements, though slightly lower, highlight ISTGCN's reliability in minimizing percentage errors. The highest gains are observed for the 15 min interval, particularly for RMSE and MAE, with the improvements slightly diminishing for longer horizons, as expected in time-series predictions. Overall, the ISTGCN proves to be robust and effective, delivering consistently better predictive performance \begin{table}
\begin{tabular}{l l c c c c c c c c c} \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**15 min**} & \multicolumn{4}{c}{**30 min**} & \multicolumn{4}{c}{**45 min**} \\ \cline{3-10}  & & **RMSE** & **MAE** & **MAPE** & **RMSE** & **MAE** & **MAPE** & **RMSE** & **MAE** & **MAPE** \\ \hline \multirow{5}{*}{PeMSD7} & ISTGCN [Proposed] & **1.03** & **1.87** & **3.67** & **1.60** & **2.74** & **3.87** & **2.09** & **2.34** & **4.97** \\ \cline{2-10}  & USTGCN [36] & 2.01 & 3.48 & 4.67 & 2.46 & 4.43 & 5.96 & 2.89 & 5.07 & 7.00 \\ \cline{2-10}  & LSGCN [35] & 2.22 & 3.98 & 5.14 & 2.96 & 5.47 & 7.18 & 3.43 & 6.39 & 8.51 \\ \cline{2-10}  & Graph WaveNet [37] & 2.17 & 3.87 & 4.85 & 2.90 & 5.40 & 6.86 & 3.23 & 6.29 & 8.06 \\ \cline{2-10}  & ASTGCN [34] & 2.85 & 5.15 & 7.25 & 3.35 & 6.12 & 8.67 & 3.70 & 6.77 & 9.73 \\ \cline{2-10}  & DCRNN [38] & 2.22 & 4.25 & 5.16 & 3.04 & 6.02 & 7.46 & 3.64 & 7.24 & 9.00 \\ \hline \multirow{5}{*}{PeMSD8} & ISTGCN [Proposed] & **0.98** & **1.87** & **1.06** & **1.12** & **1.65** & **1.45** & **1.08** & **2.97** & **1.98** \\ \cline{2-10}  & USTGCN [36] & 1.14 & 2.15 & 2.07 & 1.25 & 2.58 & 2.35 & 1.52 & 3.01 & 2.88 \\ \cline{1-1} \cline{2-10}  & LSTGCN [35] & 1.16 & 2.45 & 2.24 & 1.46 & 3.28 & 3.02 & 1.66 & 3.75 & 3.51 \\ \cline{1-1} \cline{2-10}  & ASTGCN [34] & 1.49 & 3.18 & 3.16 & 1.67 & 3.69 & 3.59 & 1.81 & 3.92 & 3.98 \\ \cline{1-1} \cline{2-10}  & DCRNN [38] & 1.17 & 2.59 & 2.32 & 1.49 & 3.56 & 3.21 & 1.71 & 4.13 & 3.83 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison analysis with another model. across both short and moderately extended time intervals, making it a strong choice for real-world applications requiring accurate and reliable forecasts. \[Improvement\ \%=\frac{(Performance\ of\ Other\ model-Performance\ of\ ISTGCN)\times 100}{Performance\ of\ other\ model}\]  
The graph is based on a mathematical formula that calculates the percentage improvement of the ISTGCN (proposed) model compared to other models. The formula measures the relative reduction in error achieved by ISTGCN for metrics such as RMSE, MAE, and MAPE. Specifically, the improvement percentage is determined by subtracting ISTGCN's error value from the error value of another model, dividing this difference by the other model's error value, and then multiplying the result by 100 to express it as a percentage. This calculation is performed for each metric across three time intervals (15, 30, and 45 min) and for both datasets (PeMSD7 and PeMSD8). The resulting percentage improvements are then plotted in the graph to highlight ISTGCN's consistent superiority over its counterparts in minimizing errors, particularly for shorter time intervals and across all metrics (Figures 5-10). ISTGCN stands out significantly by achieving the lowest error rates across all metrics and time intervals, making it the best-performing model. For example, on the PeMSD7 dataset, ISTGCN records an RMSE of 1.03 at 15 min, which is considerably lower than other models like USTGCN and LSGCN, which have RMSE values above 2. Similarly, on the PeMSD8 dataset, ISTGCN maintains its superior performance with an RMSE of 0.98 at 15 min.