## 3 Results
### Discussion of Results
#### 3.2.3. Parametric Study of the ANN-PSO Hybrid Model for Queue Length in the Queue and in the System  
For queue length in the queue, the best results were obtained when the model had six neurons, a swarm population size of 200, and acceleration factors of C\({}_{1}\) = 1 and C\({}_{2}\) = 2.75. This configuration yielded a training R\({}^{2}\) of 0.91187 and MSE of 39.1201, with a testing R\({}^{2}\) of 0.7692. These results indicate that while the model learns queue length dynamics effectively, its generalization performance requires further optimization, as the testing R\({}^{2}\) is relatively lower compared to other outputs (Results highlighted in bold and italic in Table 5).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Number of** **Neurons**} & \multirow{2}{*}{**Swarm Population**} & \multicolumn{2}{c}{**Acceleration Factor**} & \multirow{2}{*}{**Training \(R^{2}\)**} & \multirow{2}{*}{**MSE**} & \multirow{2}{*}{**Testing \(R^{2}\)**} \\  & & & & & & \\ \hline  
5 & 2.25 & 0.9221 & 34.6919 & 0.5307 \\ \hline \hline \end{tabular}
\end{table}
Table 5: ANN-PSO sensitive analysis for queue length in the queue.  
Similarly, for queue length in the system, the optimal configuration involved five neurons, a swarm size of 200, and acceleration factors of \(C_{1}=1.5\) and \(C_{2}=2.0\). The model achieved a training \(R^{2}\) of 0.90548, with an MSE of 42.4288, and a testing \(R^{2}\) of 0.8091. The slightly higher MSE values suggest that queue length predictions are more sensitive to parameter tuning, and future improvements may require further refinement of training techniques or increased dataset diversity (Results highlighted in bold and italic in Table 6).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Number of** & **Swarm Population** & \multicolumn{2}{c}{**Acceleration Factor**} & & \\ \cline{3-6}
**Neurons** & **Size** & \(\mathbf{c_{1}}\) & \(\mathbf{c_{2}}\) & **Training \(R^{2}\)** & **MSE** & **Testing \(R^{2}\)** \\ \hline  
5 & 2.25 & 0.8941 & 47.4761 & 0.7765 \\ \hline \hline \end{tabular}
\end{table}
Table 6: ANN-PSO sensitive analysis for queue length in the system.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Number of** & **Swarm Population** & \multicolumn{2}{c}{**Acceleration Factor**} & & \\ \cline{3-6}
**Neurons** & **Size** & \(\mathbf{c_{1}}\) & \(\mathbf{c_{2}}\) & **Training \(R^{2}\)** & **MSE** & **Testing \(R^{2}\)** \\ \hline
9 & 400 & 1 & 2.50 & 0.8989 & 44.4485 & 0.6000 \\ \hline
10 & 10 & 1 & 2.75 & 0.7755 & 100.7906 & 0.5777 \\ \hline
10 & 20 & 1.5 & 2.50 & 0.7944 & 87.7819 & 0.3527 \\ \hline
10 & 50 & 1.5 & 2.50 & 0.8749 & 54.6040 & 0.9175 \\ \hline
10 & 100 & 1 & 2.75 & 0.9069 & 41.1036 & 0.5078 \\ \hline
10 & 200 & 1 & 2.75 & 0.9362 & 28.6671 & 0.4767 \\ \hline
10 & 400 & 1.5 & 2.50 & 0.9214 & 34.9661 & 0.3721 \\ \hline \hline \end{tabular}
\end{table}
Table 5: _Cont._A notable trend observed in both queue length metrics is that larger swarm sizes (e.g., 200) resulted in improved prediction accuracy. This suggests that complex outputs require a higher number of particles in the swarm to explore the search space more effectively and capture intricate patterns in the data.