## 5 Simulation Test and Data Analysis  
### Arena Simulation Validation  
As the scale of the four-way shuttle system varies according to the size of the business volume, this paper lists seven different four-way shuttle system scales with different numbers of layers and columns and sets five different arrival rates. The other assumptions of the system are consistent with the model established in this paper, i.e., only pickup operations are considered; the first come, first served principle is adopted; and the random storage strategy is adopted to verify the reliability and accuracy of the model at different scales and arrival rates. The reliability and accuracy of the model are verified for different sizes and arrival rates. The initial system parameters set in the simulation are shown in Table 4, the system size is shown in Table 5 and the arrival rate is set to \(\lambda_{r}\) = 50, 100, 150, 200, 250 per hour.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c} \hline \hline
**Number** & \multicolumn{3}{c}{**1**} & \multicolumn{3}{c}{**2**} & \multicolumn{3}{c}{**3**} & \multicolumn{3}{c}{**4**} & \multicolumn{3}{c}{**5**} & \multicolumn{3}{c}{**6**} \\ \hline \(\lambda_{r}=50\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) \\ \hline \(E(T)\) & 86.26 & 88.46 & 2.55 & 94.11 & 98.25 & 4.40 & 106.07 & 107.69 & 1.53 & 110.44 & 113.90 & 3.14 & 133.58 & 139.57 & 4.48 & 148.24 & 153.02 & 3.22 \\ \hline \(W_{r}\) & 37.03 & 37.40 & 0.99 & 62.42 & 60.18 & 3.59 & 67.98 & 64.70 & 4.82 & 69.71 & 66.25 & 4.96 & 90.12 & 87.11 & 3.34 & 100.01 & 95.91 & 4.10 \\ \hline \(L_{qq}\) & 0.51 & 0.52 & 0.99 & 0.87 & 0.84 & 3.59 & 0.94 & 0.90 & 4.82 & 0.97 & 0.92 & 4.96 & 1.25 & 1.21 & 3.34 & 1.39 & 1.33 & 4.10 \\ \hline \(\rho_{s}\) & 0.15 & 0.15 & 0.21 & 0.16 & 0.16 & 1.00 & 0.14 & 0.15 & 5.82 & 0.14 & 0.13 & 3.53 & 0.15 & 0.15 & 0.13 & 0.15 & 0.15 & 0.39 \\ \hline \(\lambda_{r}=100\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) \\ \hline \(E(T)\) & 95.27 & 96.78 & 1.58 & 102.78 & 106.94 & 4.05 & 110.25 & 114.73 & 4.06 & 114.18 & 110.59 & 3.15 & 140.14 & 145.26 & 3.65 & 154.77 & 166.82 & 7.79 \\ \hline \(W_{r}\) & 64.13 & 63.71 & 0.65 & 69.01 & 68.85 & 0.23 & 74.18 & 73.76 & 0.56 & 76.43 & 77.56 & 1.48 & 97.24 & 97.78 & 0.56 & 108.81 & 109.68 & 0.80 \\ \hline \(L_{qq}\) & 1.78 & 1.77 & 0.65 & 1.92 & 1.91 & 0.23 & 2.06 & 2.05 & 0.56 & 2.12 & 2.15 & 1.48 & 2.70 & 2.72 & 0.56 & 3.02 & 3.05 & 0.80 \\ \hline \(\rho_{s}\) & 0.34 & 0.35 & 2.94 & 0.32 & 0.32 & 0.94 & 0.29 & 0.30 & 4.21 & 0.28 & 0.27 & 2.07 & 0.32 & 0.30 & 5.17 & 0.30 & 0.30 & 1.53 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of simulation results and theoretical values.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Take Value** & **Parameters** & **Take Value** \\ \hline \(V_{S}\) (m/s) & 2 & \(\gamma_{I}\) (s) & 2 \\ \(\varepsilon_{s}\) (s) & 3 & \(L\) (m) & 1.2 \\ \(\gamma_{s}\)(s) & 2 & \(W\) (m) & 1 \\ \(VI\) (m/s) & 3 & \(W\)A (m) & 1 \\ \(\varepsilon_{t}\) (s) & 1 & \(H\) (m) & 1.5 \\ \(N\) & 3 & \(M\) & 7 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Simulation parameter values.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline
**Size** & \multicolumn{3}{c}{**Small Scale**} & \multicolumn{3}{c}{**Large Scale**} \\ \hline Serial & \multirow{2}{*}{1} & \multirow{2}{*}{2} & \multirow{2}{*}{3} & \multirow{2}{*}{4} & \multirow{2}{*}{5} & \multirow{2}{*}{6} & \multirow{2}{*}{7} \\ number & & & & & & & & & & & & & \\ layers & 5 & 6 & 7 & 8 & 9 & 10 & 11 \\ columns & 36 & 40 & 44 & 48 & 64 & 72 & 80 \\ Capacities & 360 & 480 & 616 & 768 & 1152 & 1440 & 1760 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Simulation scale.