## 5 Simulation Test and Data Analysis
### Analysis of the Improved Solution Method  
This subsection compares the solution method employing the parallel strategy with the open-loop queueing network solution method developed by [PERSON] [42] with respect to the general service times. This paper improves the model developed by [PERSON] in the following ways:  
1. It replaces the general service time with the Coxian distribution. 2. The method of decomposing complex queuing networks is applied with the parallel operation strategy. \begin{table}
\begin{tabular}{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 \(\lambda_{r}=150\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) \\ \hline \(E(T)\) & 110.37 & 105.89 & 4.06 & 117.37 & 116.50 & 0.74 & 123.70 & 124.53 & 0.67 & 126.45 & 124.69 & 1.39 & 153.86 & 163.77 & 6.44 & 174.07 & 182.07 & 4.60 \\ \hline \(W_{r}\) & 76.89 & 78.77 & 2.45 & 80.94 & 85.56 & 5.71 & 84.63 & 89.92 & 6.25 & 85.75 & 88.43 & 3.13 & 111.26 & 120.10 & 7.95 & 123.62 & 130.86 & 5.86 \\ \hline \(L_{qq}\) & 3.20 & 3.28 & 0.10 & 3.37 & 3.57 & 5.71 & 3.53 & 3.75 & 0.26 & 3.57 & 3.68 & 0.13 & 4.64 & 5.00 & 7.95 & 5.15 & 5.45 & 5.86 \\ \hline \(\rho_{s}\) & 0.51 & 0.53 & 2.35 & 0.48 & 0.48 & 0.39 & 0.45 & 0.45 & 0.69 & 0.41 & 0.42 & 1.46 & 0.45 & 0.46 & 0.44 & 0.45 & 0.46 & 0.88 \\ \hline \(\lambda_{r}=200\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) \\ \hline \(E(T)\) & 124.14 & 119.83 & 3.47 & 144.07 & 133.11 & 7.61 & 145.05 & 136.89 & 5.63 & 145.37 & 140.10 & 3.63 & 188.47 & 177.51 & 5.81 & 208.30 & 197.58 & 5.15 \\ \hline \(W_{r}\) & 92.91 & 90.63 & 2.45 & 107.31 & 107.39 & 0.07 & 107.20 & 106.40 & 0.75 & 102.74 & 105.45 & 2.64 & 139.47 & 141.07 & 1.15 & 155.13 & 153.68 & 0.94 \\ \hline \(L_{qq}\) & 5.16 & 5.04 & 0.14 & 5.96 & 5.97 & 0.07 & 5.96 & 5.91 & 0.04 & 5.71 & 5.86 & 0.15 & 7.75 & 7.84 & 1.15 & 8.62 & 8.54 & 0.94 \\ \hline \(\rho_{s}\) & 0.70 & 0.70 & 0.46 & 0.78 & 0.77 & 1.41 & 0.60 & 0.60 & 0.72 & 0.55 & 0.56 & 0.91 & 0.61 & 0.61 & 0.20 & 0.61 & 0.61 & 0.59 \\ \hline \(\lambda_{r}=250\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) & \(R_{1}\) & \(R_{2}\) & \(\zeta\) \\ \hline \(E(T)\) & 128.23 & 127.45 & 0.61 & 172.63 & 153.42 & 11.13 & 164.92 & 146.27 & 11.31 & 170.04 & 152.16 & 10.51 & 215.88 & 190.03 & 11.98 & 254.21 & 211.70 & 16.72 \\ \hline \(W_{r}\) & 98.23 & 99.92 & 1.72 & 155.41 & 124.10 & 20.15 & 130.98 & 118.18 & 9.77 & 139.65 & 121.48 & 13.01 & 184.04 & 156.66 & 14.88 & 198.91 & 171.99 & 13.53 \\ \hline \(L_{qq}\) & 5.46 & 5.55 & 1.72 & 10.79 & 8.62 & 1.40 & 9.10 & 8.21 & 0.68 & 9.70 & 8.44 & 0.90 & 12.78 & 10.88 & 14.88 & 13.81 & 11.94 & 13.53 \\ \hline \(\rho_{s}\) & 0.87 & 0.88 & 0.58 & 0.80 & 0.81 & 0.10 & 0.75 & 0.76 & 0.67 & 0.69 & 0.69 & 0.57 & 0.76 & 0.76 & 0.17 & 0.91 & 0.76 & 16.45 \\ \hline \end{tabular}
\end{table} 
Table 6: \(Cont.\)  
Figure 11: Simulation error range. The maximum entropy value method is used to calculate the open-loop queuing network. [PERSON]'s paper stated that the number of customers present in the network at the same time must not exceed a given value, i.e., a limited load, which is the same as the limit on the number of shuttles described in this paper. Although it does not involve parallel queuing networks, the decomposition method is similar for complex networks, and given the same parameters, can be used for comparison and validation.