## 5 Simulation Test and Data Analysis
### Analysis of the Improved Solution Method
The method of solving the parallel operation strategy applied in this paper was compared with [PERSON]'s method in nine environments with different mean values \(\tau\) and squared coefficients of variation \(cv^{2}\). The specific environmental parameters are shown in Table 7.  
Using the system response time \(E(T)\) and the external queue waiting for pickup \(L_{eq}\) as parameters for calculating the simulation results and the error of the method in this paper and that of [PERSON], a comparison of the data is presented in Table 8 (the data in the table are retained to two decimal places). This paper calculates the system response time more accurately, with an average error of 3.6%, while [PERSON] reported an average error of 9.2%. For the external queue waiting for pickup, the method described in this paper is better overall than Dallery, with an average error of 9.46%, while the average error of Dallery is 51.9%. The average error for the nine environments is shown in Figure 12. Most of the error values in this paper are within 10%, with a minimum error of 1.31% and a maximum error of 18.3%, representing an overall reduction in error of 20% compared with Dallery. In summary, the methods applied both by [PERSON] and in this paper can be applied to solve the system performance index of the response time. However, for the external queue waiting for pickup, a comparison of the error rates between the two methods with respect to these two parameters is shown in Figure 13. The solution method described in this paper outperformed Dallery, reducing the error by approximately 40%. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Serial Number** & **Configuration** & **Server Node 1** & **Server Node 2** \\ \hline
1 & M = \(3,\lambda=0.1\) & \((\tau,cv^{2})=(3,5)\) & \((\tau,cv^{2})=(3,5)\) \\
2 & M = \(5,\lambda=0.1\) & \((\tau,cv^{2})=(3,5)\) & \((\tau,cv^{2})=(3,5)\) \\
3 & M = \(7,\lambda=0.1\) & \((\tau,cv^{2})=(3,5)\) & \((\tau,cv^{2})=(3,5)\) \\
4 & M = \(3,\lambda=0.1\) & \((\tau,cv^{2})=(2,5)\) & \((\tau,cv^{2})=(3,5)\) \\
5 & M = \(5,\lambda=0.1\) & \((\tau,cv^{2})=(2,5)\) & \((\tau,cv^{2})=(3,5)\) \\
6 & M = \(7,\lambda=0.1\) & \((\tau,cv^{2})=(2,5)\) & \((\tau,cv^{2})=(3,5)\) \\
7 & M = \(3,\lambda=0.1\) & \((\tau,cv^{2})=(1,5)\) & \((\tau,cv^{2})=(4,5)\) \\
8 & M = \(5,\lambda=0.1\) & \((\tau,cv^{2})=(1,5)\) & \((\tau,cv^{2})=(4,5)\) \\
9 & M = \(7,\lambda=0.1\) & \((\tau,cv^{2})=(1,5)\) & \((\tau,cv^{2})=(4,5)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Model comparison environment. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Response Time**} & \multicolumn{4}{c}{**External Waiting Captain**} \\ \hline
**Serial** & **Simulation** & **This** & **Error** & **Dallery** & **Error (\%)** & **Simulation** & **This** & **Error (\%)** & **Dallery** & **Error (\%)** \\ \hline
1 & 22.42 & 22.80 & 0.02 & 16.44 & 0.27 & 0.11 & 0.11 & 0.03 & 0.17 & 0.60 \\
2 & 23.12 & 23.90 & 0.03 & 18.23 & 0.21 & 0.08 & 0.09 & 0.07 & 0.15 & 0.82 \\
3 & 22.25 & 24.77 & 0.11 & 19.98 & 0.10 & 0.06 & 0.07 & 0.18 & 0.14 & 1.33 \\
4 & 22