# Simulation-Based Optimization of Transport Efficiency of an Urban Rail Transit Network
## 4 Result Analysis
### DEA Analysis of Simulation Results  
When using the DEA method to evaluate the network transport efficiency after compound optimization, it is necessary to first determine the input and output index of each DMU, which is set to 24 experimental schemes. The most basic inputs of urban rail transit are the length of the line, the number of stations and vehicles, and the vehicle kilometers affected by the operation plan. According to the previous analysis, the important output of network transport efficiency is the travel time saved by passengers. The input and output indicators of the DEA method are shown in Table 8.  
Among the 24 schemes, the scale of passenger flow can be classified into three levels: original passenger flow, a 10% reduction in passenger flow and a 10% increase in passenger flow which, respectively, represent three periods of the rail transit network. The DEA model is used to evaluate different schemes at the three levels, and the adaptability of different rail network scales and capacity levels to the passenger flow scale is analyzed. 1. DEA evaluation of original passenger flow scale  
The schemes under the original passenger flow scale include schemes 1, 4, 7, 10, 13, 16, 19 and 22, and the DEA evaluation results, and calculated network efficiency are shown in Table 9 below. Scheme 10 is the benchmark scheme, that is, the Changping Line and Line 6 are deleted, and the departure intervals of Line 2 during morning rush hours are increased by 30 s.  
The first column in Table 9 is the decision-making unit, and the second, third and fourth columns are technical efficiency, pure technical efficiency and scale efficiency, respectively. There is a certain correlation among them: scale efficiency = technical efficiency/pure technical efficiency. Through these three indicators, the technical efficiency and scale efficiency of the object to be studied can be explained. The last column is the scale reward. It can be seen that the scale reward of scheme 1 (original rail network, original departure density and original passenger flow scale) remains unchanged, while the scale reward of scheme 13 (deleting Line 6/constructing the Changping Line, original departure density and original passenger flow scale) increases, and the rest of the schemes decrease. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Name** & **Index** \\ \hline \multirow{3}{*}{Input} & X1 & number of vehicles (vehicle) \\  & X2 & number of stations (station) \\  & X3 & length of operating lines (km) \\  & X4 & kilometers of train operation (vehicle kilometer) \\ \hline Output & Y & travel time saving (s) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: DEA Input-output of Network Transport Efficiency. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**DEA Evaluation Results**} & \multicolumn{4}{c}{**Network Efficiency**} \\ \hline
**Optimum Scheme** & **Technical Efficiency** & **Pure Technical Efficiency** & **Scale Efficiency** & **Scale Reward** & **Input 1** & **Output 2** & **Shadow Efficiency** \\ \hline
1 & 1 & 1 & 1 & unchanged & 11,310,210 & 2,376,650 & 0.21013 \\
4 & 0.975696 & 1 & 0.975696 & decreased by degrees & 11,273,050 & 2,183,510 & 0.19369 \\
7 & 0.759642 & 1 & 0.759642 & decreased by degrees & 37,162.8 & 373,910 & 10.06150 \\
10 & 0.685759 & 1 & 0.685759 & decreased by degrees & 0 & 0 & - \\
13 & 0.792031 & 0.998691 & 0.793069 & increased by degrees & 4,686,273 & 634,960 & 0.13549 \\
16 & 0.723491 & 1 & 0.723491 & decreased by degrees & 4,649,110 & 279,680 & 0.06015 \\
19 & 0.98784 & 1 & 0.98784 & decreased by degrees & 6,661,103 & 1,972,950 & 0.29619 \\
22 & 0.958522 & 1 & 0.958522 & decreased by degrees & 6,623,940 & 1,811,400 & 0.27346 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: DEA evaluation results of each program for the original passenger flow scale. The pure technical efficiency of other schemes, except scheme 13 is 1, which means the utilization rate of various inputs has reached the optimal value, and there is no waste phenomenon.