# Simulation-Based Optimization of Transport Efficiency of an Urban Rail Transit Network
## 3 Simulation Model
### Experimental Design
#### 3.2.1 Simulation Experiment Design for Line Construction  
Different orders of line construction will have different effects on the network forms and passenger flow distribution, affecting the efficiency of network operation. The experimental scene of constructing a new line in the existing rail network is designed by following the steps below:  
Step 1: Several lines in the rail network are selected as the research objects and recorded as \"lines to be built\" (\(L_{1}\),\(L_{2}\),..., \(L_{n}\)). Step 2: The above lines are deleted in the network topology diagram, and the input and output passenger volume of each station are transferred to nearby stations in a certain proportion, as shown in the following formulas. \[P_{i,j}^{tt}=\alpha_{i,j}^{t}\cdot P_{i}^{t} \tag{3}\]  
\[0\leq\sum_{j=1}^{m^{t}}\alpha_{i,j}^{t}\leq 1 \tag{4}\]  
where \(P_{i,j}^{tt}\) is the transfer passenger flow of the alternative station \(j\) of station \(i\) on line \(t\); \(P_{i}^{t}\) is the original inbound or outbound volume of station \(i\) on line \(t\) (the transfer probability of input and output volume can be the same or different according to the actual situation); \(\alpha_{i,j}^{t}\) is the transfer ratio; \(m_{i}^{t}\) is the number of alternative stations for station \(i\) on line \(t\). The proportion of transferred passenger flow needs to be determined according to the actual situation. When the total transfer ratio is less than 1, it is equivalent to the loss of the surplus passenger flow. After the completion of the line, the induced passenger flow ratio can be calculated as follows:  
\[\beta_{i}^{t}=1-\sum_{j=1}^{m^{t}}\alpha_{i,j}^{t} \tag{5}\]  
Step 3: The passenger flow simulation is carried out on the rail network after deleting the \"lines to be built\", and the passenger travel time of the required period and OD is counted, which is recorded as T0. This scheme is regarded as the \"benchmark scheme\". Step 4: According to the order of experimental design, the lines in the \"lines to be built\" are added in turn, and the passenger travel time is separately counted and recorded as \(T(1)=\{T_{1},T_{2},\cdots,T_{n}\}\), as the first set of statistical results. Designing multiple sets of construction sequences will produce multiple sets of experimental data \(T(1)\), \(T(2)\),..., \(T(m)\). Step 5: Comparison is made among \(T(1)\), \(T(2)\),..., \(T(m)\), and the simulation results are analyzed. A single optimization simulation experiment based on the 2015 Beijing urban rail transit network is carried out based on the above experimental designs. Firstly, Line 6 and the Changping Line are removed simultaneously as a benchmark scheme, and the passenger flow of each station of the two lines is transferred to the surrounding alternative stations according to a certain proportion. Then, Line 6 and the Changping Line are removed, respectively, the former corresponding to the construction of the Changping Line first, and the latter to the construction of Line 6 first, based on the benchmark scenario. The transferred stations and corresponding proportions are shown in Tables 2 and 3. The passenger travel time during morning rush hour for the three simulation experiments are counted as shown in Table 4.