## 3 Case Study
### Discussion
#### 3.2.1 Analysis of the Construction Sequence
\[AC_{i}=\frac{E_{net}-E_{n-i}}{l_{i}\cdot E_{net}}=\frac{\frac{1}{M(M-1)}\sum \limits_{p\
eq q\in S}\frac{1}{2_{pq}}-\frac{1}{M_{i}^{\prime}(M_{i}^{\prime}- 1)}\sum\limits_{p\
eq q\in S_{i}^{\prime}}\frac{1}{d_{pq}}}{l_{i}\cdot\frac{1} {M(M-1)}\sum\limits_{p\
eq q\in S}\frac{1}{d_{pq}}} \tag{24}\]  
where \(E_{net}\) is the URT network efficiency, \(E_{n-i}\) is the network efficiency after removing line \(i\), \(M\) is the number of nodes, \(M_{i}^{\prime}\) is the number of nodes after removing line \(i\), \(S\) is the collection of nodes, \(S^{\prime}\) is the collection of nodes after removing line \(i\), \(d_{pq}\) is shortest connected distance of node \(p\) to node \(q\), and \(l_{i}\) is the length of line \(i\). \(C_{7}\) is the urban location coefficient, which is calculated according to data in the overall urban planning of Chengdu (2016-2030) and research on the future development of Chengdu (2016 version). It represents the importance of the area served by the line. The more important the area served by the line, the greater the priority that should be given to the construction of the line. The function for this is shown as Equation (25). \[R_{i}=\sum\limits_{j=1}^{M}l_{ij}/li\cdot r_{j} \tag{25}\]  
where \(M\) is the number of grades classified by the importance of urban regional development, \(l_{ij}\) is the mileage of the line \(i\) in the developmental grades of \(j\), \(l_{i}\) is the mileage of line \(j\), and \(r_{j}\) is the development coefficient of the region with the second development level. (2) The construction sequence  
The decision indicator values of the seven lines are shown in radar charts (Figure 5). Specifically, the value of each indicator in the radar chart is relative to its origin. The higher the value, the better the performance will be. Figure 4: Network topology of the Chengdu rail transit network. There are 450 points in the figure, and each point represents a subway station, while the letters A to O represent the lines 1 to 15. Figure 5: Ranking the seven lines in terms of indicator values. (**a**) The value of indicators of Line 1, (**b**) the value of indicators of Line 2; (**c**) the value of indicators of Line 3; (**d**) the value of indicators of Line 4. None of them stands out; (**e**) the value of indicators of Line 5; (**f**) the value of indicators of Line 7. There are three outstanding indicators; (**g**) the value of indicators of Line 10. None of them stands out. The discussion of the lines with striking differences between the calculated and actual sequence and timing (Lines 7, 4, and 10) is as follows. For Line 7, which is ranked first in the model calculation construction sequence (Table 8), the values of four indicators (\(C_{1}\), \(C_{5}\), \(C_{6}\), and \(C_{7}\)) are the highest of any of the lines (Figure 5f). This can be attributed to the fact that Line 7 is in the most densely populated area (between the second and third ring roads of Chengdu). Meanwhile, it connects three large railway stations (Chengdu Station and of Chengdu East Station and Chengdu South Station). In addition, it can be seen from Figure 3 that Line 7 is a loop line which can connect with all other lines. Therefore, the model indicator values \(C_{1}\), \(C_{5}\), \(C_{6}\), and \(C_{7}\) are excellent, and the calculation result of Line 7 is the highest. The values of indicators \(C_{2}\) and \(C_{3}\) are calculated from forecast data from the Chengdu Metro Network Planning Report (2016). The report predicted that indicators \(C_{2}\) and \(C_{3}\) (average passenger volume and peak hour passenger numbers) of Line 7 would be relatively low (see the Appendix A Tables A1 and A2).