# Subway Station Capacity Maintained by Optimizing a Maintenance Schedule of Key Equipment
## 6 Simulation Study
### Maintenance Schedule Optimization  
The optimal fault distribution of each components of the key equipment and the corresponding parameters are determined. In addition, the maintenance cost data is obtained from the maintenance account records. The maintenance cost of the gate software, \(c_{p1}\) is 100 RMB and \(c_{f1}\) is 300 RMB. For the gate hardware, \(c_{p2}\) is 250 RMB and \(c_{f2}\) is 1000 RMB. For the electrical system of the escalator, \(c_{p3}\) is 500 RMB and \(c_{f3}\) is 1500 RMB. For the mechanical system of the escalator, \(c_{p4}\) is 1000 RMB and \(c_{f4}\) is 3000 RMB. The lower bound of equipment reliability is determined by sensitivity analysis based on the equipment reliability-expected station capacity curve. The lower bound of reliability of gate is 0.7, and the lower bound of reliability of escalator is 0.8. The relevant parameters of the equipment are taken into the maintenance schedule optimization model, and MATLAB is used to get a solution of the model. As a result, the optimal software maintenance schedule of the gate \(T_{1}\) is 3 days, and the optimal hardware maintenance schedule of the gate \(T_{2}\) is 8 days. The optimal maintenance schedule of the electrical system of the escalator \(T_{3}\) is 7 days, and the optimal maintenance schedule of the mechanical system of the escalator \(T_{4}\) is 16 days. Therefore, the optimal maintenance strategy of the gates is as follows: the maintenance schedule of software is 3 days, and the maintenance schedule of the gate is one week. The optimal maintenance strategy of the escalators is as follows: the maintenance schedule of the electrical system is one week, and the maintenance schedule of the escalator is half a month. The current maintenance schedule of gates is half a year and the gates are repaired after failure in the majority of cases. The current maintenance schedule of escalators is 2 weeks. The equipment reliability between the current maintenance schedules and the optimal maintenance schedules are compared. The comparison result of gates is shown in Figure 16 and the comparison result of escalators is shown in Figure 17. As shown in Figure 16, the initial reliability of the gate is 1, and the reliability decreases as the operation time goes by. After the maintenance for software system of gates on the third day, the reliability of the gate is restored to 0.9 on the fourth day. The reliability of gates is decreased further as operation time goes on and decreases to 0.7 at the seventh day. After the maintenance for the entire gate on the seventh day, the reliability of the gate is restored to 1 again on the eighth day. The change of the escalator reliability before and after maintenance is shown in Figure 7.  
Figure 15: Goodness of fit test for mechanical system fault. Figure 18 shows the variation of the expected DSSC during rush hours over operation time after maintenance schedule optimization, which is evaluated with expected travel time of passengers. In the beginning, the reliability of gates and escalators is 1, and the expected travel time is 326 s. As operation time goes by, the reliability of key equipment decreases and the expected travel time increases. After the maintenance for software system of gates on the third day, the reliability of gates is restored to 0.9, and the expected travel time reduces to 337 s. The expected travel time increases again with operation time. After the maintenance for gates and electrical system of escalators on the seventh day, the reliability of gates and escalators is restored to 1 and 0.95, respectively, and the expected travel time decreases again. After the maintenance for software system of the gates on the eleventh day, the expected travel time remains almost unchanged. Finally, the expected DSSC is restored to the initial level after equipment maintenance every half a month. Before the maintenance schedule optimization, the failure probability of key equipment increases and the expected DSSC declines without timely maintenance.