## 5 Case Study
### Optimization of Timetable to Address Varying Passenger Demands  
After the start of official operation of the Shanghai Suburban Railway airport link line, there is likely to be an increase in passenger demand. To further illustrate the generality of the proposed solution and model, this section examines the timetable optimization to address varying passenger demand. Based on the OD passenger arrival rate \(O_{sk}\) shown in Figure 9, when \(O_{sk}\) is doubled, such as to 2\(O_{sk}\) and 3\(O_{sk}\), it is possible to study the timetable of TUOS-ELS during the official operation period. Figure 17: Train loading rate in the upstream of TUOS-ELS and T-TPOS. (**a**) Train loading rate in the upstream of TUOS-ELS; (**b**) Train loading rate in the upstream of T-TPOS. Figure 18: Train loading rate in the downstream of TUOS-ELS and T-TPOS. (**a**) Train loading rate in the downstream of TUOS-ELS; (**b**) Train loading rate in the downstream of T-TPOS. When the OD passenger arrival rate is \(2O_{sk}\) in the official operation period, the optimization result indicates that ten trains should operate in the upstream direction, while four trains should run in the downstream direction. The optimized timetable of TUOS-ELS is shown in Figure 19. The optimized results using the TUOS-ELS are compared with those obtained from the T-TPOS (Figure 20), as shown in Tables 5 and 6. The operator's and passenger's travel costs are reduced by 35.28% after optimization, and shows that the multi-strategy combination method still maintains a stable optimization effect in scenarios of increased numbers of traveling passengers. To illustrate the trains' loading rate in more detail, per-train loading rate heat maps are presented in Figures 21 and 22. The total number of passengers waiting in the upstream direction for both TUOS-ELS and T-TPOS is 14,910. Meanwhile, the total number of passengers waiting in the downstream direction for both is 2280. From these two figures, it can be clearly seen that the brighter and yellower the color is, the higher the train loading rate is. The rate is close to 1.2, i.e., 120%. This reflects more crowding of passengers inside the carriages. Figures 21a and 22a show the trains' loading rates in the upstream direction for both TUOS-ELS and T-TPOS; the average loading rates were 64.33% and 75.54%, respectively. In the upstream direction, as the number of trains increased and headways shortened under TUOS-ELS, the loading rate notably declined, beginning with train 2 in Sections 4-6. The degree of passenger crowding was effectively alleviated. Figures 21b and 22b indicate that trains operating in the downstream direction suffered from the problem of loading fewer passengers; their average loading rates were 18.54% and 12.03%, respectively. In the TUOS-ELS, loading rates of between 30% and 50% are achieved by train 2 and train 3 in Sections 2-6. The loading rate of all trains in all sections is less than 20% under T-TPOS, which is a strong indication that TUOS-ELS is effective in improving the trains' loading rates and increasing the use of train resources. Similar to the results of the previous trial operation phase, TUOS-ELS still shows significant advantages over T-TPOS in terms of improving passenger service quality and reducing operational costs. TUOS-ELS reduced the number of stranded passengers by 3013, total passenger waiting time by 327.5 h, and the total number of stops by two. It also decreased the average loading rate in the upstream direction by 11.21% and increased the average loading rate of the downstream direction by 5.61%. Figure 21: Heat maps of train loading rate under TUOS-ELS. (**a**) Heat maps of train loading rate in the upstream of TUOS-ELS; (**b**) Heat maps of train loading rate in the downstream of TUOS-ELS. Figure 22: Heat maps of train loading rate under T-TPOS. (**a**) Heat maps of train loading rate in the upstream of T-TPOS; (**b**) Heat maps of train loading rate in the downstream of T-TPOS.