Demand-driven timetable design for metro services

Timetable design is crucial to the metro service reliability. A straightforward and commonly adopted strategy in daily operation is a peak/off-peak-based schedule. However, such a strategy may fail to meet dynamic temporal passenger demand, resulting in long passenger waiting time at platforms and over-crowding in trains. Thanks to the emergence of smart card-based automated fare collection systems, we can now better quantify spatial-temporal demand on a microscopic level. In this paper, we formulate three optimization models to design demand-sensitive timetables by demonstrating train operation using equivalent time (interval). The first model aims at making the timetable more dynamic; the second model is an extension allowing for capacity constraints. The third model aims at designing a capacitated demand-sensitive peak/off-peak timetable. We assessed the performance of these three models and conducted sensitivity analyzes on different parameters on a metro line in Singapore, finding that dynamical timetable built with capacity constraints is most advantageous. Finally, we conclude our study and discuss the implications of the three models: the capacitated model provides a timetable which shows best performance under fixed capacity constraints, while the uncapacitated model may offer optimal temporal train configuration. Although we imposed capacity constraints when designing the optimal peak/off-peak timetable, its performance is not as good as models with dynamical headways. However, it shows advantages such as being easier to operate and more understandable to the passengers.