Evaluating First-Train-Timetable-Network Performance in Urban Rail Transit with Percolation Theory

As modern large cities heavily rely on urban rail transit (URT) systems as their most crucial transportation infrastructure to meet daily commuting demands, the irrational design of the first train timetable and the lack of effective connections between different lines could result in excessively long travel times for passengers. Therefore, it is necessary to explore the flow organization mechanism of the URT system. In this paper, based on the temporal network theory, the concept of the First-Train-Timetable-Network (FTTN) is proposed, and the FTTN organization mechanism of Beijing and Shanghai’s URT systems is studied based on the percolation theory. We discovered an important parameter that can characterize the rationality of the first train timetable arrangement, namely, the critical time \({\text{t}}_{\text{c}}\) . Additionally, we observed the FTTN’s percolation transition phenomenon and evaluated the network performance. The results show that the FTTN model proposed in this study, together with the URT network performance evaluation method, can effectively reflect the actual situation of the URT network, providing valuable insights for URT operators to formulate the first train timetable.