Temporal and Spatial Evolution of Passenger Flow in an Urban Rail Transit Network During Station Closure

In this study, we focused on the evolution of passenger flow in an urban rail transit network in both temporal and spatial dimensions under the event of station closure. We constructed an extended space-time-state hyper network so that we could utilize a better-defined three-dimensional solution space to describe passenger behaviors and pedestrian characters. The space-time-state network was extended by adding dummy arcs and setting the “block space-time domain” based on the original spatiotemporal network. Based on the extended space-time-state hyper network, a passenger flow evolution model that aimed to minimize the usage cost during station closure was established considering the strict capacity constraints (including corridor passing capacity, platform load capacity and train transport capacity). For a large-scale urban rail network, we developed a decomposition solution framework in which the Lagrangian relaxation and semi-assignment algorithms were adopted. A real-world instance was implemented based on the Beijing subway network with complete smart card data for each passenger for his/her origin and destination, while the specific space-time trajectories of all passengers and time-dependent passenger volumes in trains and transfer corridors were estimated. The results of a numerical experiment suggest that the proposed passenger flow evolution method can provide a rich set of passenger volume inferences for advanced transit planning and management applications, such as passenger flow control, passenger flow guidance, and real- time train scheduling.