Behavior-adaptive sync-flow framework : integrating frequency setting and passenger routing in oversaturated urban rail transit networks

Urban rail transit (URT) networks serve a large amount of travel demand in metropolitan areas. One of the fundamental challenges in URT demand management is the dynamic interaction between train frequencies and passenger routing behaviors, which becomes even more complicated in oversaturated scenarios. Introducing the behavior-adaptive sync-flow (BASF) framework, this study holistically addresses the tactical frequency settings (train flows) for URT networks and the responsive route choice behaviors of passengers (passenger flows). The proposed integrated model incorporates a schedule-based passenger assignment within space–time networks to model passengers’ routing behaviors based on time-dependent route travel costs. In addition to travel time, the often-overlooked factors such as in-train congestion, number of passengers being left behind, and number of transfers are considered as components influencing travel costs and, consequently, routing behaviors at an individual level. A gradient descent-based heuristic iterative solution approach is developed to address the integrated model by dividing it into three sub-problems. In this iterative process, passengers respond according to a logit-based route choice model based on time-dependent route travel costs, while frequencies are updated using a gradient descent-based strategy. Central to the proposed BASF framework are the mutual adaptations between URT line frequencies and passenger route choices. Numerical examples and a case study of the Beijing URT network highlight the effectiveness and scalability of the model framework in tackling complex, large-scale URT networks, particularly in oversaturated conditions, thus revealing the significance of supply–demand matching.