Modeling activity capacity of multimodal transportation network: a bi-level optimization framework with land use constraints

Urban residents’ activity-travel demands exhibit continuous enrichment and diversification, necessitating urgent evaluations of urban facility and resource supply adequacy and sustainability. Within urban planning and management, capacity is a key indicator for assessing urban resource quantity and sustainable states, encompassing domains like transportation, housing, and energy. While traffic network capacity remains fundamental in assessing network performance, the Origin–Destination (O-D) demand framework exhibits critical analytical constraints. This approach insufficiently captures three behavioral dimensions: trip timing variations, travel mode combinations, and activity-driven travel purposes, so it does not support activity-centric urban planning, such as optimal activity facility placement and activity resource allocation strategies. This paper introduces an innovative network level capacity concept, i.e., activity capacity, answering two critical questions: (1) Given constraints from land-use allocations, traffic infrastructure limits, and activity-demand structure, what constitutes the maximum daily sustainable activity flow volume in an activity-travel network? (2) How do corresponding activity demand and flow distributions emerge? To calculate activity capacity, a bi-level optimization framework is developed, comprising an upper-level Activity Capacity (AC) model that maximizes activity demand through integrated spatial–temporal constraints, paired with a lower-level Activity-Travel Assignment (ATA) framework operating on a multimodal transportation network. Computational efficiency is attained through a customized Sensitivity Analysis-Based (SAB) algorithm combined with a Gradient Projection (GP) method. Case analysis demonstrates the application prospects of AC in travel strategy evaluation, activity facility location selection, activity policy analysis, and Transit-Oriented Development (TOD) mode validation, which demonstrate the possibility of providing valuable information for urban planners and administrators.