Joint optimization of fleet size and operating speed for service planning in oversaturated urban rail transit networks

Oversaturated operations have become increasingly common in urban rail transit (URT) systems, where peak-period passenger demand often exceeds available service capacity. This demand–capacity imbalance leads to platform queues, in-train crowding, and denied boarding, making service planning particularly challenging when fleet resources are limited. To address the coupled supply–demand interactions, this study proposes a novel Behavior–Energy-Adaptive Service planning (BEAS) framework for network-wide URT service planning, in which fleet allocation and line-level operating speed are jointly optimized while passengers’ adaptive route choices are explicitly modeled. An integrated nonlinear integer programming model is developed to link fleet–speed service-plan decisions, subject to fleet budget limits and speed-dependent traction energy costs, with passenger assignment and path-size logit (PSL)-based route choice in a capacity-constrained space–time network. By enforcing train capacity and first-in-first-out (FIFO) boarding, the model reproduces platform queueing and denied boarding, and captures how the resulting time-dependent travel costs drive adaptive rerouting under oversaturated conditions. To solve the resulting large-scale coupled problem, a decomposition-based iterative algorithm is developed, in which the demand-side subproblem simulates individual passenger assignment under time-dependent costs and the supply-side subproblem optimizes fleet and speed decisions through an incremental approximation that yields a tractable multiple-choice knapsack structure. Numerical experiments on both a small illustrative network and a large-scale Beijing metro network demonstrate the computational efficiency, scalability, and practical value of the proposed framework. The results show that coordinated fleet–speed service planning can substantially reduce waiting time and left-behind passengers under resource constraints, while supporting passenger-oriented, operator-oriented, and balanced service planning.