Dynamic Schedule-Based Assignment Model for Beijing Urban Rail Transit Network with Capacity Constraints

There is a great need for estimation of passenger flow distribution both in temporal and spatial in Urban Rail Transit network. Literature review indicates that passenger flow assignment model considering capacity constraints with overload delay factor for in-vehicle crowding are limited in schedule-based network. As an extension of Lam, Gao and Chan's study in 1999, this paper proposes a stochastic user equilibrium model for solving the assignment problem in a schedule-based rail transit network with considering capacity constraint. As splitting the Origin-Destination demands into the developed schedule expanded network with time-space paths, the model transformed into a dynamic schedule-based assignment model. In this paper, passengers are assumed to select the optimal paths that minimize their perceptive travel time cost. The generalized travel time cost function includes four components: (1) in-vehicle time with crowding penalty; (2) waiting time; (3) transfer time with penalty; (4) overload delay. All trains have independent and constant capacity and run based on reliable schedules. Passengers are willing to get on the coming trains, if they can’t board due to the train capacity, they must wait for the next one, and hence the user equilibrium conditions can be equivalent to the equilibrium passenger overload delay with crowding penalty in the transit network. The proposal model can estimate the path choice probability according to the equilibrium condition when passengers minimize their perceptive cost in a schedule based network. Numerical example in Beijing urban rail transit (BURT) network is used to demonstrate the performance of the model, and estimate the passenger flow distribution temporal and spatial more reasonably and dynamically with train capacity constraints.