Strategy-based transit stochastic user equilibrium model with capacity and number-of-transfers constraints

Vehicle capacity and number-of-transfers constraints are critical in transit network equilibrium because (1) transit vehicles cannot carry passengers over their capacity and (2) transit passengers typically avoid paths with numerous transfers. In this paper, we propose a strategy-based transit stochastic user equilibrium (SUE) model that considers capacity and number-of-transfers constraints for an urban congested transit network. A route-section-based method is used for the transit network representation. The transit passengers’ route choice behavior is assumed to obey the logit model, and a route-section-based path size correction factor is developed to handle the route overlapping issue. The transit line capacity and maximum number-of-transfers constraints are considered in the model. We then formulate the strategy-based transit SUE problem as a variational inequality (VI) problem. A transit path-set generation procedure is proposed to identify a transit path with a limited number of transfers using the route-section-based network representation. The diagonalization method is chosen to solve the VI problem due to the asymmetric cost function, and the diagonalized problem can be solved using a path-based partial linearization algorithm embedded with an iterative balancing scheme, which is used here to handle the numerous capacity constraints. Numerical examples are conducted to demonstrate the features of the proposed model and performance of the developed algorithm. The results show that the vehicle capacity and number of transfers would strongly impact the passenger flow patterns.