Logit-based transit assignment: Approach-based formulation and paradox revisit

This paper proposes an approach-based transit assignment model under the assumption of logit-based stochastic user equilibrium (SUE) with fixed demand. This model is proven to have a unique solution. A cost-averaging version of the self-regulated averaging method (SRAM) is developed to solve the proposed approach-based SUE transit assignment problem. It is proven that the algorithm converges to the model solution. Numerical examples with discussions are presented to investigate the model properties, a paradoxical phenomenon due to the stochastic nature of the model, capacity paradox, and the performance of the proposed algorithm. The sensitivity analysis of different model and algorithm parameters are performed. A performance comparison between the cost-averaging SRAM, the flow-averaging SRAM, and the method of successive averages is made. The proposed methodology is demonstrated to be able to solve the Winnipeg transit network.