Transit Equilibrium Assignment: A Model and Solution Algorithms

This paper proposes a model for the transit equilibrium assignment problem (TEAP) and develops two algorithms for its solution. The behavior of the transit users is modeled by using the concept for hyperpaths on an appropriate network that is obtained from the road network and the transit lines by a transformation that makes explicit the walk, wait, in-vehicle, transfer, and alight arcs. The TEAP is stated and formulated as a variational inequality problem, in the space of hyperpath flows, and then solved by the linearized Jacobi method and the projection method. The global convergence of these two algorithms for strongly monotone arc cost mappings is proven and the implementation of the algorithms and computational experiments are presented as well.