Transit Equilibrium Assignment: A Model and Solution Algorithms

In this paper we propose a model for the transit equilibrium assignment problem (TEAP) and develop two algorithms for its solution. The behavior of the transit users is modeled by using the concept of hyperpaths (strategies) on an appropriate network (general network) which is obtained from the road network and the transit lines by a transformation which makes explicit the walk, wait, in-vehicle, transfer and alight arcs. The waiting (generalized) cost is a function of both frequency of the transit lines and congestion effects due to queues at stops. 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. We prove the global convergence of these two algorithms for strongly monotone arc cost mappings. The implementation of the algorithms and computational experiments are presented as well.