A Variational Inequality Reformulation of a Congested Transit Assignment Model by Cominetti, Correa, Cepeda, and Florian

In the paper by Cominetti and Correa (2001) [Common-lines and passenger assignment in congested transit networks. Transportation Sci. 35(3):250-267], an extension to the common-lines problem for general multidestination networks under congestion is analyzed. Their transit equilibrium assignment model allows for a full representation of congestion effects caused by the variation of effective frequencies experienced by passengers at transit stops. This model is the first to address these characteristics consistently with the concept of strategies. In a subsequent paper by Cepeda, Cominetti, and Florian (2006) [A frequency-based assignment model for congested transit networks with strict capacity constraints: Characterization and computation of equilibria. Transportation Res. 40B(6):437-459], the computation of equilibrium is performed heuristically by the minimization of a gap function, using the method of successive averages. In this paper, a reformulation of this congested transit equilibrium assignment model is performed, demonstrating that the problem can be expressed as an equivalent variational inequality. The case of strictly capacitated transit networks is explored under the scope of this new reformulation, and new, broader conditions for the existence of solutions to this congested transit assignment model are determined.