In the paper by Cominetti and Correa (2001) [Common-lines and passenger assignment in congested transit networks. Transportation Science 35 (3), pp 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 et al. (2006) [Cepeda, M., Cominetti, and R. Florian, M. (2006) A frequency-based assignment model for congested transit networks with strict capacity constraints: characterization and computation of equilibria. Trans. Res B 40, 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.
This paper introduces the windy clustered prize-collecting arc-routing problem. It is an arc-routing problem
where each demand edge is associated with a profit that is collected once if the edge is serviced, independent
of the number of times the edge is traversed. It is further required that if a demand edge is serviced, then all
the demand edges of its component are also serviced. A mathematical programming formulation is given and
some polyhedral results including several facet-defining and valid inequalities are presented. The separation
problem for the different families of inequalities is studied. Numerical results from computational experiments