The corridor problem with discrete multiple bottlenecks

This paper presents a transparent approach to the analysis of dynamic user equilibrium and clarifies the properties of a departure‐time choice equilibrium of a corridor problem where discrete multiple bottlenecks exist along a freeway. The basis of our approach is the transformation of the formulation of equilibrium conditions in a conventional ‘Eulerian coordinate system’ into one in a ‘Lagrangian‐like coordinate system.’ This enables us to evaluate dynamic travel times easily, and to achieve a deep understanding of the mathematical structure of the problem, in particular, about the properties of the demand and supply (queuing) sub‐models, relations with dynamic system optimal assignment, and differences between the morning and evening rush problems. Building on these foundations, we establish rigorous results on the existence and uniqueness of equilibria.