The corridor problem with discrete multiple bottlenecks

• A departure-time choice equilibrium for discrete multiple bottlenecks is analyzed.
• A transparent approach to the analysis of the equilibrium is presented.
• The equilibrium conditions are formulated in a Lagrangian-like coordinate system.
• Deep insights on mathematical structure and properties of the problem are obtained.
• Rigorous results on the existence and uniqueness of equilibria are established.

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.