A link-based variational inequality formulation of ideal dynamic user-optimal route choice problem

The ideal dynamic user-optimal (DUO) route choice problem is to determine vehicle flows on each link at each instant of time resulting from drivers using actual minimal-time routes. Actual route time is the travel time incurred while driving along the route. In a previous paper, the authors presented a route-based optimal control model for the ideal DUO route choice problem. However, this model is not appropriate for large-scale transportation networks because some degree of route enumeration is necessary to solve the model. In this paper, the authors first present the traffic network constraints and link-based DUO route choice conditions. Then, they introduce a link-based variational inequality (VI) formulation for the ideal DUO route choice problem so that route enumeration can be avoided in both the formulation and solution procedure. By providing the necessity and sufficiency of this VI, the authors demonstrate that the VI formulation is equivalent to the link-based DUO route choice conditions.