Ideal Dynamic User-Optimal Route Choice: A Link-Based Variational Inequality Formulation

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, we presented a route-based optimal control model for the ideal DUO route choice problem. However, this model is not appropriate for largescale transportation networks because some degree of route enumeration is necessary to solve the model. In this paper, we first present the traffic network constraints and link-based DUO route choice conditions. Then, we 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 the solution procedure. By proving the necessity and sufficiency of this VI, we demonstrate that the VI formulation is equivalent to the link-based DUO route choice conditions.