A link-based variational inequality model for dynamic departure time/route choice

The dynamic user-optimal (DUG) departure time and route choice problem is to determine travelers' best departure times and route choices at each instant of time. In a previous paper, we presented a route-based two-level optimal control model for the DUO departure time/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, we present a link-based variational in equality (VI) formulation for the DUO departure time/route choice problem so that route enumeration can be avoided in both the formulation and the solution procedure. The model extends our previous VI model for the DUO route choice problem to the case where both departure lime and route over a general road network must be chosen simultaneously. By proving the necessity and sufficiency of this VI, we establish the equivalence of the VI formulation and the link-based DUO departure time/route choice conditions.