Analysis of dynamic traffic equilibrium with departure time choice

We present and analyse a model of the combined choice of departure time and route in a congested road network. Using the property of equilibrium solutions that for each origin–destination pair the total cost associated with travel is identical for all travellers, we establish a general result that relates assignments to various components of cost. The analysis is developed to include time-varying tolls and to establish a formula that will induce any specified inflow profile as an equilibrium. We introduce an iteration operator to calculate equilibrium inflow profiles, and present the results of example calculations for a range of test problems.