Finding a DUE solution (i.e., a set of time-varying link and route volumes and travel
times that satisfy the DUE condition for a given network and time-varying O-D demand pattern)
is a nontrivial exercise, because each traveler’s best route choice (that is, least experienced travel
time route) depends on congestion levels throughout the journey, which in turn depend on the
route choices and progress through the network of other travelers who depart earlier, at the same
time or later (Figure 1). This interdependence means that solutions must be found through an
iterative process, starting from some initial set of route choices, and gradually improving them.
This improvement process can continue indefinitely; in realistic-sized networks, finding an exact
equilibrium is challenging. Rather, the goal of many current DTA models is to find an
approximate equilibrium that is sufficiently converged to true equilibrium for the application at
hand and that is obtainable in a reasonable amount of time.