User-equilibrium route flows and the condition of proportionality

User-equilibrium (UE) static deterministic traffic assignment is a widely accepted model among researchers, and is extensively applied in travel forecasting practice. UE route flows are also quite commonly used in methodological research as well as in practical applications, even though it is well known that route flows are not uniquely determined by the UE conditions. One way to resolve this dilemma is by imposing an additional condition, such as the condition of proportionality.