Traffic user equilibrium and proportionality

• We study the problem of proportionality and uniqueness for route flows in the classical traffic user equilibrium model.
• We re-discuss the well-known relation between proportionality and entropy maximization.
• We exhibit a special set of proportionality conditions which uniquely determine the route flow.

We discuss the problem of proportionality and uniqueness for route flows in the classical traffic user equilibrium model. It is well-known that under appropriate assumptions the user equilibrium (f,x)(f,x) is unique in the link flow x but typically not in the route flow f. We consider the concept of proportionality in detail and re-discuss the well-known relation between the so-called bypass proportionality and entropy maximization. We exhibit special proportionality conditions which uniquely determine the route flow f. The results are illustrated with some simple example networks.