On the variational theory of traffic flow: well-posedness, duality and applications

This paper describes some simplifications allowed by thevariational theory of traffic flow(VT). It presents generalconditions guaranteeing that the solution of a VT problem withbottlenecks exists, is unique and makes physical sense; i.e., thatthe problem is well-posed. The requirements for well-posedness aremild and met by practical applications. They are consistent withnarrower results available for kinematic wave or Hamilton-Jacobitheories. The paper also describes some duality ideas relevant tothese theories. Duality and VT are used to establish theequivalence of eight traffic models. Finally, the paper discusseshow its ideas can be used to model networks of multi-lane trafficstreams.