Network equilibrium: Optimization formulations with both quantities
and prices as variables
Transportation Research Part B: Methodological, Volume 21, Issue 1, February 1987, Pages 69-77
Malachy Carey
School of Urban and Public Affairs, Carnegie-Mellon University, Pittsburgh, PA 15213, U.S.A.
Received 6 October 1983; revised 25 November 1985.
Abstract
The optimization formulation of the traffic assignment problem is usually stated in terms of flow (quantity)
variables but can also be stated entirely in terms of price variables (the dual formulation), and recently it has
also been stated in terms of a combination of both quantity and price variables. Here we consider properties
and problems associated with the latter optimization formulations and relate these formulations to the traffic
equilibrium conditions and to the purely quantity formulation.