A Toll Pricing Framework for Traffic Assignment Problems with Elastic Demand

Abstract

This paper extends the notion of toll pricing and the toll pricing framework previously developed for fixed demand traffic assignment (Bergendorff, Hearn and Ramana, 1997; Hearn and Ramana, 1998) to the problem with elastic demand. The system problem maximizes net benefit to the network users (Gartner, 1980; Yang and Huang, 1998) and the user problem is the usual one of finding equilibrium with elastic demand. We define and characterize T, the set of all tolls for the user problem that achieve the system optimal solution. When solutions to the two problems are unique, T is a polyhedron defined by the optimal solution of the system problem, similar to the case in (Bergendorff, Hearn and Ramana, 1997; Hearn and Ramana, 1998). The Toll Pricing Framework in (Hearn and Ramana, 1998) is also extended to allow optimization of secondary criteria over T. Examples include minimizing the number of toll booths and minimizing the maximum toll on any link. A numerical example illustrates the results.