# 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.

## Keywords

Elastic Demand User Problem System Problem User Equilibrium Traffic Assignment## Preview

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