Toll pricing framework under logit-based stochastic user equilibrium constraints

Zhiyuan Liu, Shuaian Wang, Qiang Meng

Research output: Journal article publicationJournal articleAcademic researchpeer-review

32 Citations (Scopus)


This paper addresses the toll pricing framework for the first-best pricing with logit-based stochastic user equilibrium (SUE) constraints. The first-best pricing is usually known as marginal-cost toll, which can be obtained by solving a traffic assignment problem based on the marginal cost functions. The marginal-cost toll, however, has rarely been implemented in practice, because it requires every specific link on the network to be charged. Thus, it is necessary to search for a substitute of the marginal cost pricing scheme, which can reduce the toll locations but still minimize the total travel time. The toll pricing framework is the set of all the substitute toll patterns of the marginal cost pricing. Assuming the users' route choice behavior following the logit-based SUE principle, this paper has first derived a mathematical expression for the toll pricing framework. Then, by proposing an origin-based variational inequality model for the logit-based SUE problem, another toll pricing framework is built, which avoids path enumeration/storage. Finally, the numerical test shows that many alternative pricing patterns can inherently reduce the charging locations and total toll collected, while achieving the same equilibrium link flow pattern.
Original languageEnglish
Pages (from-to)1121-1137
Number of pages17
JournalJournal of Advanced Transportation
Issue number8
Publication statusPublished - 1 Jan 2014
Externally publishedYes


  • first-best pricing
  • linear duality theory
  • stochastic user equilibrium
  • toll pricing framework
  • variational inequality

ASJC Scopus subject areas

  • Automotive Engineering
  • Economics and Econometrics
  • Mechanical Engineering
  • Computer Science Applications
  • Strategy and Management


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