Optimal joint distance and time toll for cordon-based congestion pricing

Zhiyuan Liu, Shuaian Wang, Qiang Meng

Research output: Journal article publicationJournal articleAcademic researchpeer-review

81 Citations (Scopus)


This paper addresses the optimal toll design problem for the cordon-based congestion pricing scheme, where both a time-toll and a nonlinear distance-toll (i.e., joint distance and time toll) are levied for each network user's trip in a pricing cordon. The users' route choice behaviour is assumed to follow the Logit-based stochastic user equilibrium (SUE). We first propose a link-based convex programming model for the Logit-based SUE problem with a joint distance and time toll pattern. A mathematical program with equilibrium constraints (MPEC) is developed to formulate the optimal joint distance and time toll design problem. The developed MPEC model is equivalently transformed into a semi-infinite programming (SIP) model. A global optimization method named Incremental Constraint Method (ICM) is designed for solving the SIP model. Finally, two numerical examples are used to assess the proposed methodology.
Original languageEnglish
Pages (from-to)81-97
Number of pages17
JournalTransportation Research Part B: Methodological
Publication statusPublished - 1 Nov 2014
Externally publishedYes


  • Cordon-based pricing
  • Mathematical program with equilibrium constraints
  • Nonlinear distance pricing
  • Stochastic system optimum
  • Tangent plane approximation method

ASJC Scopus subject areas

  • Transportation


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