Variational inequality model for cordon-based congestion pricing under side constrained stochastic user equilibrium conditions

Zhiyuan Liu, Qiang Meng, Shuaian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

22 Citations (Scopus)


A major objective of the practical implemented cordon-based congestion pricing schemes is to maintain the traffic conditions within the cordon area, which is rarely considered in most of the existing studies. Thus, this paper addresses the optimal toll charge pattern that can restrict the total inbound flow of each cordon to a predetermined threshold. The toll charges on all the entry links of one cordon are required to be identical, for the ease of implementation and users' recognition. The users' route choice behaviour is assumed to follow stochastic user equilibrium (SUE) with asymmetric link travel time functions. It is shown that such an optimal toll charge pattern can be attained by solving a SUE problem with side constraints. A variational inequality (VI) model is first proposed for the optimal toll pattern, where the monotone property of this model is rigorously proved. Then, a convergent self-adaptive prediction and correction method can be adopted for solving the VI model. It is shown that when used in practice, the solution method only needs traffic counts on entry links of each cordon.
Original languageEnglish
Pages (from-to)693-704
Number of pages12
JournalTransportmetrica A: Transport Science
Issue number8
Publication statusPublished - 1 Jan 2014
Externally publishedYes


  • cordon-based pricing
  • side constraint
  • stochastic user equilibrium
  • variational inequality

ASJC Scopus subject areas

  • Transportation
  • Engineering(all)

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