The optimal transit fare structure under different market regimes with uncertainty in the network

Zhi Chun Li, Hing Keung William Lam, S. C. Wong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

68 Citations (Scopus)


This paper proposes a network-based model for investigating the optimal transit fare structure under monopoly and oligopoly market regimes with uncertainty in the network. The proposed model treats the interaction between transit operators and transit passengers in the market as a two-level hierarchical problem with the transit operator sub-model at the upper-level and the transit passenger sub-model at the lower-level. The upper-level problem is to determine the fare structure so as to optimize the objective function of the transit operators, whereas the lower-level problem represents the path choice equilibrium of the transit passengers. In order to consider the uncertainty effects on transit network, the proposed model incorporates the unreliability component of transit services into the passenger disutility function, which is mainly due to variations of the in-vehicle travel time and the dwelling time of transit vehicles at stops. With the use of the proposed model, a numerical example is given to assess the impacts of the market regimes and the unreliability of the transit services on the optimal transit fare structure.
Original languageEnglish
Pages (from-to)191-216
Number of pages26
JournalNetworks and Spatial Economics
Issue number2
Publication statusPublished - 4 Jun 2009


  • Market regime
  • Monopoly
  • Network equilibrium
  • Oligopolistic competition
  • Reliability
  • Social optimum
  • Transit fare

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications
  • Artificial Intelligence


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