Modeling intermodal equilibrium for bimodal transportation system design problems in a linear monocentric city

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

Research output: Journal article publicationJournal articleAcademic researchpeer-review

74 Citations (Scopus)


This paper investigates the intermodal equilibrium, road toll pricing, and bus system design issues in a congested highway corridor with two alternative modes - auto and bus - which share the same roadway along this corridor. On the basis of an in-depth analysis of the demand and supply sides of the bimodal transportation system, the mode choice equilibrium of travelers along the continuum corridor is first presented and formulated as an equivalent variational inequality problem. The solution properties of the bimodal continuum equilibrium formulation are analytically explored. Two models, which account for different infrastructure/system regulatory regimes (public and private), are then proposed. In the public regulatory model, the road toll location and charge level are simultaneously optimized together with the bus service fare and frequency. In the private regulatory model, the fare and frequency of bus services, which are operated by a profit-driven private operator, are optimized for exogenously given toll pricing schemes. Finally, an illustrative example is given to demonstrate the application of the proposed models. Sensitivity analysis of residential/household distribution along the corridor is carried out together with a comparison of four different toll pricing schemes (no toll, first best, distance based, and location based). Insightful findings are reported on the interrelationships among modal competition, market regulatory regimes, toll pricing schemes, and urban configurations as well as their implications in practice.
Original languageEnglish
Pages (from-to)30-49
Number of pages20
JournalTransportation Research Part B: Methodological
Issue number1
Publication statusPublished - 1 Jan 2012


  • Bimodal transportation system design
  • Intermodal equilibrium
  • Linear monocentric city
  • Regulatory regimes
  • Residential/household distribution

ASJC Scopus subject areas

  • Transportation
  • Management Science and Operations Research


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