Environmentally sustainable toll design for congested road networks with uncertain demand

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

Research output: Journal article publicationJournal articleAcademic researchpeer-review

84 Citations (Scopus)


This article proposes a new road toll-design model for congested road networks with uncertain demand that can be used to create a sustainable urban transportation system. For policy assessment and strategic planning purposes, the proposed model extends traditional congestion pricing models to simultaneously consider congestion and environmental externalities due to vehicular use. Based on analyses of physical and environmental capacity constraints, the boundary conditions under which a road user on a link should pay either a congestion toll or an extra environmental tax are identified. The sustainable toll design model is formulated as a two-stage robust optimization problem. The first-stage problem before the realization of the future travel demand aims to minimize a risk-averse objective by determining the optimal toll. The second stage after the uncertain travel demand has been determined is a scenario-based route choice equilibrium formulation with physical and environmental capacity constraints. A heuristic algorithm that combines the sample average approximation approach and a sensitivity analysisbased method is developed to solve the proposed model. The upper and lower bounds of the model solution are also estimated. Two numerical examples are given to show the properties of the proposed model and solution algorithm and to investigate the effects of demand variation and the importance of including risk and environmental taxation in toll design formulations.
Original languageEnglish
Pages (from-to)127-155
Number of pages29
JournalInternational Journal of Sustainable Transportation
Issue number3
Publication statusPublished - 1 May 2012


  • Sample average approximation
  • Sustainable toll design
  • Two-stage optimization
  • Uncertain demand

ASJC Scopus subject areas

  • Environmental Engineering
  • Geography, Planning and Development
  • Civil and Structural Engineering
  • Renewable Energy, Sustainability and the Environment
  • Automotive Engineering
  • Transportation


Dive into the research topics of 'Environmentally sustainable toll design for congested road networks with uncertain demand'. Together they form a unique fingerprint.

Cite this