Time-dependent area-based pricing for multimodal systems with heterogeneous users in an agent-based environment

Nan Zheng, Guillaume Rérat, Nikolas Geroliminis

Research output: Contribution to journalArticleResearchpeer-review

71 Citations (Scopus)


In this paper, we investigate an area-based pricing scheme for congested multimodal urban networks with the consideration of user heterogeneity. We propose a time-dependent pricing scheme where the tolls are iteratively adjusted through a Proportional-Integral type feedback controller, based on the level of vehicular traffic congestion and traveler's behavioral adaptation to the cost of pricing. The level of congestion is described at the network level by a Macroscopic Fundamental Diagram, which has been recently applied to develop network-level traffic management strategies. Within this dynamic congestion pricing scheme, we differentiate two groups of users with respect to their value-of-time (which related to income levels). We then integrate incentives, such as improving public transport services or return part of the toll to some users, to motivate mode shift and increase the efficiency of pricing and to attain equitable savings for all users. A case study of a medium size network is carried out using an agent-based simulator. The developed pricing scheme demonstrates high efficiency in congestion reduction. Comparing to pricing schemes that utilize similar control mechanisms in literature which do not treat the adaptivity of users, the proposed pricing scheme shows higher flexibility in toll adjustment and a smooth behavioral stabilization in long-term operation. Significant differences in behavioral responses are found between the two user groups, highlighting the importance of equity treatment in the design of congestion pricing schemes. By integrating incentive programs for public transport using the collected toll revenue, more efficient pricing strategies can be developed where savings in travel time outweigh the cost of pricing, achieving substantial welfare gain.

Original languageEnglish
Pages (from-to)133-148
Number of pages16
JournalTransportation Research Part C: Emerging Technologies
Publication statusPublished - 1 Jan 2016
Externally publishedYes


  • Agent-based
  • Congestion pricing
  • Macroscopic fundamental diagram
  • Multimodal
  • User adaptation
  • User heterogeneity

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