A Credit-Based Congestion Management Scheme in General Two-Mode Networks with Multiclass Users

Yang Liu*, Yu (Marco) Nie

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


This paper examines the design of the credit-based congestion management schemes that achieve Pareto-improving outcome in general two-mode networks. It is assumed that transit is a slower but cheaper alternative to driving alone. The distributional welfare effects of congestion pricing on users with the different value of time (VOT) in Liu and Nie (Trans Res Board 2283:34–43, 2012) are used in developing Pareto-improving credit schemes. We show that, similar to the single-mode model, the sufficient and necessary condition for the existence of a discriminatory Pareto-improving credit scheme is the reduction in the total system cost. A sufficient condition for the existence of an anonymous Pareto-improving credit scheme is also derived. A cross-OD subsidization scheme is proposed when the sufficient condition is not satisfied for each origin-destination (O-D) pair. Numerical experiments on the expanded Sioux Falls networks with a log-normal VOT distribution demonstrate that the proposed Pareto-improving scheme can generate positive net revenue in the presence of good transit coverage.

Original languageEnglish (US)
Pages (from-to)681-711
Number of pages31
JournalNetworks and Spatial Economics
Issue number3
StatePublished - Sep 1 2017


  • Congestion pricing
  • Multiclass
  • Pareto-improving
  • Transit
  • Travel credit scheme

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications
  • Artificial Intelligence


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