Stochastic Congestion and Pricing Model with Endogenous Departure Time Selection and Heterogeneous Travelers

Wuping Xin, David Levinson

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


In a stochastic roadway congestion and pricing model, one scheme (omniscient pricing) relies on the full knowledge of each individual journey cost and of early and late penalties of the traveler. A second scheme (observable pricing) is based on observed queuing delays only. Travelers are characterized by late-acceptance levels. The effects of various late-acceptance levels on congestion patterns with and without pricing are compared through simulations. The omniscient pricing scheme is most effective in suppressing the congestion at peak hours and in distributing travel demands over a longer time horizon. Heterogeneity of travelers reduces congestion when pricing is imposed, and congestion pricing becomes more effective when cost structures are diversified rather than identical. Omniscient pricing better reduces the expected total social cost; however, more travelers improve welfare individually with observable pricing. The benefits of a pricing scheme depend on travelers’ cost structures and on the proportion of late-tolerant, late-averse, and late-neutral travelers in the population.

Original languageEnglish (US)
Pages (from-to)37-52
Number of pages16
JournalMathematical Population Studies
Issue number1
StatePublished - Jan 2 2015


  • commute
  • congestion pricing
  • omniscient and observable pricing schemes
  • road pricing
  • second-best pricing
  • social cost and individual welfare
  • stochastic network equilibrium
  • traveler departure patterns

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