Morning commute problem considering route choice, user heterogeneity and alternative system optima

Yang Liu, Yu (Marco Nie*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

59 Scopus citations


This paper extends the bottleneck model to study congestion behavior of morning commute and its implications to transportation economics. The proposed model considers simultaneous route and departure time choices of heterogenous users who are distinguished by their valuation of travel time and punctual arrival. Moreover, two dynamic system optima are considered: one minimizes system cost in the unit of monetary value (i.e., the conventional system optimum, or SO) and the other minimizes system cost in the unit of travel time (i.e., the time-based SO, or TSO). Analytical solutions of no-toll equilibrium, SO and TSO are provided and the welfare effects of the corresponding dynamic congestion pricing options are examined, with and without route choice. The analyses suggest that TSO provides a Pareto-improving solution to the social inequity issue associated with SO. Although a TSO toll is generally discriminatory, anonymous TSO tolls do exist under certain circumstances. Unlike in the case with homogenous users, an SO toll generally alters users' route choices by tolling the poorer users off the more desirable road, which worsens social inequity. Numerical examples are presented to verify analytical results.

Original languageEnglish (US)
Pages (from-to)619-642
Number of pages24
JournalTransportation Research Part B: Methodological
Issue number4
StatePublished - May 2011


  • Alternative system optima
  • Bottleneck model
  • Congestion pricing
  • Social inequity
  • User heterogeneity

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation


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