Dynamic pricing, Heterogeneous users and perception error: Probit-based bi-criterion dynamic stochastic user equilibrium assignment

Kuilin Zhang, Hani S. Mahmassani*, Chung Cheng Lu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


A probit-based bi-criterion dynamic stochastic user equilibrium (BDSUE) model is presented to capture path choice behavior of heterogeneous users with distinct values of time (VOT) and different perception of travel costs in response to pricing and congestion in a transportation network. Across the population of travelers, the VOT is represented by a continuously distributed random variable, and path travel cost perception errors are multivariate normally distributed. The BDSUE problem is formulated as a fixed point problem in the infinite dimensional space, and solved by a column generation framework which embeds (i) a parametric analysis method (PAM) to transform the continuous problem to the finite dimensional space by finding breakpoints that partition the entire range of VOT into subintervals and define a multi-class dynamic stochastic user equilibrium (MDSUE) problem; (ii) a column generation algorithm to augment a feasible path set for each user class; (iii) a probit-based stochastic path flow updating scheme to solve a restricted MDSUE problem defined by the set of feasible paths using an averaging method; and (iv) dynamic network loading using a particle-based traffic simulator to capture traffic dynamics and determine experienced travel times for a given path flow pattern. Numerical experiments on a medium size network are conducted to explore convergence of the solution algorithm and to illustrate heterogeneous user responses to dynamic tolls.

Original languageEnglish (US)
Pages (from-to)189-204
Number of pages16
JournalTransportation Research Part C: Emerging Technologies
StatePublished - Feb 2013


  • Dynamic road pricing
  • Heterogeneous users
  • Network modeling
  • Perception error
  • Probit-based bi-criterion dynamic stochastic user equilibrium
  • Simulation-based dynamic traffic assignment
  • Value of time

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Automotive Engineering
  • Transportation
  • Computer Science Applications


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