Modeling heterogeneous network user route and departure time responses to dynamic pricing

Chung-Cheng Lu*, Hani S. Mahmassani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


The ability to realistically capture trip-makers' responses to time-varying road charges is essential for network equilibrium assignment models typically applied to predict network flows in the presence of dynamic road (congestion) pricing. User responses to pricing are governed by individual trip-makers' preferences, such as their value of time (VOT), and the cost they attach to late vs. early arrival relative to the destination. These behavioral characteristics vary across users. This paper presents a joint route and departure time network equilibrium assignment model explicitly considering heterogeneous users with different preferred arrival times at destinations, VOT, and values of early and late schedule delays (VOESD and VOLSD). The model is formulated as an infinite-dimensional variational inequality and solved by a column generation-based algorithmic framework that embeds: (i) an extreme non-dominated alternative-generating algorithm to obtain combinations of VOT, VOESD, and VOLSD subintervals (or breakpoints) that define multiple user classes, and the corresponding least trip cost alternative (joint departure time and path) for each user class, (ii) a traffic simulator to capture traffic flow dynamics and determine experienced travel costs; and (iii) a multi-class alternative flow updating scheme to solve the reduced multi-class simultaneous route and departure time user equilibrium problem defined by a subset of feasible alternatives. Application to an actual network illustrates the properties of the algorithm, and underscores the importance of capturing user heterogeneity and temporal shifts in the appraisal of dynamic pricing schemes.

Original languageEnglish
Pages (from-to)320-337
Number of pages18
JournalTransportation Research Part C: Emerging Technologies
Issue number2
StatePublished - Apr 2011


  • Dynamic road pricing
  • Dynamic traffic assignment
  • Simultaneous route and departure time user equilibrium
  • User heterogeneity
  • User responses to pricing


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