A bi-criterion dynamic user equilibrium traffic assignment model and solution algorithm for evaluating dynamic road pricing strategies

Chung-Cheng Lu, Hani S. Mahmassani*, Xuesong Zhou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

59 Scopus citations


To support the evaluation of dynamic road pricing strategies in a network context, this study develops a bi-criterion dynamic user equilibrium (BDUE) model, which aims to capture users' path choices in response to time-varying toll charges, and hence explicitly considers heterogeneous users with different value of time (VOT) preferences in the underlying path choice decision framework. The VOT is represented as a continuously distributed random variable across the population of trips, and an infinite dimensional variational inequality formulation is established to characterize the solutions to the BDUE problem. This study proposes a simulation-based heuristic approach to find the BDUE path flow patterns. Specifically, embedded in the algorithmic framework are (i) a bi-criterion time-dependent least generalized cost path algorithm applied to generate the extreme efficient path set and the corresponding set of breakpoints that naturally defines the multiple user classes, thereby generating the descent direction from a multi-class auxiliary path flow vector, and (ii) a traffic simulator used to describe the traffic flow propagation and determine experienced travel times and costs. To circumvent the difficulty of storing the memory-intensive path set and routing policies for large-scale network applications, a vehicle-based implementation technique is proposed to use the vehicle path set as a proxy for keeping track of the path assignment results. A set of numerical experiments are conducted on several real road networks to explore the convergence behavior and solution quality of the BDUE algorithm, as well as to investigate how VOT distributions affect the path flow pattern and toll road usage under dynamic road pricing scenarios.

Original languageEnglish
Pages (from-to)371-389
Number of pages19
JournalTransportation Research Part C: Emerging Technologies
Issue number4
StatePublished - 1 Jan 2008


  • Bi-criterion dynamic user equilibrium
  • Dynamic road pricing
  • Dynamic traffic assignment
  • Heterogeneous driver preferences
  • Network models
  • Value of time


Dive into the research topics of 'A bi-criterion dynamic user equilibrium traffic assignment model and solution algorithm for evaluating dynamic road pricing strategies'. Together they form a unique fingerprint.

Cite this