Variable toll pricing and heterogeneous users: Model and solution algorithm for bicriterion dynamic traffic assignment problem

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

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

12 Scopus citations


A dynamic traffic assignment model and its solution algorithm for the bicriterion dynamic user equilibrium (BDUE) problem that allows for heterogeneous users with different value-of-time (VOT) preferences are presented. Assuming the VOT as a continuously distributed random variable across the population of trips, the BDUE problem is formulated as a system of infinite-dimensional variational inequalities (Vis). Rather than solving the VI formulation directly, this study employs a generalized Frank-Wolfe algorithm to und the BDUE flow pattern. A bicriterion time-dependent least-cost path algorithm is applied to generate the extreme efficient path set, and the corresponding breakpoints naturally define the multiple user classes and thereby generate the descent direction for a multiclass dynamic network loading. A traffic simulator is used to describe the traffic flow propagation and the spatial and temporal interactions. 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, with the vehicle path set as a proxy for keeping track of the path assignment results. A set of numerical experiments is conducted to explore the convergence behavior of the BDUE algorithm and investigate how VOT distributions affect the path flow pattern and toll road usage under different dynamic road pricing scenarios.

Original languageEnglish
Title of host publicationNetwork Modeling 2006
PublisherNational Research Council
Number of pages8
ISBN (Print)0309099730, 9780309099738
StatePublished - 1 Jan 2006

Publication series

NameTransportation Research Record
ISSN (Print)0361-1981


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