Dynamic network equilibrium for daily activity-trip chains of heterogeneous travelers: application to large-scale networks

Hooram Halat, Ali Zockaie, Hani S Mahmassani*, Xiang Xu, Omer Verbas

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Applications of dynamic network equilibrium models have, mostly, considered the unit of traffic demand either as one-way trip, or as multiple independent trips. However, individuals’ travel patterns typically follow a sequence of trips chained together. In this study we aim at developing a general simulation-based dynamic network equilibrium algorithm for assignment of activity-trip chain demand. The trip chain of each individual trip maker is defined by the departure time at origin, sequence of activity destination locations, including the location of their intermediate destinations and their final destination, and activity duration at each of the intermediate destinations. Spatial and temporal dependency of subsequent trips on each other necessitate time and memory consuming calculations and storage of node-to-node time-dependent least generalized cost path trees, which is not practical for very large metropolitan area networks. We first propose a reformulation of the trip-based demand gap function formulation for the variational inequality formulation of the Bi-criterion Dynamic User Equilibrium (BDUE) problem. Next, we propose a solution algorithm for solving the BDUE problem with daily chain of activity-trips. Implementation of the algorithm for very large networks circumvents the need to store memory-intensive node-to-node time-dependent shortest path trees by implementing a destination-based time-dependent least generalized cost path finding algorithm, while maintaining the spatial and temporal dependency of subsequent trips. Numerical results for a real-world large scale network suggest that recognizing the dependency of multiple trips of a chain, and maintaining the departure time consistency of subsequent trips provide sharper drops in gap values, hence, the convergence could be achieved faster (compared to when trips are considered independent of each other).

Original languageEnglish (US)
Pages (from-to)1041-1059
Number of pages19
Issue number6
StatePublished - Nov 1 2016


  • Convergence
  • Dynamic user equilibrium
  • Gap function
  • Heterogeneity
  • Large-scale network applications
  • Mega-regional networks
  • Trip chains
  • activity-based model

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Development
  • Transportation


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