Abstract
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).
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Acknowledgments
The authors appreciate the assistance of Chicago Metropolitan Agency for Planning (CMAP) staff in making data available to the study, especially Kermit Wies at CMAP. The study team has also benefited from the advice of Dr. Peter Vovsha of Parsons Brinckerhoff, Inc., who developed the Activity-Based Model for CMAP. The authors naturally remain solely responsible for all contents of the paper.
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Halat, H., Zockaie, A., Mahmassani, H.S. et al. Dynamic network equilibrium for daily activity-trip chains of heterogeneous travelers: application to large-scale networks. Transportation 43, 1041–1059 (2016). https://doi.org/10.1007/s11116-016-9724-4
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DOI: https://doi.org/10.1007/s11116-016-9724-4