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

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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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References

  • Abdelghany, A.F., Mahmassani, H.S.: Temporal-spatial microassignment and sequencing of travel demand with activity-trip chains. Transp. Res. Rec. J. Transp. Res. Board 1831, 89–97 (2003). doi:10.3141/1831-10

    Article  Google Scholar 

  • Abdelghany, A.F., Mahmassani, H.S., Chiu, Y.-C.: Spatial microassignment of travel demand with activity trip chains. Transp. Res. Rec. J. Transp. Res. Board 1777, 36–46 (2001). doi:10.3141/1777-04

    Article  Google Scholar 

  • Brownstone, D., Small, K.A.: Valuing time and reliability: assessing the evidence from road pricing demonstrations. Transp. Res. A 39(4), 279–293 (2005). doi:10.1016/j.tra.2004.11.001

    Google Scholar 

  • Ettema, D., Borgers, A., Timmermans, H.: Simulation model of activity scheduling behavior. Transp. Res. Rec. 1, 1 (1993)

    Google Scholar 

  • Ettema, D., Borgers, A., Timmermans, H.: SMASH (simulation model of activity scheduling heuristics): some simulations. Transp. Res. Rec. J. Transp. Res. Board 1551, 88–94 (1996). doi:10.3141/1551-12

    Article  Google Scholar 

  • Han, D., Yang, H.: The multi-class, multi-criterion traffic equilibrium and the efficiency of congestion pricing. Transp. Res. E 44(5), 753–773 (2008). doi:10.1016/j.tre.2007.07.011

    Article  Google Scholar 

  • Huang, H.-J., Lam, W.H.K.: Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues. Transp. Res. B 36(3), 253–273 (2002). doi:10.1016/S0191-2615(00)00049-7

    Article  Google Scholar 

  • Jayakrishnan, R., Mahmassani, H.S., Hu, T.-Y.: An evaluation tool for advanced traffic information and management systems in urban networks. Transp. Res. C 2(3), 129–147 (1994). doi:10.1016/0968-090X(94)90005-1

    Article  Google Scholar 

  • Jiang, L., Mahmassani, H.S.: Toll pricing: computational tests for capturing heterogeneity of user preferences. Transp. Res. Rec. J. Transp. Res. Board 2343, 105–115 (2013). doi:10.3141/2343-13

    Article  Google Scholar 

  • Jiang, L., Mahmassani, H.S., Zhang, K.: Congestion pricing, heterogeneous users, and travel time reliability: multicriterion dynamic user equilibrium model and efficient implementation for large-scale networks. Transp. Res. Rec. J. Transp. Res. Board 2254, 58–67 (2011)

    Article  Google Scholar 

  • Joh, C.-H., Arentze, T., Timmermans, H.: Modeling individuals’ activity-travel rescheduling heuristics: theory and numerical experiments. Transp. Res. Rec. J. Transp. Res. Board 1807, 16–25 (2002). doi:10.3141/1807-03

    Article  Google Scholar 

  • Lam, W.H.K., Yin, Y.: An activity-based time-dependent traffic assignment model. Transp. Res. B 35(6), 549–574 (2001). doi:10.1016/S0191-2615(00)00010-2

    Article  Google Scholar 

  • Leurent, F.: Cost versus time equilibrium over a network. Eur. J. Oper. Res. 71(2), 205–221 (1993). doi:10.1016/0377-2217(93)90049-S

    Article  Google Scholar 

  • Li, Z.-C., Lam, W.H.K., Wong, S.C.: Bottleneck model revisited: An activity-based perspective. Transp. Res. B 68, 262–287 (2014). doi:10.1016/j.trb.2014.06.013

    Article  Google Scholar 

  • Lin, D.-Y., Eluru, N., Waller, S., Bhat, C.: Integration of activity-based modeling and dynamic traffic assignment. Transp. Res. Rec. J. Transp. Res. Board 2076, 52–61 (2008). doi:10.3141/2076-06

    Article  Google Scholar 

  • Lu, C.-C., Mahmassani, H.S., Zhou, X.: A bi-criterion dynamic user equilibrium traffic assignment model and solution algorithm for evaluating dynamic road pricing strategies. Transp. Res C 16(4), 371–389 (2008). doi:10.1016/j.trc.2007.08.002

    Article  Google Scholar 

  • Lu, C.-C., Mahmassani, H.S., Zhou, X.: Equivalent gap function-based reformulation and solution algorithm for the dynamic user equilibrium problem. Transp. Res C 43(3), 345–364 (2009). doi:10.1016/j.trb.2008.07.005

    Article  Google Scholar 

  • Mahmassani, H.S.: Dynamic network traffic assignment and simulation methodology for advanced system management applications. Netw. Spat. Econ. 1(3–4), 267–292 (2001). doi:10.1023/A:1012831808926

    Article  Google Scholar 

  • Mahmassani, H.S., Zhou, X., Lu, C.-C.: Toll pricing and heterogeneous users: approximation algorithms for finding bicriterion time-dependent efficient paths in large-scale traffic networks. Transp. Res. Rec. J. Transp. Res. Board 1923, 28–36 (2005). doi:10.3141/1923-04

    Article  Google Scholar 

  • Peeta, S., Ziliaskopoulos, A.: Foundations of dynamic traffic assignment: the past, the present and the future. Netw. Spat. Econ. 1(3–4), 233–265 (2001). doi:10.1023/A:1012827724856

    Article  Google Scholar 

  • Ramadurai, G., Ukkusuri, S.: Dynamic user equilibrium model for combined activity-travel choices using activity-travel supernetwork representation. Netw. Spat. Econ. 10(2), 273–292 (2010). doi:10.1007/s11067-008-9078-3

    Article  Google Scholar 

  • Rdc, I.: Activity-based modeling system for travel demand forecasting. Metropolitan Washington Council of Governments, U.S. Department of Transportation, U.S. Environmental Protection Agency, Washington DC (1995)

    Google Scholar 

  • Sbayti, H., Lu, C.-C., Mahmassani, H.S.: Efficient implementation of method of successive averages in simulation-based dynamic traffic assignment models for large-scale network applications. Transp. Res. Rec. J. Transp. Res. Board 2029, 22–30 (2007). doi:10.3141/2029-03

    Article  Google Scholar 

  • Small, K.A., Yan, J.: The value of “value pricing” of roads: second-best pricing and product differentiation. J. Urban Econ. 49(2), 310–336 (2001). doi:10.1006/juec.2000.2195

    Article  Google Scholar 

  • Smith, M.J.: The existence, uniqueness and stability of traffic equilibria. Transp. Res. B 13(4), 295–304 (1979). doi:10.1016/0191-2615(79)90022-5

    Article  Google Scholar 

  • Smith, M.J.: A new dynamic traffic model and the existence and calculation of dynamic user equilibria on congested capacity-constrained road networks. Transp. Res. B 27(1), 49–63 (1993). doi:10.1016/0191-2615(93)90011-X

    Article  Google Scholar 

  • Smith, M.J., Wisten, M.B.: A continuous day-to-day traffic assignment model and the existence of a continuous dynamic user equilibrium. Ann. Oper. Res. 60(1), 59–79 (1995). doi:10.1007/BF02031940

    Article  Google Scholar 

  • Tong, C.O., Wong, S.C.: A predictive dynamic traffic assignment model in congested capacity-constrained road networks. Transp. Res. B 34(8), 625–644 (2000). doi:10.1016/S0191-2615(99)00045-4

    Article  Google Scholar 

  • Verbas, İ., Mahmassani, H.S., Zhang, K.: Time-dependent origin-destination demand estimation: challenges and methods for large-scale networks with multiple vehicle classes. Transp. Res. Rec. J. Transp. Res. Board 2263, 45–56 (2011)

    Article  Google Scholar 

  • Wardrop, J.G.: Road Paper. Some theoretical aspects of road traffic research. In: ICE Proceedings: Engineering Divisions, vol. 2, pp. 325–378. Thomas Telford (1952)

  • Yang, H., Tang, W.H., Man Cheung, W., Meng, Q.: Profitability and welfare gain of private toll roads in a network with heterogeneous users. Transp. Res. A 36(6), 537–554 (2002). doi:10.1016/S0965-8564(01)00021-0

    Article  Google Scholar 

  • Ziliaskopoulos, A.K., Waller, S.T., Li, Y., Byram, M.: Large-scale dynamic traffic assignment: implementation issues and computational analysis. J. Transp. Eng. 130(5), 585–593 (2004)

    Article  Google Scholar 

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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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Authors and Affiliations

  1. Transportation Center, Northwestern University, 600 Foster Street, Evanston, IL, 60208, USA

    Hooram Halat, Hani S. Mahmassani, Xiang Xu & Omer Verbas

  2. Civil and Environmental Engineering Department, Michigan State University, East Lansing, MI, USA

    Ali Zockaie

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  1. Hooram Halat
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  2. Ali Zockaie
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  3. Hani S. Mahmassani
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  4. Xiang Xu
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Correspondence to Hani S. Mahmassani.

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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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