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A Discrete Time, Nested Cost Operator Approach to the Dynamic Network User Equilibrium Problem

Author

Listed:
  • Byung-Wook Wie

    (School of Travel Industry Management, University of Hawaii, Honolulu, Hawaii 96822)

  • Roger L. Tobin

    (GTE Laboratories Incorporated, Waltham, Massachusetts 02254)

  • Terry L. Friesz

    (Departments of Systems Engineering and Operations Research and Engineering, George Mason University, Fairfax, Virginia 22030)

  • David Bernstein

    (Department of Civil Engineering and Operations Research, Princeton University, Princeton, New Jersey 08544)

Abstract

In this paper we formulate the dynamic network user equilibrium problem as a variational inequality problem in discrete time in terms of unit path cost functions. We then show how arc exit flow functions and nested cost operators can be used to calculate unit path costs given the departure time and route choices of network users. We also demonstrate that, assuming certain regularity conditions hold, a discrete time dynamic network user equilibrium is guaranteed to exist. Finally, a heuristic algorithm and numerical results are presented.

Suggested Citation

  • Byung-Wook Wie & Roger L. Tobin & Terry L. Friesz & David Bernstein, 1995. "A Discrete Time, Nested Cost Operator Approach to the Dynamic Network User Equilibrium Problem," Transportation Science, INFORMS, vol. 29(1), pages 79-92, February.
    • Handle: RePEc:inm:ortrsc:v:29:y:1995:i:1:p:79-92
    DOI: 10.1287/trsc.29.1.79
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    Cited by:

    1. Li-Jun Tian & Hai-Jun Huang & Zi-You Gao, 2012. "A Cumulative Perceived Value-Based Dynamic User Equilibrium Model Considering the Travelers’ Risk Evaluation on Arrival Time," Networks and Spatial Economics, Springer, vol. 12(4), pages 589-608, December.
    2. Lago, Alejandro, 2003. "Spatial Models of Morning Commute Consistent with Realistic Traffic Behavior," University of California Transportation Center, Working Papers qt4nd315bv, University of California Transportation Center.
    3. Li, Jun & Fujiwara, Okitsugu & Kawakami, Shogo, 2000. "A reactive dynamic user equilibrium model in network with queues," Transportation Research Part B: Methodological, Elsevier, vol. 34(8), pages 605-624, November.
    4. Huang, Hai-Jun & Lam, William H. K., 2002. "Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 253-273, March.
    5. Friesz, Terry L. & Kim, Taeil & Kwon, Changhyun & Rigdon, Matthew A., 2011. "Approximate network loading and dual-time-scale dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 176-207, January.
    6. Wie, Byung-Wook & Tobin, Roger L., 1998. "Dynamic congestion pricing models for general traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 32(5), pages 313-327, June.
    7. Zhi-Yang Lin & S. C. Wong & Peng Zhang & Keechoo Choi, 2018. "A Predictive Continuum Dynamic User-Optimal Model for the Simultaneous Departure Time and Route Choice Problem in a Polycentric City," Service Science, INFORMS, vol. 52(6), pages 1496-1508, December.
    8. Lam, William H.K. & Li, Zhi-Chun & Huang, Hai-Jun & Wong, S.C., 2006. "Modeling time-dependent travel choice problems in road networks with multiple user classes and multiple parking facilities," Transportation Research Part B: Methodological, Elsevier, vol. 40(5), pages 368-395, June.
    9. Wie, Byung-Wook & Tobin, Roger L. & Carey, Malachy, 2002. "The existence, uniqueness and computation of an arc-based dynamic network user equilibrium formulation," Transportation Research Part B: Methodological, Elsevier, vol. 36(10), pages 897-918, December.
    10. Wu, J. H. & Chen, Y. & Florian, M., 1998. "The continuous dynamic network loading problem: a mathematical formulation and solution method," Transportation Research Part B: Methodological, Elsevier, vol. 32(3), pages 173-187, April.
    11. Jang, Wonjae & Ran, Bin & Choi, Keechoo, 2005. "A discrete time dynamic flow model and a formulation and solution method for dynamic route choice," Transportation Research Part B: Methodological, Elsevier, vol. 39(7), pages 593-620, August.
    12. William Lam & Hai-jun Huang, 2002. "A combined activity/travel choice model for congested road networks with queues," Transportation, Springer, vol. 29(1), pages 5-29, February.
    13. Celikoglu, Hilmi Berk, 2013. "Reconstructing freeway travel times with a simplified network flow model alternating the adopted fundamental diagram," European Journal of Operational Research, Elsevier, vol. 228(2), pages 457-466.
    14. Mounce, Richard & Carey, Malachy, 2011. "Route swapping in dynamic traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 102-111, January.
    15. Wang, Jian & Peeta, Srinivas & He, Xiaozheng, 2019. "Multiclass traffic assignment model for mixed traffic flow of human-driven vehicles and connected and autonomous vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 139-168.
    16. Daoli Zhu & Patrice Marcotte, 2000. "On the Existence of Solutions to the Dynamic User Equilibrium Problem," Transportation Science, INFORMS, vol. 34(4), pages 402-414, November.
    17. Qipeng Zheng & Ashwin Arulselvan, 2011. "Discrete time dynamic traffic assignment models and solution algorithm for managed lanes," Journal of Global Optimization, Springer, vol. 51(1), pages 47-68, September.
    18. Takashi Akamatsu, 2001. "An Efficient Algorithm for Dynamic Traffic Equilibrium Assignment with Queues," Transportation Science, INFORMS, vol. 35(4), pages 389-404, November.
    19. Lu, Gongyuan & Nie, Yu(Marco) & Liu, Xiaobo & Li, Denghui, 2019. "Trajectory-based traffic management inside an autonomous vehicle zone," Transportation Research Part B: Methodological, Elsevier, vol. 120(C), pages 76-98.
    20. Lago, Alejandro, 2003. "Spatial Models of Morning Commute Consistent with Realistic Traffic Behavior," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt6wk3t20s, Institute of Transportation Studies, UC Berkeley.
    21. Szeto, W. Y. & Lo, Hong K., 2004. "A cell-based simultaneous route and departure time choice model with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 38(7), pages 593-612, August.
    22. Yu Nie & H. Zhang, 2010. "Solving the Dynamic User Optimal Assignment Problem Considering Queue Spillback," Networks and Spatial Economics, Springer, vol. 10(1), pages 49-71, March.

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