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Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation

Author

Listed:
  • Ke Han

    (Imperial College London)

  • Gabriel Eve

    (Imperial College London)

  • Terry L. Friesz

    (Pennsylvania State University)

Abstract

Dynamic user equilibrium (DUE) is the most widely studied form of dynamic traffic assignment (DTA), in which road travelers engage in a non-cooperative Nash-like game with departure time and route choices. DUE models describe and predict the time-varying traffic flows on a network consistent with traffic flow theory and travel behavior. This paper documents theoretical and numerical advances in synthesizing traffic flow theory and DUE modeling, by presenting a holistic computational theory of DUE, which is numerically implemented in a MATLAB package. In particular, the dynamic network loading (DNL) sub-problem is formulated as a system of differential algebraic equations based on the Lighthill-Whitham-Richards fluid dynamic model, which captures the formation, propagation and dissipation of physical queues as well as vehicle spillback on networks. Then, the fixed-point algorithm is employed to solve the DUE problems with simultaneous route and departure time choices on several large-scale networks. We make openly available the MATLAB package, which can be used to solve DUE problems on user-defined networks, aiming to not only facilitate benchmarking a wide range of DUE algorithms and solutions, but also offer researchers a platform to further develop their own models and applications. The MATLAB package and computational examples are available at https://github.com/DrKeHan/DTA .

Suggested Citation

  • Ke Han & Gabriel Eve & Terry L. Friesz, 2019. "Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation," Networks and Spatial Economics, Springer, vol. 19(3), pages 869-902, September.
    • Handle: RePEc:kap:netspa:v:19:y:2019:i:3:d:10.1007_s11067-018-9433-y
    DOI: 10.1007/s11067-018-9433-y
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    1. Georgia Perakis & Guillaume Roels, 2006. "An Analytical Model for Traffic Delays and the Dynamic User Equilibrium Problem," Operations Research, INFORMS, vol. 54(6), pages 1151-1171, December.
    2. Han, Ke & Gayah, Vikash V., 2015. "Continuum signalized junction model for dynamic traffic networks: Offset, spillback, and multiple signal phases," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 213-239.
    3. 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.
    4. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part III: Multi-destination flows," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 305-313, August.
    5. 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.
    6. Friesz, Terry L. & Mookherjee, Reetabrata, 2006. "Solving the dynamic network user equilibrium problem with state-dependent time shifts," Transportation Research Part B: Methodological, Elsevier, vol. 40(3), pages 207-229, March.
    7. Bliemer, Michiel C. J. & Bovy, Piet H. L., 2003. "Quasi-variational inequality formulation of the multiclass dynamic traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 37(6), pages 501-519, July.
    8. 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.
    9. Lo, Hong K. & Szeto, W. Y., 2002. "A cell-based variational inequality formulation of the dynamic user optimal assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 36(5), pages 421-443, June.
    10. Ke Han & Tao Yao & Chaozhe Jiang & Terry L. Friesz, 2017. "Lagrangian-based Hydrodynamic Model for Traffic Data Fusion on Freeways," Networks and Spatial Economics, Springer, vol. 17(4), pages 1071-1094, December.
    11. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part II: Queueing at freeway bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 289-303, August.
    12. Jin, Wen-Long, 2015. "Continuous formulations and analytical properties of the link transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 74(C), pages 88-103.
    13. Ukkusuri, Satish V. & Han, Lanshan & Doan, Kien, 2012. "Dynamic user equilibrium with a path based cell transmission model for general traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1657-1684.
    14. Tong, C. O. & Wong, S. C., 2000. "A predictive dynamic traffic assignment model in congested capacity-constrained road networks," Transportation Research Part B: Methodological, Elsevier, vol. 34(8), pages 625-644, November.
    15. Daganzo, Carlos F., 1995. "The cell transmission model, part II: Network traffic," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 79-93, April.
    16. Han, Ke & Friesz, Terry L. & Szeto, W.Y. & Liu, Hongcheng, 2015. "Elastic demand dynamic network user equilibrium: Formulation, existence and computation," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 183-209.
    17. Terry L. Friesz, 2010. "Dynamic Optimization and Differential Games," International Series in Operations Research and Management Science, Springer, number 978-0-387-72778-3, December.
    18. Ban, Xuegang (Jeff) & Pang, Jong-Shi & Liu, Henry X. & Ma, Rui, 2012. "Modeling and solving continuous-time instantaneous dynamic user equilibria: A differential complementarity systems approach," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 389-408.
    19. 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.
    20. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    21. Friesz, Terry L. & Han, Ke & Neto, Pedro A. & Meimand, Amir & Yao, Tao, 2013. "Dynamic user equilibrium based on a hydrodynamic model," Transportation Research Part B: Methodological, Elsevier, vol. 47(C), pages 102-126.
    22. Jeihani, Mansoureh, 2007. "A Review of Dynamic Traffic Assignment Computer Packages," Journal of the Transportation Research Forum, Transportation Research Forum, vol. 46(2).
    23. Han, Ke & Gayah, Vikash V. & Piccoli, Benedetto & Friesz, Terry L. & Yao, Tao, 2014. "On the continuum approximation of the on-and-off signal control on dynamic traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 61(C), pages 73-97.
    24. Kuwahara, Masao & Akamatsu, Takashi, 1997. "Decomposition of the reactive dynamic assignments with queues for a many-to-many origin-destination pattern," Transportation Research Part B: Methodological, Elsevier, vol. 31(1), pages 1-10, February.
    25. Michiel C. J. Bliemer & Mark P. H. Raadsen & Luuk J. N. Brederode & Michael G. H. Bell & Luc J. J. Wismans & Mike J. Smith, 2017. "Genetics of traffic assignment models for strategic transport planning," Transport Reviews, Taylor & Francis Journals, vol. 37(1), pages 56-78, January.
    26. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    27. Terry L. Friesz & David Bernstein & Tony E. Smith & Roger L. Tobin & B. W. Wie, 1993. "A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem," Operations Research, INFORMS, vol. 41(1), pages 179-191, February.
    28. Laval, Jorge A. & Leclercq, Ludovic, 2013. "The Hamilton–Jacobi partial differential equation and the three representations of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 52(C), pages 17-30.
    29. Jin, Wen-Long, 2010. "Continuous kinematic wave models of merging traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1084-1103, September.
    30. Daganzo, Carlos F., 1994. "The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory," Transportation Research Part B: Methodological, Elsevier, vol. 28(4), pages 269-287, August.
    31. Han, Lanshan & Ukkusuri, Satish & Doan, Kien, 2011. "Complementarity formulations for the cell transmission model based dynamic user equilibrium with departure time choice, elastic demand and user heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1749-1767.
    32. 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.
    33. Daganzo, Carlos F., 2005. "A variational formulation of kinematic waves: Solution methods," Transportation Research Part B: Methodological, Elsevier, vol. 39(10), pages 934-950, December.
    34. Osorio, Carolina & Flötteröd, Gunnar & Bierlaire, Michel, 2011. "Dynamic network loading: A stochastic differentiable model that derives link state distributions," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1410-1423.
    35. Mounce, Richard, 2006. "Convergence in a continuous dynamic queueing model for traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 40(9), pages 779-791, November.
    36. Daganzo, Carlos F., 2005. "A variational formulation of kinematic waves: basic theory and complex boundary conditions," Transportation Research Part B: Methodological, Elsevier, vol. 39(2), pages 187-196, February.
    37. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part I: General theory," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 281-287, August.
    38. Costeseque, Guillaume & Lebacque, Jean-Patrick, 2014. "A variational formulation for higher order macroscopic traffic flow models: Numerical investigation," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 112-133.
    39. Jiancheng Long & Hai-Jun Huang & Ziyou Gao & W. Y. Szeto, 2013. "An Intersection-Movement-Based Dynamic User Optimal Route Choice Problem," Operations Research, INFORMS, vol. 61(5), pages 1134-1147, October.
    40. 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.
    41. 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.
    42. Y. W. Xu & J. H. Wu & M. Florian & P. Marcotte & D. L. Zhu, 1999. "Advances in the Continuous Dynamic Network Loading Problem," Transportation Science, INFORMS, vol. 33(4), pages 341-353, November.
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