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Quasi-variational inequality formulation of the multiclass dynamic traffic assignment problem

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  • Bliemer, Michiel C. J.
  • Bovy, Piet H. L.

Abstract

We consider the extension of a single user-class macroscopic dynamic traffic assignment model to include multiple user-classes. The distinction between user-classes is typically based on vehicle characteristics, e.g. cars and trucks. Interactions between the user-classes sharing the same road infrastructure are taken into account. To deal with various different asymmetries that may occur, such as interuser-class interaction, interspatial and intertemporal asymmetries, the model is specified as a (quasi) variational inequality problem. A nested modified projection method is proposed to solve the assignment problem. The solution of the problem depends heavily on the choice of some very important input: the multiclass link travel time functions. Under mild restrictions there exists a solution, which needs however not be unique. A case study illustrates the model.

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  • 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.
    • Handle: RePEc:eee:transb:v:37:y:2003:i:6:p:501-519
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    1. NESTEROV, Yu. & SCRIMALI, Laura, 2006. "Solving strongly monotone variational and quasi-variational inequalities," LIDAM Discussion Papers CORE 2006107, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. 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.
    3. Wilfredo Yushimito & Xuegang Ban & José Holguín-Veras, 2015. "Correcting the Market Failure in Work Trips with Work Rescheduling: An Analysis Using Bi-level Models for the Firm-workers Interplay," Networks and Spatial Economics, Springer, vol. 15(3), pages 883-915, September.
    4. Francisco Facchinei & Christian Kanzow & Sebastian Karl & Simone Sagratella, 2015. "The semismooth Newton method for the solution of quasi-variational inequalities," Computational Optimization and Applications, Springer, vol. 62(1), pages 85-109, September.
    5. Ciarcià, Carla & Daniele, Patrizia, 2016. "New existence theorems for quasi-variational inequalities and applications to financial models," European Journal of Operational Research, Elsevier, vol. 251(1), pages 288-299.
    6. Xinhua Mao & Jianwei Wang & Changwei Yuan & Wei Yu & Jiahua Gan, 2018. "A Dynamic Traffic Assignment Model for the Sustainability of Pavement Performance," Sustainability, MDPI, vol. 11(1), pages 1-19, December.
    7. Axel Dreves & Simone Sagratella, 2020. "Nonsingularity and Stationarity Results for Quasi-Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 711-743, June.
    8. Laval, Jorge A., 2009. "Graphical solution and continuum approximation for the single destination dynamic user equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 108-118, January.
    9. 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.
    10. Xia Yang & Xuegang Jeff Ban & Rui Ma, 2017. "Mixed Equilibria with Common Constraints on Transportation Networks," Networks and Spatial Economics, Springer, vol. 17(2), pages 547-579, June.
    11. Karakostas, George & Kim, Taeyon & Viglas, Anastasios & Xia, Hao, 2011. "On the degradation of performance for traffic networks with oblivious users," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 364-371, February.
    12. Friesz, Terry L. & Han, Ke, 2019. "The mathematical foundations of dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 309-328.
    13. Michael W. Levin & Melissa Duell & S. Travis Waller, 2020. "Arrival Time Reliability in Strategic User Equilibrium," Networks and Spatial Economics, Springer, vol. 20(3), pages 803-831, September.
    14. Chang, Justin Sueun & Mackett, Roger Laurence, 2006. "A bi-level model of the relationship between transport and residential location," Transportation Research Part B: Methodological, Elsevier, vol. 40(2), pages 123-146, February.
    15. Christian Kanzow & Daniel Steck, 2018. "Augmented Lagrangian and exact penalty methods for quasi-variational inequalities," Computational Optimization and Applications, Springer, vol. 69(3), pages 801-824, April.
    16. 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.
    17. M. Castellani & M. Giuli, 2019. "A coercivity condition for nonmonotone quasiequilibria on finite-dimensional spaces," Journal of Global Optimization, Springer, vol. 75(1), pages 163-176, September.
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