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Analytical and grid-free solutions to the Lighthill–Whitham–Richards traffic flow model

Citations

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Cited by:

  1. Bliemer, Michiel C.J. & Raadsen, Mark P.H., 2019. "Continuous-time general link transmission model with simplified fanning, Part I: Theory and link model formulation," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 442-470.
  2. Zhuang, Yifan & Liu, Zhigang & Schadschneider, Andreas & Yang, Lizhong & Huang, Jiajun, 2021. "Exploring the behavior of self-organized queuing for pedestrian flow through a non-service bottleneck," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 562(C).
  3. 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.
  4. Chow, Andy H.F. & Li, Shuai & Zhong, Renxin, 2017. "Multi-objective optimal control formulations for bus service reliability with traffic signals," Transportation Research Part B: Methodological, Elsevier, vol. 103(C), pages 248-268.
  5. Canepa, Edward S. & Claudel, Christian G., 2017. "Networked traffic state estimation involving mixed fixed-mobile sensor data using Hamilton-Jacobi equations," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 686-709.
  6. Wada, Kentaro & Usui, Kento & Takigawa, Tsubasa & Kuwahara, Masao, 2018. "An optimization modeling of coordinated traffic signal control based on the variational theory and its stochastic extension," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 907-925.
  7. Čičić, Mladen & Johansson, Karl Henrik, 2022. "Front-tracking transition system model for traffic state reconstruction, model learning, and control with application to stop-and-go wave dissipation," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 212-236.
  8. Chen, Jie & Cao, Jinde & Hu, Maobin, 2024. "A rapid semi-analytical approach for modeling traffic flow on changing road conditions and its application," Applied Mathematics and Computation, Elsevier, vol. 481(C).
  9. 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.
  10. Wang, Xuan & Zeng, Junwei & Qian, Yongsheng & Wei, Xuting & Zhang, Futao, 2024. "Heterogeneous traffic flow of expressway with Level 2 autonomous vehicles considering moving bottlenecks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 650(C).
  11. Tumash, Liudmila & Canudas-de-Wit, Carlos & Delle Monache, Maria Laura, 2022. "Multi-directional continuous traffic model for large-scale urban networks," Transportation Research Part B: Methodological, Elsevier, vol. 158(C), pages 374-402.
  12. Lebacque, Jean-Patrick & Khoshyaran, Megan M., 2013. "A variational formulation for higher order macroscopic traffic flow models of the GSOM family," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 245-265.
  13. Hänseler, Flurin S. & Bierlaire, Michel & Farooq, Bilal & Mühlematter, Thomas, 2014. "A macroscopic loading model for time-varying pedestrian flows in public walking areas," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 60-80.
  14. Raadsen, Mark P.H. & Bliemer, Michiel C.J., 2019. "Continuous-time general link transmission model with simplified fanning, Part II: Event-based algorithm for networks," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 471-501.
  15. Himpe, Willem & Corthout, Ruben & Tampère, M.J. Chris, 2016. "An efficient iterative link transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 170-190.
  16. Tilg, Gabriel & Ambühl, Lukas & Batista, Sergio & Menendez, Monica & Busch, Fritz, 2021. "On the application of variational theory to urban networks," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 435-456.
  17. Laval, Jorge A. & Costeseque, Guillaume & Chilukuri, Bargavarama, 2016. "The impact of source terms in the variational representation of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 204-216.
  18. Bar-Gera, Hillel & Carey, Malachy, 2017. "Representation requirements for perfect first-in-first-out verification in continuous flow dynamic models," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 284-301.
  19. van der Gun, Jeroen P.T. & Pel, Adam J. & van Arem, Bart, 2017. "Extending the Link Transmission Model with non-triangular fundamental diagrams and capacity drops," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 154-178.
  20. Jin, Wen-Long & Gan, Qi-Jian & Lebacque, Jean-Patrick, 2015. "A kinematic wave theory of capacity drop," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 316-329.
  21. 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.
  22. Raadsen, Mark P.H. & Bliemer, Michiel C.J. & Bell, Michael G.H., 2016. "An efficient and exact event-based algorithm for solving simplified first order dynamic network loading problems in continuous time," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 191-210.
  23. 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.
  24. Hans, Etienne & Chiabaut, Nicolas & Leclercq, Ludovic, 2015. "Applying variational theory to travel time estimation on urban arterials," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 169-181.
  25. Li, Jia & Zhang, H.M., 2013. "The variational formulation of a non-equilibrium traffic flow model: Theory and implications," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 314-325.
  26. Simoni, Michele D. & Claudel, Christian G., 2017. "A fast simulation algorithm for multiple moving bottlenecks and applications in urban freight traffic management," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 238-255.
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