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A non-equilibrium traffic model devoid of gas-like behavior

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  1. Lebacque, Jean-Patrick & Mammar, Salim & Haj-Salem, Habib, 2007. "The Aw-Rascle and Zhang's model: Vacuum problems, existence and regularity of the solutions of the Riemann problem," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 710-721, August.
  2. Salim Mammar & Jean-Patrick Lebacque & Habib Haj Salem, 2009. "Riemann Problem Resolution and Godunov Scheme for the Aw-Rascle-Zhang Model," Transportation Science, INFORMS, vol. 43(4), pages 531-545, November.
  3. McCrea, Jennifer & Moutari, Salissou, 2010. "A hybrid macroscopic-based model for traffic flow in road networks," European Journal of Operational Research, Elsevier, vol. 207(2), pages 676-684, December.
  4. Andronikos Paliathanasis & Peter G. L. Leach, 2022. "Lie Symmetry Analysis of the Aw–Rascle–Zhang Model for Traffic State Estimation," Mathematics, MDPI, vol. 11(1), pages 1-11, December.
  5. Mohammadian, Saeed & Zheng, Zuduo & Haque, Mazharul & Bhaskar, Ashish, 2023. "NET-RAT: Non-equilibrium traffic model based on risk allostasis theory," Transportation Research Part A: Policy and Practice, Elsevier, vol. 174(C).
  6. Tie-Qiao Tang & Yun-Peng Wang & Xiao-Bao Yang & Hai-Jun Huang, 2014. "A Multilane Traffic Flow Model Accounting for Lane Width, Lane-Changing and the Number of Lanes," Networks and Spatial Economics, Springer, vol. 14(3), pages 465-483, December.
  7. Ranju Mohan & Gitakrishnan Ramadurai, 2015. "Submission to the DTA2012 Special Issue: A Case for Higher-Order Traffic Flow Models in DTA," Networks and Spatial Economics, Springer, vol. 15(3), pages 765-790, September.
  8. Gabriel Obed Fosu & Francis Tabi Oduro & Carlo Caligaris, 2021. "Multilane analysis of a viscous second-order macroscopic traffic flow model," Partial Differential Equations and Applications, Springer, vol. 2(1), pages 1-17, February.
  9. Zheng, Liang & Jin, Peter J. & Huang, Helai, 2015. "An anisotropic continuum model considering bi-directional information impact," Transportation Research Part B: Methodological, Elsevier, vol. 75(C), pages 36-57.
  10. Zhang, Peng & Wu, Chun-Xiu & Wong, S.C., 2012. "A semi-discrete model and its approach to a solution for a wide moving jam in traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 456-463.
  11. Xin, Xueli & Sun, Meina, 2024. "The vanishing pressure limits of Riemann solutions for the Aw-Rascle hydrodynamic traffic flow model with the logarithmic equation of state," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
  12. Sun, Fengxin & Wang, Jufeng & Cheng, Rongjun, 2019. "An improved anisotropic continuum model considering the driver’s desire for steady driving," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1449-1462.
  13. Wang, Yi & Szeto, W.Y. & Han, Ke & Friesz, Terry L., 2018. "Dynamic traffic assignment: A review of the methodological advances for environmentally sustainable road transportation applications," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 370-394.
  14. Mohammadian, Saeed & Zheng, Zuduo & Haque, Md. Mazharul & Bhaskar, Ashish, 2021. "Performance of continuum models for realworld traffic flows: Comprehensive benchmarking," Transportation Research Part B: Methodological, Elsevier, vol. 147(C), pages 132-167.
  15. 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.
  16. Zhai, Cong & Wu, Weitiao, 2022. "A continuum model considering the uncertain velocity of preceding vehicles on gradient highways," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
  17. Wu, Chun-Xiu & Zhang, Peng & Wong, S.C. & Choi, Keechoo, 2014. "Steady-state traffic flow on a ring road with up- and down-slopes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 85-93.
  18. García-Chan, N. & Alvarez-Vázquez, L.J. & Martínez, A. & Vázquez-Méndez, M.E., 2021. "Designing an ecologically optimized road corridor surrounding restricted urban areas: A mathematical methodology," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 745-759.
  19. Blandin, Sébastien & Argote, Juan & Bayen, Alexandre M. & Work, Daniel B., 2013. "Phase transition model of non-stationary traffic flow: Definition, properties and solution method," Transportation Research Part B: Methodological, Elsevier, vol. 52(C), pages 31-55.
  20. Mohan, Ranju & Ramadurai, Gitakrishnan, 2021. "Multi-class traffic flow model based on three dimensional flow–concentration surface," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 577(C).
  21. Zhang, Peng & Wong, S.C. & Dai, S.Q., 2009. "A conserved higher-order anisotropic traffic flow model: Description of equilibrium and non-equilibrium flows," Transportation Research Part B: Methodological, Elsevier, vol. 43(5), pages 562-574, June.
  22. Yuan Tang & Yu Xue & Muyang Huang & Qiyun Wen & Bingling Cen & Dong Chen, 2023. "A Lattice Hydrodynamic Model for Four-Way Pedestrian Traffic with Turning Capacity," Sustainability, MDPI, vol. 15(3), pages 1-17, January.
  23. Irena Strnad & Rok Marsetič, 2023. "Differential Evolution Based Numerical Variable Speed Limit Control Method with a Non-Equilibrium Traffic Model," Mathematics, MDPI, vol. 11(2), pages 1-16, January.
  24. 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.
  25. Bharathi, Dhivya & Vanajakshi, Lelitha & Subramanian, Shankar C., 2022. "Spatio-temporal modelling and prediction of bus travel time using a higher-order traffic flow model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
  26. Ge, Qian & Fukuda, Daisuke, 2019. "A macroscopic dynamic network loading model for multiple-reservoir system," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 502-527.
  27. Coifman, Benjamin & Ponnu, Balaji & El Asmar, Paul, 2023. "LWR and shockwave analysis - Failures under a concave fundamental diagram and unexpected induced disturbances," Transportation Research Part A: Policy and Practice, Elsevier, vol. 175(C).
  28. Sun, Lu & Jafaripournimchahi, Ammar & Kornhauser, Alain & Hu, Wushen, 2020. "A new higher-order viscous continuum traffic flow model considering driver memory in the era of autonomous and connected vehicles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
  29. Pereira, Mike & Boyraz Baykas, Pinar & Kulcsár, Balázs & Lang, Annika, 2022. "Parameter and density estimation from real-world traffic data: A kinetic compartmental approach," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 210-239.
  30. Ou, Zhong-Hui & Dai, Shi-Qiang & Dong, Li-Yun & Wu, Zheng & Tao, Ming-De, 2006. "New equilibrium function of traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 525-531.
  31. Jin, Wen-Long, 2016. "On the equivalence between continuum and car-following models of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 543-559.
  32. Yuan, Yun & Zhang, Zhao & Yang, Xianfeng Terry & Zhe, Shandian, 2021. "Macroscopic traffic flow modeling with physics regularized Gaussian process: A new insight into machine learning applications in transportation," Transportation Research Part B: Methodological, Elsevier, vol. 146(C), pages 88-110.
  33. Kontorinaki, Maria & Spiliopoulou, Anastasia & Roncoli, Claudio & Papageorgiou, Markos, 2017. "First-order traffic flow models incorporating capacity drop: Overview and real-data validation," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 52-75.
  34. Zhang, Qinglong & Liu, Shuzhi, 2023. "The Riemann problem and a Godunov-type scheme for a traffic flow model on two lanes with two velocities," Applied Mathematics and Computation, Elsevier, vol. 436(C).
  35. Zhang, Yicai & Xue, Yu & Zhang, Peng & Fan, Deli & di He, Hong, 2019. "Bifurcation analysis of traffic flow through an improved car-following model considering the time-delayed velocity difference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 133-140.
  36. Yaroslav Kholodov & Andrey Alekseenko & Viktor Kazorin & Alexander Kurzhanskiy, 2021. "Generalization Second Order Macroscopic Traffic Models via Relative Velocity of the Congestion Propagation," Mathematics, MDPI, vol. 9(16), pages 1-14, August.
  37. Fan, De-li & Zhang, Yi-cai & Shi, Yin & Xue, Yu & Wei, Fang-ping, 2018. "An extended continuum traffic model with the consideration of the optimal velocity difference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 402-413.
  38. Corli, Andrea & Fan, Haitao, 2023. "String stability in traffic flows," Applied Mathematics and Computation, Elsevier, vol. 443(C).
  39. Lin Li & Serdar Coskun & Jiaze Wang & Youming Fan & Fengqi Zhang & Reza Langari, 2021. "Velocity Prediction Based on Vehicle Lateral Risk Assessment and Traffic Flow: A Brief Review and Application Examples," Energies, MDPI, vol. 14(12), pages 1-30, June.
  40. Tang, Tie-Qiao & Shi, Wei-Fang & Huang, Hai-Jun & Wu, Wen-Xiang & Song, Ziqi, 2019. "A route-based traffic flow model accounting for interruption factors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 767-785.
  41. Bouadi, Marouane & Jia, Bin & Jiang, Rui & Li, Xingang & Gao, Zi-You, 2022. "Stability analysis of stochastic second-order macroscopic continuum models and numerical simulations," Transportation Research Part B: Methodological, Elsevier, vol. 164(C), pages 193-209.
  42. 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.
  43. Jin, Wen-Long, 2017. "A Riemann solver for a system of hyperbolic conservation laws at a general road junction," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 21-41.
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