IDEAS home Printed from https://ideas.repec.org/r/eee/transb/v29y1995i4p277-286.html
   My bibliography  Save this item

Requiem for second-order fluid approximations of traffic flow

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as


Cited by:

  1. Jincheng Jiang & Nico Dellaert & Tom Van Woensel & Lixin Wu, 2020. "Modelling traffic flows and estimating road travel times in transportation network under dynamic disturbances," Transportation, Springer, vol. 47(6), pages 2951-2980, December.
  2. 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.
  3. Hoogendoorn, Serge P. & Bovy, Piet H. L., 2000. "Continuum modeling of multiclass traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 34(2), pages 123-146, February.
  4. Helbing, Dirk, 1995. "Theoretical foundation of macroscopic traffic models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 219(3), pages 375-390.
  5. 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.
  6. 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).
  7. Jiang, Rui & Wu, Qing-Song & Zhu, Zuo-Jin, 2002. "A new continuum model for traffic flow and numerical tests," Transportation Research Part B: Methodological, Elsevier, vol. 36(5), pages 405-419, June.
  8. 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.
  9. 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.
  10. 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.
  11. Wong, G. C. K. & Wong, S. C., 2002. "A multi-class traffic flow model - an extension of LWR model with heterogeneous drivers," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(9), pages 827-841, November.
  12. Chen, Dong & Sun, Dihua & Zhao, Min & Zhou, Tong & Cheng, Senlin, 2018. "Modeling and analyses for an extended car-following model accounting for drivers’ situation awareness from cyber physical perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 52-68.
  13. Hu, Zejing & Smirnova, M.N. & Zhang, Yongliang & Smirnov, N.N. & Zhu, Zuojin, 2021. "Estimation of travel time through a composite ring road by a viscoelastic traffic flow model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 501-521.
  14. Jiang, Rui & Wu, Qing-Song, 2003. "Study on propagation speed of small disturbance from a car-following approach," Transportation Research Part B: Methodological, Elsevier, vol. 37(1), pages 85-99, January.
  15. Logghe, S. & Immers, L.H., 2008. "Multi-class kinematic wave theory of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 42(6), pages 523-541, July.
  16. Qiao, Dianliang & Lin, Zhiyang & Guo, Mingmin & Yang, Xiaoxia & Li, Xiaoyang & Zhang, Peng & Zhang, Xiaoning, 2022. "Riemann solvers of a conserved high-order traffic flow model with discontinuous fluxes," Applied Mathematics and Computation, Elsevier, vol. 413(C).
  17. Ma, Tao & Zhou, Zhou & Abdulhai, Baher, 2016. "Time Series Based Hourly Traffic Flow Prediction on the GTA Freeways Using TSTVEC Model," 57th Transportation Research Forum (51st CTRF) Joint Conference, Toronto, Ontario, May 1-4, 2016 319287, Transportation Research Forum.
  18. Heidemann, Dirk, 1998. "Some critical remarks on a class of traffic flow models," Transportation Research Part B: Methodological, Elsevier, vol. 33(2), pages 153-155, April.
  19. Chiu, Yi-Chang & Zhou, Liang & Song, Houbing, 2010. "Development and calibration of the Anisotropic Mesoscopic Simulation model for uninterrupted flow facilities," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 152-174, January.
  20. Tianjun Feng & Keyi Liu & Chunyan Liang, 2023. "An Improved Cellular Automata Traffic Flow Model Considering Driving Styles," Sustainability, MDPI, vol. 15(2), pages 1-19, January.
  21. Zhang, H. M., 2003. "Driver memory, traffic viscosity and a viscous vehicular traffic flow model," Transportation Research Part B: Methodological, Elsevier, vol. 37(1), pages 27-41, January.
  22. 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.
  23. Ngoduy, D. & Liu, R., 2007. "Multiclass first-order simulation model to explain non-linear traffic phenomena," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 667-682.
  24. Zhang, H. M., 2003. "Anisotropic property revisited--does it hold in multi-lane traffic?," Transportation Research Part B: Methodological, Elsevier, vol. 37(6), pages 561-577, July.
  25. 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.
  26. Gan Yin & Jianjun Chen, 2018. "Existence and Stability of Riemann Solution to the Aw-Rascle Model with Friction," Indian Journal of Pure and Applied Mathematics, Springer, vol. 49(4), pages 671-688, December.
  27. Papageorgiou, Markos, 1998. "Some remarks on macroscopic traffic flow modelling," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(5), pages 323-329, September.
  28. 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).
  29. Zhang, H. M., 2000. "Structural properties of solutions arising from a nonequilibrium traffic flow theory," Transportation Research Part B: Methodological, Elsevier, vol. 34(7), pages 583-603, September.
  30. Cassidy, Michael J. & Windover, John R., 1998. "Driver memory: Motorist selection and retention of individualized headways in highway traffic," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(2), pages 129-137, February.
  31. 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.
  32. 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).
  33. 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.
  34. Kai Nagel & Peter Wagner & Richard Woesler, 2003. "Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling," Operations Research, INFORMS, vol. 51(5), pages 681-710, October.
  35. Juan Francisco Sánchez-Pérez & Santiago Oviedo-Casado & Gonzalo García-Ros & Manuel Conesa & Enrique Castro, 2024. "Understanding Complex Traffic Dynamics with the Nondimensionalisation Technique," Mathematics, MDPI, vol. 12(4), pages 1-14, February.
  36. Schönhof, Martin & Helbing, Dirk, 2009. "Criticism of three-phase traffic theory," Transportation Research Part B: Methodological, Elsevier, vol. 43(7), pages 784-797, August.
  37. 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.
  38. 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).
  39. Treiber, Martin & Kesting, Arne & Helbing, Dirk, 2010. "Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 983-1000, September.
  40. Kotsialos, Apostolos & Papageorgiou, Markos, 2004. "Motorway network traffic control systems," European Journal of Operational Research, Elsevier, vol. 152(2), pages 321-333, January.
  41. Ngoduy, D., 2021. "Noise-induced instability of a class of stochastic higher order continuum traffic models," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 260-278.
  42. Haghani, Milad, 2021. "The knowledge domain of crowd dynamics: Anatomy of the field, pioneering studies, temporal trends, influential entities and outside-domain impact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
  43. Alexa Delbosc, 2017. "Why write well?," Transport Reviews, Taylor & Francis Journals, vol. 37(5), pages 545-550, September.
  44. Verma, Muskan & Sharma, Sapna, 2022. "Chaotic jam and phase transitions in a lattice model with density dependent passing," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
  45. Zhang, H. M., 2002. "A non-equilibrium traffic model devoid of gas-like behavior," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 275-290, March.
  46. S H Melouk & B B Keskin & C Armbrester & M Anderson, 2011. "A simulation optimization-based decision support tool for mitigating traffic congestion," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(11), pages 1971-1982, November.
  47. 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.
  48. Ren, Weilin & Cheng, Rongjun & Ge, Hongxia, 2021. "Bifurcation analysis for a novel heterogeneous continuum model considering electronic throttle angle changes with memory," Applied Mathematics and Computation, Elsevier, vol. 401(C).
  49. 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.
  50. 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.
  51. Daganzo, Carlos F., 2014. "Singularities in kinematic wave theory: Solution properties, extended methods and duality revisited," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 50-59.
  52. 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).
  53. 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.
  54. Nelson, Paul, 1995. "On deterministic developments of traffic stream models," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 297-302, August.
  55. 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.
  56. 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.
  57. Gao, Kun & Jiang, Rui & Wang, Bing-Hong & Wu, Qing-Song, 2009. "Discontinuous transition from free flow to synchronized flow induced by short-range interaction between vehicles in a three-phase traffic flow model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3233-3243.
  58. Zhang, H. M., 1998. "A theory of nonequilibrium traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 32(7), pages 485-498, September.
  59. Yannis Pavlis & Will Recker, 2009. "A Mathematical Logic Approach for the Transformation of the Linear Conditional Piecewise Functions of Dispersion-and-Store and Cell Transmission Traffic Flow Models into Linear Mixed-Integer Form," Transportation Science, INFORMS, vol. 43(1), pages 98-116, February.
  60. 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.
  61. Coşkun, Safa Bozkurt & Atay, Mehmet Tarık & Şentürk, Erman, 2019. "Interpolated variational iteration method for solving the jamming transition problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 481-493.
  62. Xiangyang Cao & Bingzhong Zhou & Qiang Tang & Jiaqi Li & Donghui Shi, 2018. "Urban Wasteful Transport and Its Estimation Methods," Sustainability, MDPI, vol. 10(12), pages 1-15, December.
  63. Verma, Muskan & Sharma, Sapna, 2023. "Modeling heterogeneity in an open percolation backbone fractal traffic network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).
  64. 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.
  65. 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.
  66. Helbing, Dirk & Hennecke, Ansgar & Shvetsov, Vladimir & Treiber, Martin, 2001. "MASTER: macroscopic traffic simulation based on a gas-kinetic, non-local traffic model," Transportation Research Part B: Methodological, Elsevier, vol. 35(2), pages 183-211, February.
  67. Yi, Jingang & Lin, Hao & Alvarez, Luis & Horowitz, Roberto, 2003. "Stability of macroscopic traffic flow modeling through wavefront expansion," Transportation Research Part B: Methodological, Elsevier, vol. 37(7), pages 661-679, August.
  68. Yuan, Kai & Knoop, Victor L. & Hoogendoorn, Serge P., 2017. "A kinematic wave model in Lagrangian coordinates incorporating capacity drop: Application to homogeneous road stretches and discontinuities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 472-485.
  69. Kachani, Soulaymane & Perakis, Georgia, 2006. "Fluid dynamics models and their applications in transportation and pricing," European Journal of Operational Research, Elsevier, vol. 170(2), pages 496-517, April.
  70. Zhai, Cong & Wu, Weitiao, 2021. "A continuous traffic flow model considering predictive headway variation and preceding vehicle’s taillight effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
  71. Zhang, H. M., 2003. "On the consistency of a class of traffic flow models," Transportation Research Part B: Methodological, Elsevier, vol. 37(1), pages 101-105, January.
IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.