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Anisotropic property revisited--does it hold in multi-lane traffic?

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  • Zhang, H. M.

Abstract

The anisotropic property of traffic flow has brought much discussion about some existing traffic flow models and diverging views on the further development of traffic flow theories. This paper shows that the anisotropic property cannot be expected to hold in multi-lane traffic. Moreover, it develops a mathematical criterion to judge the anisotropic property of a traffic flow model, shows how non-anisotropic behavior arises from multi-lane traffic, and why some higher-order models do not always behave anisotropically.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:transb:v:37:y:2003:i:6:p:561-577
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    References listed on IDEAS

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    1. 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.
    2. Daganzo, Carlos F., 1999. "A Behavioral Theory of Multi-Lane Traffic Flow Part II: Merges and the Onset of Congestion," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt3qj018c9, Institute of Transportation Studies, UC Berkeley.
    3. Zhang, H. M., 1998. "A theory of nonequilibrium traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 32(7), pages 485-498, September.
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    5. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    6. Daganzo, Carlos F., 1999. "A Behavioral Theory of Multi-Lane Traffic Flow Part I: Long Homogeneous Freeway Sections," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt8n96n91w, Institute of Transportation Studies, UC Berkeley.
    7. Daganzo, Carlos F., 1995. "Requiem for second-order fluid approximations of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 277-286, August.
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    Cited by:

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    3. Li, Jia & Zhang, H.M., 2013. "Modeling space–time inhomogeneities with the kinematic wave theory," Transportation Research Part B: Methodological, Elsevier, vol. 54(C), pages 113-125.
    4. Jiang, Yan-Qun & Zhou, Shu-Guang & Duan, Ya-Li & Huang, Xiao-Qian, 2023. "A viscous continuum model with smoke effect for pedestrian evacuation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 621(C).
    5. 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.
    6. 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.
    7. Maiti, Nandan & Chilukuri, Bhargava Rama, 2023. "Does anisotropy hold in mixed traffic conditions?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    8. 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).
    9. 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).
    10. 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).
    11. 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.
    12. Liu, Huaqing & Zheng, Pengjun & Zhu, Keqiang & Ge, Hongxia, 2015. "KdV–Burgers equation in the modified continuum model considering anticipation effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 26-31.

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