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Analysis of the macroscopic effect of a driver’s desired velocity on traffic flow characteristics

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  • Cen, Bing-ling
  • Xue, Yu
  • Xia, Yu-xian
  • Zhang, Kun
  • Zhou, Ji

Abstract

In Prigogine's traffic kinetic model, the expected velocity of each driver is assumed to be independent of time, and its relaxation term is ignored. In Paveri–Fontana’s model, the vehicle accelerates to the desired velocity by means of a relaxation term. Méndez’s model assumed that the desired velocity is proportional to the instantaneous velocity, reflecting that all drivers want to drive at a higher velocity, which is a characteristic of aggressive drivers. In order to restrain the character of drivers, considering the relationship between a driver’s desired velocity and the surrounding environment and local instantaneous velocity, a new relaxation process is adopted, which describes that the desired velocity is adaptively adjusted toward the local equilibrium velocity within the relaxation time. We use Chapman-Enskog method and Grad’s moments method to derive the Navier-Stokes traffic equation. The stability condition is obtained by the linear stability analysis. Compared with the steady situation of both Kerner–Konhäuser model and Helbing’s model, it is shown that the extended continuum model has the ability to simulate stop-and-go traffic under medium and high density. Numerical simulation results show that the extended continuum model has a better control effect of traffic congestion than the Paveri–Fontana equation. Finally, the rationality of the extended continuum model is verified by simulations of partially reduced lane traffic and high-density traffic flow.

Suggested Citation

  • Cen, Bing-ling & Xue, Yu & Xia, Yu-xian & Zhang, Kun & Zhou, Ji, 2024. "Analysis of the macroscopic effect of a driver’s desired velocity on traffic flow characteristics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
  • Handle: RePEc:eee:phsmap:v:637:y:2024:i:c:s0378437124000864
    DOI: 10.1016/j.physa.2024.129578
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Wagner, C., 1997. "A Navier-Stokes-like traffic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(1), pages 124-138.
    4. Hoogendoorn, Serge P. & Bovy, Piet H. L., 2001. "Generic gas-kinetic traffic systems modeling with applications to vehicular traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 35(4), pages 317-336, May.
    5. Marques, W. & Méndez, A.R., 2013. "On the kinetic theory of vehicular traffic flow: Chapman–Enskog expansion versus Grad’s moment method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(16), pages 3430-3440.
    6. Zhang, H. M., 1998. "A theory of nonequilibrium traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 32(7), pages 485-498, September.
    7. Marques, W. & Méndez, A.R. & Velasco, R.M., 2021. "The vehicle length effect on the traffic flow fundamental diagram," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).
    8. Antoniou, I. & Ivanov, V.V. & Kalinovsky, Yu.L., 2002. "Kinetic model of network traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 308(1), pages 533-544.
    9. Méndez, A.R. & Velasco, R.M., 2008. "An alternative model in traffic flow equations," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 782-797, November.
    10. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    11. Arvind Kumar Gupta & Isha Dhiman, 2014. "Analyses of a continuum traffic flow model for a nonlane-based system," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 25(10), pages 1-24.
    12. Gupta, A.K. & Katiyar, V.K., 2006. "A new anisotropic continuum model for traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(2), pages 551-559.
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