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The impact of the predictive effect on traffic dynamics in a lattice model with passing

Author

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  • Daljeet Kaur

    (School of Mathematics, Thapar Institute of Engineering and Technology)

  • Sapna Sharma

    (School of Mathematics, Thapar Institute of Engineering and Technology)

Abstract

In this paper, we study the impact of the predictive effect with passing for a unidirectional single-lane highway. The model is further analyzed theoretically by the means of stability analysis. The influence of the predictive effect is examined on traffic stream stability through linear stability analysis when passing is permitted. It is shown that the accurate expected behavior of the vehicles ahead can enhance the stability of traffic flow for any rate of passing. Using nonlinear stability analysis, we obtained the critical value of passing constant for which kink soliton solution of mKdV equation exist. When the passing constant is smaller than critical value, the jamming transition occurs between uniform flow and kink flow while for higher value of passing constant, the jamming transitions occur from uniform flow to kink density wave flow through a chaotic phase. Numerical simulation verifies the theoretical predictions which confirms that the traffic congestion can be suppressed efficiently by considering the predictive effect in a single-lane traffic system when passing is allowed. Graphical abstract

Suggested Citation

  • Daljeet Kaur & Sapna Sharma, 2020. "The impact of the predictive effect on traffic dynamics in a lattice model with passing," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(3), pages 1-10, March.
    • Handle: RePEc:spr:eurphb:v:93:y:2020:i:3:d:10.1140_epjb_e2020-100469-5
    DOI: 10.1140/epjb/e2020-100469-5
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    Citations

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    Cited by:

    1. Madaan, Nikita & Sharma, Sapna, 2022. "Delayed-feedback control in multi-lane traffic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    2. Kaur, Daljeet & Sharma, Sapna & Gupta, Arvind Kumar, 2022. "Analyses of lattice hydrodynamic area occupancy model for heterogeneous disorder traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    3. 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).
    4. Nikita Madaan & Sapna Sharma, 2022. "Influence of driver’s behavior with empirical lane changing on the traffic dynamics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(1), pages 1-11, January.
    5. Huimin Liu & Rongjun Cheng & Tingliu Xu, 2021. "Analysis of a Novel Two-Dimensional Lattice Hydrodynamic Model Considering Predictive Effect," Mathematics, MDPI, vol. 9(19), pages 1-13, October.
    6. 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).

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    Keywords

    Statistical and Nonlinear Physics;

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