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Driver’s attention effect in car-following model with passing under V2V environment

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Abstract

As vehicles become more autonomous, there is a greater need for reliable and accurate information about neighbouring vehicles. In the V2V environment, information about nearby vehicles plays a significant role in predicting traffic flow behavior and this information becomes more effective during passing. To better understand how a driver’s attention can impact the average velocity of their vehicle and those around them, an improved car-following model has been developed with a passing effect. The stability condition of the model is obtained via linear stability analysis, moreover, nonlinear analysis is used to determine the mKdV equation, which describes the evolution properties of the traffic density wave in the jammed region. The numerical and analytical results are discussed for smaller as well as larger rates of passing. It is found that for a smaller rate of passing, the phase transition occurs between the kink jam and the free flow. In the kink jam region, the initial perturbations are evolved in the form of a kink-antikink wave which moves in a backward direction and the amplitude of the headway profile decreases with an increase in the value of the driver’s attention coefficient. While for the higher rate of passing, the phase change is between the uniform to the kink jam zone through the chaotic jam zone. In the chaotic region, the behavior of the headway waves is chaotic which band with one another, break up and propagate in the backward direction. Moreover, it has been observed that with the driver’s increased attention on the average speed of any nearby vehicles, the unstable region is reduced for any rate of passing. Also, numerical findings are in accordance with theoretical results and noticed that this model is successful in increasing the efficiency of vehicle movement, reducing congestion, and improving safety on roads. To reduce collision accidents, the improved model can be implemented as active safety technology.

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References

  1. Pipes, L.A.: Car following models and the fundamental diagram of road traffic. Transportation Research/UK/ (1966)

  2. Chandler, R.E., Herman, R., Montroll, E.W.: Traffic dynamics: studies in car following. Oper. Res. 6(2), 165–184 (1958)

    MathSciNet  Google Scholar 

  3. Gazis, D.C., Herman, R., Potts, R.B.: Car-following theory of steady-state traffic flow. Oper. Res. 7(4), 499–505 (1959)

    MathSciNet  MATH  Google Scholar 

  4. Punzo, V., Simonelli, F.: Analysis and comparison of microscopic traffic flow models with real traffic microscopic data. Transp. Res. Rec. 1934(1), 53–63 (2005)

    Google Scholar 

  5. Hossain, M.A., Tanimoto, J.: A microscopic traffic flow model for sharing information from a vehicle to vehicle by considering system time delay effect. Phys. A 585, 126437 (2022)

    MathSciNet  MATH  Google Scholar 

  6. Nagatani, T.: The physics of traffic jams. Rep. Prog. Phys. 65(9), 1331 (2002)

    Google Scholar 

  7. Wang, Y.-Q., Jia, B., Jiang, R., Gao, Z.-Y., Li, W.-H., Bao, K.-J., Zheng, X.-Z.: Dynamics in multi-lane taseps coupled with asymmetric lane-changing rates. Nonlinear Dyn. 88, 2051–2061 (2017)

    MATH  Google Scholar 

  8. Gupta, A.K., Dhiman, I.: Analyses of a continuum traffic flow model for a nonlane-based system. Int. J. Mod. Phys. C 25(10), 1450045 (2014)

    MathSciNet  Google Scholar 

  9. Verma, M., Sharma, S.: The role of occupancy and transition rate on traffic flow in a percolation-backbone fractal. Chaos, Solit Fract 170, 113335 (2023)

    MathSciNet  Google Scholar 

  10. Herman, R., Montroll, E.W., Potts, R.B., Rothery, R.W.: Traffic dynamics: analysis of stability in car following. Oper. Res. 7(1), 86–106 (1959)

    MathSciNet  MATH  Google Scholar 

  11. Gazis, D.C., Herman, R., Rothery, R.W.: Nonlinear follow-the-leader models of traffic flow. Oper. Res. 9(4), 545–567 (1961)

    MathSciNet  MATH  Google Scholar 

  12. Gipps, P.G.: A behavioural car-following model for computer simulation. Transport. Res. Part B: Methodol. 15(2), 105–111 (1981)

    Google Scholar 

  13. Yang, D., Jin, P., Pu, Y., Ran, B.: Safe distance car-following model including backward-looking and its stability analysis. Eur. Phys. J. B 86(3), 1–11 (2013)

    MathSciNet  Google Scholar 

  14. Qiang, S., Jia, B., Huang, Q., Jiang, R.: Simulation of free boarding process using a cellular automaton model for passenger dynamics. Nonlinear Dyn. 91, 257–268 (2018)

    Google Scholar 

  15. Jiang, Y., Wang, S., Yao, Z., Zhao, B., Wang, Y.: A cellular automata model for mixed traffic flow considering the driving behavior of connected automated vehicle platoons. Phys. A 582, 126262 (2021)

    Google Scholar 

  16. Jiang, R., Wu, Q.-S., Zhu, Z.-J.: A new continuum model for traffic flow and numerical tests. Transport. Res. Part B: Methodol. 36(5), 405–419 (2002)

    Google Scholar 

  17. Cheng, R., Ge, H., Wang, J.: KDV-burgers equation in a new continuum model based on full velocity difference model considering anticipation effect. Phys. A 481, 52–59 (2017)

    MathSciNet  MATH  Google Scholar 

  18. Gupta, A.K., Sharma, S.: Analysis of the wave properties of a new two-lane continuum model with the coupling effect. Chin. Phys. B 21(1), 015201 (2012)

    Google Scholar 

  19. Nagatani, T.: Jamming transition in a two-dimensional traffic flow model. Phys. Rev. E 59(5), 4857 (1999)

    Google Scholar 

  20. Peng, G., Kuang, H., Qing, L.: Feedback control method in lattice hydrodynamic model under honk environment. Phys. A 509, 651–656 (2018)

    MATH  Google Scholar 

  21. Verma, M., Sharma, S.: Chaotic jam and phase transitions in a lattice model with density dependent passing. Chaos, Solit. Fract. 162, 112435 (2022)

    MathSciNet  MATH  Google Scholar 

  22. Redhu, P., Gupta, A.K.: Effect of forward looking sites on a multi-phase lattice hydrodynamic model. Phys. A 445, 150–160 (2016)

    MathSciNet  MATH  Google Scholar 

  23. Bando, M., Hasebe, K., Nakayama, A., Shibata, A., Sugiyama, Y.: Structure stability of congestion in traffic dynamics. Jpn. J. Ind. Appl. Math. 11(2), 203–223 (1994)

    MathSciNet  MATH  Google Scholar 

  24. Zhao, X.M., Gao, Z.Y.: A new car-following model: full velocity and acceleration difference model. Eur. Phys. J. B-Condens. Matter Comp. Syst. 47(1), 145–150 (2005)

    Google Scholar 

  25. Liu, F., Cheng, R., Ge, H., Yu, C.: A new car-following model with consideration of the velocity difference between the current speed and the historical speed of the leading car. Phys. A 464, 267–277 (2016)

    MathSciNet  MATH  Google Scholar 

  26. Peng, G., Cheng, R.: A new car-following model with the consideration of anticipation optimal velocity. Phys. A 392(17), 3563–3569 (2013)

    MathSciNet  MATH  Google Scholar 

  27. Yi Rong, K., Di Hua, S., Shu Hong, Y.: A new car-following model considering driver’s individual anticipation behavior. Nonlinear Dyn. 82(3), 1293–1302 (2015)

    MathSciNet  MATH  Google Scholar 

  28. Zheng, L.J., Tian, C., Sun, D.H., Liu, W.N.: A new car-following model with consideration of anticipation driving behavior. Nonlinear Dyn. 70(2), 1205–1211 (2012)

    MathSciNet  Google Scholar 

  29. Tang, T.Q., He, J., Yang, S.C., Shang, H.Y.: A car-following model accounting for the driver’s attribution. Phys. A 413, 583–591 (2014)

    Google Scholar 

  30. Zhang, G., Sun, D., Liu, H., Zhao, M.: Analysis of drivers’ characteristics in car-following theory. Mod. Phys. Lett. B 28(24), 1450191 (2014)

    MathSciNet  Google Scholar 

  31. Pan, Y., Wang, Y., Miao, B., Cheng, R.: Stabilization strategy of a novel car-following model with time delay and memory effect of the driver. Sustainability 14(12), 7281 (2022)

    Google Scholar 

  32. Jafaripournimchahi, A., Sun, L., Hu, W.: Driver’s anticipation and memory driving car-following model. J. Adv. Transport. 2020, 1523 (2020)

    Google Scholar 

  33. Cao, B.G.: A new car-following model considering driver’s sensory memory. Phys. A 427, 218–225 (2015)

    MathSciNet  Google Scholar 

  34. Wang, T., Cheng, R., Wu, Y.: Stability analysis of heterogeneous traffic flow influenced by memory feedback control signal. Appl. Math. Modell. 109, 693 (2022)

    MathSciNet  MATH  Google Scholar 

  35. Tie Qiao, T., Hai Jun, H., Wong, S., Rui, J.: A new car-following model with consideration of the traffic interruption probability. Chin. Phys. B 18(3), 975 (2009)

    Google Scholar 

  36. Li, X., Zhou, Y., Peng, G.: Impact of interruption probability of the current optimal velocity on traffic stability for car-following model. Int. J. Mod. Phys. C 33(03), 2250041 (2022)

    MathSciNet  Google Scholar 

  37. Peng, G.: A new car-following model with driver’s anticipation effect of traffic interruption probability. Chin. Phys. B 29(8), 084501 (2020)

    Google Scholar 

  38. Wang, J., Sun, F., Ge, H.: Effect of the driver’s desire for smooth driving on the car-following model. Phys. A 512, 96–108 (2018)

    MATH  Google Scholar 

  39. Sun, Y., Ge, H., Cheng, R.: An extended car-following model considering driver’s desire for smooth driving on the curved road. Phys. A 527, 121426 (2019)

    MathSciNet  MATH  Google Scholar 

  40. Hossain, M.A., Kabir, K.A., Tanimoto, J.: Improved car-following model considering modified backward optimal velocity and velocity difference with backward-looking effect. J. Appl. Math. Phys. 9(2), 242–259 (2021)

    Google Scholar 

  41. Ma, M., Ma, G., Liang, S.: Density waves in car-following model for autonomous vehicles with backward looking effect. Appl. Math. Model. 94, 1–12 (2021)

    MathSciNet  MATH  Google Scholar 

  42. Ma, G., Ma, M., Liang, S., Wang, Y., Guo, H.: Nonlinear analysis of the car-following model considering headway changes with memory and backward looking effect. Phys. A 562, 125303 (2021)

    MathSciNet  MATH  Google Scholar 

  43. Gasser, I., Sirito, G., Werner, B.: Bifurcation analysis of a class of car-following traffic models. Phys. D 197(3–4), 222–241 (2004)

    MathSciNet  MATH  Google Scholar 

  44. Zhang, Y., Xue, Y., Zhang, P., Fan, D., di He, H.: Bifurcation analysis of traffic flow through an improved car-following model considering the time-delayed velocity difference. Phys. A 514, 133–140 (2019)

    MathSciNet  MATH  Google Scholar 

  45. Padial, J.F., Casal, A.: Bifurcation in car-following models with time delays and driver and mechanic sensitivities, Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A. Matemáticas 116(4), 1–19 (2022)

    Google Scholar 

  46. Zhai, C., Wu, W.: A new car-following model considering driver’s characteristics and traffic jerk. Nonlinear Dyn. 93(4), 2185–2199 (2018)

    Google Scholar 

  47. Liu, F., Cheng, R., Zheng, P., Ge, H.: TDGL and MKDV equations for car-following model considering traffic jerk. Nonlinear Dyn. 83(1), 793–800 (2016)

    Google Scholar 

  48. Song, H., Ge, H., Chen, F., Cheng, R.: TDGL and MKDV equations for car-following model considering traffic jerk and velocity difference. Nonlinear Dyn. 87(3), 1809–1817 (2017)

    Google Scholar 

  49. Li, Y., Zhang, L., Peeta, S., He, X., Zheng, T., Li, Y.: A car-following model considering the effect of electronic throttle opening angle under connected environment. Nonlinear Dyn. 85(4), 2115–2125 (2016)

    Google Scholar 

  50. Li, S., Cheng, R., Ge, H.: An improved car-following model considering electronic throttle dynamics and delayed velocity difference. Phys. A 558, 125015 (2020)

    MathSciNet  MATH  Google Scholar 

  51. Sun, Y., Ge, H., Cheng, R.: A car-following model considering the effect of electronic throttle opening angle over the curved road. Phys. A 534, 122377 (2019)

    MathSciNet  MATH  Google Scholar 

  52. Peng, G., Yang, S., Xia, D., Li, X.: Delayed-feedback control in a car-following model with the combination of v2v communication. Phys. A 526, 120912 (2019)

    MathSciNet  MATH  Google Scholar 

  53. Jin, Y., Xu, M.: Stability analysis in a car-following model with reaction-time delay and delayed feedback control. Phys. A 459, 107–116 (2016)

    MathSciNet  MATH  Google Scholar 

  54. Jin, Y., Meng, J., Xu, M.: Dynamical analysis for a car-following model with delayed-feedback control of both velocity and acceleration differences. Commun. Nonlinear Sci. Numer. Simul. 111, 106458 (2022)

    MathSciNet  MATH  Google Scholar 

  55. Zhang, R.F., Bilige, S.: Bilinear neural network method to obtain the exact analytical solutions of nonlinear partial differential equations and its application to p-gbkp equation. Nonlinear Dyn. 95, 3041–3048 (2019)

    MATH  Google Scholar 

  56. Zhang, R.F., Li, M.C.: Bilinear residual network method for solving the exactly explicit solutions of nonlinear evolution equations. Nonlinear Dyn. 108(1), 521–531 (2022)

    Google Scholar 

  57. Zhang, R.F., Li, M.C., Cherraf, A., Vadyala, S.R.: The interference wave and the bright and dark soliton for two integro-differential equation by using BNNM. Nonlinear Dyn. 1, 1–10 (2023)

    Google Scholar 

  58. Nagatani, T.: Chaotic jam and phase transition in traffic flow with passing. Phys. Rev. E 60(2), 1535 (1999)

    Google Scholar 

  59. Gupta, A.K., Redhu, P.: Analyses of the driver’s anticipation effect in a new lattice hydrodynamic traffic flow model with passing. Nonlinear Dyn. 76(2), 1001–1011 (2014)

    MathSciNet  MATH  Google Scholar 

  60. Kaur, D., Sharma, S.: The impact of the predictive effect on traffic dynamics in a lattice model with passing. Eur. Phys. J. B 93, 1–10 (2020)

    MathSciNet  Google Scholar 

  61. Redhu, P., Gupta, A.K.: Delayed-feedback control in a lattice hydrodynamic model. Commun. Nonlinear Sci. Numer. Simul. 27(1–3), 263–270 (2015)

    MathSciNet  MATH  Google Scholar 

  62. Redhu, P., Gupta, A.K.: Jamming transitions and the effect of interruption probability in a lattice traffic flow model with passing. Phys. A Stat. Mech. Appl. 421, 249–260 (2015)

    MATH  Google Scholar 

  63. Gupta, A.K., Sharma, S., Redhu, P.: Effect of multi-phase optimal velocity function on jamming transition in a lattice hydrodynamic model with passing. Nonlinear Dyn. 80(3), 1091–1108 (2015)

    Google Scholar 

  64. Jiao, S., Zhang, S., Zhou, B., Zhang, Z., Xue, L.: An extended car-following model considering the drivers’ characteristics under a V2V communication environment. Sustainability 12(4), 1552 (2020)

    Google Scholar 

  65. Xue Dong, H., Wei, W., Hao, W.: A car-following model with the consideration of vehicle-to-vehicle communication technology. Acta Phys. Sinica 65(1), 10053 (2016)

    Google Scholar 

  66. Wen-Xing, Z., Li-Dong, Z.: A new car-following model for autonomous vehicles flow with mean expected velocity field. Phys. A 492, 2154–2165 (2018)

    MathSciNet  MATH  Google Scholar 

  67. Kuang, H., Wang, M.-T., Lu, F.-H., Bai, K.-Z., Li, X.-L.: An extended car-following model considering multi-anticipative average velocity effect under V2V environment. Phys. A 527, 121268 (2019)

    MATH  Google Scholar 

  68. Altan, A., Hacıoğlu, R.: Model predictive control of three-axis gimbal system mounted on UAV for real-time target tracking under external disturbances. Mech. Syst. Signal Process. 138, 106548 (2020)

    Google Scholar 

  69. Lorenz, E.: The butterfly effect. World Sci. Seri. Nonlinear Sci. Ser. A 39, 91–94 (2000)

    MATH  Google Scholar 

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Acknowledgements

The first author gratefully acknowledges financial support from the“Council of Scientific and Industrial Research (CSIR), New Delhi, India”, under file no. 09/382(0245)/2019-EMR-I.

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  1. Department of Mathematics, Maharshi Dayanand University, Rohtak, Haryana, 124001, India

    Sunita Yadav & Poonam Redhu

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  1. Sunita Yadav
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  2. Poonam Redhu
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Sunita: The problem’s implementation, simulation, and analysis. Poonam Redhu: Investigated the underlying physics, interpret the results, and supervised the proposed work. Sunita and Poonam Redhu wrote the manuscript.

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Yadav, S., Redhu, P. Driver’s attention effect in car-following model with passing under V2V environment. Nonlinear Dyn 111, 13245–13261 (2023). https://doi.org/10.1007/s11071-023-08548-x

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