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Impact of lattice’s self-anticipative density on traffic stability of lattice model on two lanes

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Abstract

The self-anticipative density (SAD) term is embedded to traffic modeling for two-lane freeway in this paper. In view of linear stability analysis, SAD effect on two lanes is uncovered from the linear stability condition, which reveals that SAD effect in two-lane system stabilizes traffic flow. Moreover, numerical simulation verifies that SAD effect can increase the traffic stability and depress the traffic jam efficiently in new two-lane lattice model.

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References

  1. Newell, G.F.: A simplified car-following theory: a lower order model. Transp. Res. B 36, 195–205 (2002)

    Article  Google Scholar 

  2. Bando, M., Hasebe, K., Nakayama, A., Shibata, A., Sugiyama, Y.: Dynamical model of traffic congestion and numerical simulation. Phys. Rev. E 51, 1035–1042 (1995)

    Article  Google Scholar 

  3. Helbing, D., Tilch, B.: Generalized force model of traffic dynamics. Phys. Rev. E 58, 133–138 (1998)

    Article  Google Scholar 

  4. Jiang, R., Wu, Q., Zhu, Z.: Full velocity difference model for a car-following theory. Phys. Rev. E 64, 017101 (2001)

    Article  Google Scholar 

  5. Li, Z.P., Liu, Y.C., Liu, F.Q.: A dynamical model with next-nearest-neighbor interaction in relative velocity. Int. J. Modern Phys. C 18, 819–832 (2007)

    Article  Google Scholar 

  6. Li, Z.P., Zhang, R., Xu, S.Z., Qian, Y.Q., Xu, J.: Stability analysis of dynamic collaboration model with control signals on two lanes. Commun. Nonlinear Sci. Numer. Simul. 19, 4148–4160 (2014)

    Article  Google Scholar 

  7. Li, Z.P., Li, W.Z., Xu, S.Z., Qian, Y.Q.: Analyses of vehicle’s self-stabilizing effect in an extended optimal velocity model by utilizing historical velocity in an environment of intelligent transportation system. Nonlinear Dyn. 80, 529–540 (2015)

    Article  Google Scholar 

  8. Li, Z.P., Liu, L.M., Xu, S.Z., Qian, Y.Q.: Impact of driving aggressiveness on the traffic stability based on an extended optimal velocity mode. Nonlinear Dyn. 81, 2059–2070 (2015)

    Article  Google Scholar 

  9. Zhu, W.X., Yu, R.L.: A new car-following model considering the related factors of a gyroidal road. Physica A 393, 101–111 (2014)

    Article  MathSciNet  Google Scholar 

  10. Zhu, W.X., Zhang, L.D.: A speed feedback control strategy for car-following model. Physica A 413, 343–351 (2014)

    Article  MathSciNet  Google Scholar 

  11. Zhu, W.X.: Motion energy dissipation in traffic flow on a curved road. Int. J. Modern Phys. C 24, 1350046 (2013)

    Article  MathSciNet  Google Scholar 

  12. Zhu, W.X., Zhang, C.H.: Analysis of energy dissipation in traffic flow with a variable slope. Physica A 392, 3301–3307 (2013)

    Article  Google Scholar 

  13. Zhou, J., Shi, Z.K., Cao, J.L.: Nonlinear analysis of the optimal velocity difference model with reaction-time delay. Physica A 396, 77–87 (2014)

    Article  MathSciNet  Google Scholar 

  14. Zhou, J., Shi, Z.K., Cao, J.L.: An extended traffic flow model on a gradient highway with the consideration of the relative velocity. Nonlinear Dyn. 78, 1765–1779 (2014)

    Article  Google Scholar 

  15. Tang, T.Q., Shi, W.F., Shang, H.Y., Wang, Y.P.: A new car-following model with consideration of inter-vehicle communication. Nonlinear Dyn. 76, 2017–2023 (2014)

    Article  Google Scholar 

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

    Article  Google Scholar 

  17. Tang, T.Q., Shi, W.F., Shang, H.Y., Wang, Y.P.: An extended car-following model with consideration of the reliability of inter-vehicle communication. Measurement 58, 286–293 (2014)

    Article  Google Scholar 

  18. Tang, T.Q., Huang, H.J., Shang, H.Y.: Influences of the driver’s bounded rationality on micro driving behavior, fuel consumption and emissions. Transp. Res. D 41, 423–432 (2015)

    Article  Google Scholar 

  19. Ge, H.X., Yu, J., Lo, S.M.: A control method for congested traffic in the car-following model. Chin. Phys. Lett. 29, 050502 (2012)

    Article  Google Scholar 

  20. Ge, H.X., Lv, F., Zheng, P.J., Cheng, R.J.: The time-dependent Ginzburg–Landau equation for car-following model considering anticipation-driving behavior. Nonlinear Dyn. 76, 1497–1501 (2014)

    Article  Google Scholar 

  21. Ge, H.X., Meng, X.P., Zhu, H.B., Li, Z.P.: Feedback control for car following model based on two-lane traffic flow. Physica A 408, 28–39 (2014)

    Article  MathSciNet  Google Scholar 

  22. Ge, H.X., Zheng, P.J., Wang, W., Cheng, R.J.: The car following model considering traffic jerk. Physica A 433, 274–278 (2015)

    Article  MathSciNet  Google Scholar 

  23. Nagel, K., Schreckenberg, M.: A cellular automaton model for freeway traffic. J. Phys. I 2, 2221–2229 (1992)

    Google Scholar 

  24. Knospe, W., Santen, L., Schadschneider, A., Schreckenberg, M.: Disorder effects in cellular automaton for two-lane traffic. Physica A 265, 614–633 (1998)

    Article  Google Scholar 

  25. Nishinari, K., Takahashi, D.: Analytical properties of ultradiscrete Burgers equation and rule-184 cellular automaton. J. Phys. A 31, 5439–5450 (1998)

    Article  Google Scholar 

  26. Nishinari, K., Takahashi, D.: Multi-value cellular automaton models and metastable states in a congested phase. J. Phys. A 33, 7709–7720 (2000)

    Article  MathSciNet  Google Scholar 

  27. Jiang, R., Jia, B., Wu, Q.S.: Stochastic multi-value cellular automata models for bicycle flow. J. Phys. A 37, 2063–2072 (2004)

    Article  MathSciNet  Google Scholar 

  28. Zhang, X.Q., Wang, Y., Hu, Q.H.: Research and simulation on cellular automaton model of mixed traffic flow at intersection. Acta Physica Sin. 63, 10508 (2014)

    Google Scholar 

  29. Ge, H.X., Wu, S.Z., Cheng, R.J., Lo, S.M.: Theoretical analysis of a modified continuum model. Chin. Phys. Lett. 28, 090501 (2011)

    Article  Google Scholar 

  30. Ge, H.X., Lo, S.M.: The KdV-Burgers equation in speed gradient viscous continuum model. Physica A 391, 1652–1656 (2012)

    Article  Google Scholar 

  31. Tang, T.Q., Caccetta, L., Wu, Y.H., Huang, H.J., Yang, X.B.: A macro model for traffic flow on road networks with varying road conditions. J. Adv. Transp. 48, 304–317 (2014)

    Article  Google Scholar 

  32. Tang, T.Q., Huang, H.J., Shang, H.Y.: An extended macro traffic flow model accounting for the driver’s bounded rationality and numerical tests. Physica A 468, 322–333 (2017)

    Article  Google Scholar 

  33. Nagatani, T.: Modified KdV equation for jamming transition in the continuum models of traffic. Physica A 261, 599–607 (1998)

    Article  MathSciNet  Google Scholar 

  34. Nagatani, T.: TDGL and MKdV equations for jamming transition in the lattice models of traffic. Physica A 264, 581–592 (1999)

    Article  Google Scholar 

  35. Nagatani, T.: Jamming transition in traffic flow on triangular lattice. Physica A 271, 200–221 (1999)

    Article  Google Scholar 

  36. Nagatani, T.: Jamming transition in a two-dimensional traffic flow model. Phys. Rev. E 59, 4857–4864 (1999)

    Article  Google Scholar 

  37. Nagatani, T.: Jamming transition of high-dimensional traffic dynamics. Physica A 272, 592–611 (1999)

    Article  Google Scholar 

  38. Ge, H.X., Cheng, R.J., Lo, S.M.: Time-dependent Ginzburg-Landau equation for lattice hydrodynamic model describing pedestrian flow. Chin. Phys. B 22, 104–108 (2013)

    Google Scholar 

  39. Ge, H.X., Cheng, R.J., Lo, S.M.: A lattice model for bidirectional pedestrian flow on gradient road. Commun. Theor. Phys. 62, 259–264 (2014)

    Article  MathSciNet  Google Scholar 

  40. Redhu, P., Gupta, A.K.: Phase transition in a two-dimensional triangular flow with consideration of optimal current difference effect. Nonlinear Dyn. 78, 957–968 (2014)

    Article  MathSciNet  Google Scholar 

  41. 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, 1001–1011 (2014)

    Article  MathSciNet  Google Scholar 

  42. Redhu, P., Gupta, A.K.: Jamming transitions and the effect of interruption probability in a lattice traffic flow model with passing. Physica A 421, 249–260 (2014)

    Article  Google Scholar 

  43. Gupta, A.K., Redhu, P.: Jamming transition of a two-dimensional traffic dynamics with consideration of optimal current difference. Phys. Lett. A 377, 2027–2033 (2013)

    Article  MathSciNet  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  45. Zhang, G., Sun, D.H., Liu, H., Chen, D.: Stability analysis of a new lattice hydrodynamic model by considering lattice’s self-anticipative density effect. Physica A 486, 806–813 (2017)

    Article  MathSciNet  Google Scholar 

  46. Ge, H.X., Cheng, R.J.: The backward looking effect in the lattice hydrodynamic model. Physica A 387, 6952–6958 (2008)

    Article  Google Scholar 

  47. Ge, H.X., Cui, Y., Zhu, K.Q., Cheng, R.J.: The control method for the lattice hydrodynamic model. Commun. Nonlinear Sci. Numer. Simul. 22, 903–908 (2015)

    Article  Google Scholar 

  48. Tian, C., Sun, D.H., Zhang, M.: Nonlinear analysis of lattice model with consideration of optimal current difference. Commun. Nonlinear Sci. Numer. Simul. 16, 4524–4529 (2011)

    Article  Google Scholar 

  49. Tian, J.F., Jia, B., Li, X.G.: Flow difference effect in the lattice hydrodynamic model. Chin. Phys. B 19, 040303 (2010)

    Article  Google Scholar 

  50. Wang, T., Gao, Z.Y., Zhao, X.M.: Multiple flux difference effect in the lattice hydrodynamic model. Chin. Phys. B 21, 020512 (2012)

    Article  Google Scholar 

  51. Nagatani, T.: Jamming transitions and the modified Korteweg–de Vries equation in a two-lane traffic flow. Physica A 265, 297–310 (1999)

    Article  Google Scholar 

  52. Tang, T.Q., Huang, H.J., Xue, Y.: An improved two-lane traffic flow lattice model. Acta Physica Sin. 55, 4026–4031 (2006)

    Google Scholar 

  53. Li, Z.P., Zhang, R., Xu, S.Z., Qian, Y.Q.: Study on the effects of driver’s lane-changing aggressiveness on traffic stability from an extended two-lane lattice model. Commun. Nonlinear Sci. Numer. Simul. 24, 52–63 (2015)

    Article  MathSciNet  Google Scholar 

  54. Zhang, G., Sun, D.H., Liu, W.N.: Analysis of a new two-lane lattice hydrodynamic model with consideration of the global average flux. Nonlinear Dyn. 81, 1623–1633 (2015)

    Article  MathSciNet  Google Scholar 

  55. Zhang, G., Sun, D.H., Liu, W.N., Zhao, M., Cheng, S.L.: Analysis of two-lane lattice hydrodynamic model with consideration of drivers’ characteristics. Physica A 422, 16–24 (2015)

    Article  Google Scholar 

  56. Zhang, G., Sun, D.H., Zhao, M., Liu, W.N., Cheng, S.L.: Analysis of average density difference effect in a new two-lane lattice model. Int. J. Modern Phys. C 26, 1550062 (2015)

    Article  MathSciNet  Google Scholar 

  57. Gupta, A.K., Redhu, P.: Analyses of drivers anticipation effect in sensing relative flux in a new lattice model for two-lane traffic system. Physica A 392, 5622–5632 (2013)

    Article  Google Scholar 

  58. Sharma, S.: Lattice hydrodynamic modeling of two-lane traffic flow with timid and aggressive driving behavior. Physica A 421, 401–411 (2015)

    Article  Google Scholar 

  59. Sharma, S.: Effect of driver’s anticipation in a new two-lane lattice model with the consideration of optimal current difference. Nonlinear Dyn. 81, 991–1003 (2015)

    Article  Google Scholar 

  60. Tian, J.F., Yuan, Z.Z., Jia, B., Li, M.H., Jiang, G.J.: The stabilization effect of the density difference in the modified lattice hydrodynamic model of traffic flow. Physica A 391, 4476–4482 (2012)

    Article  Google Scholar 

  61. Wang, T., Gao, Z.Y., Zhang, J.: Stabilization effect of multiple density difference in the lattice hydrodynamic model. Nonlinear Dyn. 73, 2197–2205 (2013)

    Article  Google Scholar 

  62. Wang, T., Gao, Z.Y., Zhang, J., Zhao, X.: A new lattice hydrodynamic model for two-lane traffic with the consideration of density difference effect. Nonlinear Dyn. 75, 27–34 (2014)

    Article  MathSciNet  Google Scholar 

  63. Gupta, A.K., Redhu, P.: Analysis of a modified two-lane lattice model by considering the density difference effect. Commun. Nonlinear Sci. Numer. Simul. 19, 1600–1610 (2014)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 61673168).

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Authors and Affiliations

  1. College of Physics and Electronics, Hunan University of Arts and Science, Changde, 415000, China

    Guanghan Peng & Xiaoqin Li

  2. College of Physical Science and Technology, Guangxi Normal University, Guilin, 541004, China

    Guanghan Peng

  3. School of Computer Science and Communication Engineering, Guangxi University of Science and Technology, Liuzhou, 545006, China

    Shuhong Yang & Dongxue Xia

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  1. Guanghan Peng
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  2. Shuhong Yang
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  4. Xiaoqin Li
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Correspondence to Guanghan Peng or Shuhong Yang.

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Peng, G., Yang, S., Xia, D. et al. Impact of lattice’s self-anticipative density on traffic stability of lattice model on two lanes. Nonlinear Dyn 94, 2969–2977 (2018). https://doi.org/10.1007/s11071-018-4537-y

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