Skip to main content
SpringerLink
Log in

An improved car-following model considering the influence of optimal velocity for leading vehicle

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In the paper, an improved car-following model based on the full velocity difference model considering the influence of optimal velocity for leading vehicle on a single-lane road is proposed. The linear stability condition of the model is obtained by applying the linear stability theory. Through nonlinear analysis, the time-dependent Ginzburg–Landau (TDGL) equation and the modified Korteweg–de Vries (mKdV) equation are derived to describe the traffic flow near the critical point. In addition, the connection between the TDGL and the mKdV equations is also given. Good agreement between the simulation and the theoretical results shows that the improved model can be enhanced the stability of traffic flow.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Tang, T.Q., Wang, Y.P., Yang, X.B., Wu, Y.H.: A new car-following model accounting for varying road condition. Nonlinear Dyn. 70, 1397–1405 (2012)

    Article  MathSciNet  Google Scholar 

  2. 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 (2015)

    Article  Google Scholar 

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

    Article  Google Scholar 

  4. Li, Z.P., Liu, F.Q., Sun, J.: A lattice model with consideration of preceding mixture traffic information. Chin. Phys. B 20, 088901 (2011)

    Article  Google Scholar 

  5. Peng, G.H.: A driver’s memory lattice model of traffic flow and its numerical simulation. Nonlinear Dyn. 67, 1811–1815 (2012)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Redhu, P., Gupta, A.K.: Delayed-feedback control in a Lattice hydrodynamic model. Commun. Nonlinear Sci. Numer. Simul. 27, 263 (2015)

    Article  MathSciNet  Google Scholar 

  8. Kang, Y.R., Sun, D.H.: Lattice hydrodynamic traffic flow model with explicit driver’s physical delay. Nonlinear Dyn. 71, 531–537 (2013)

    Article  MathSciNet  Google Scholar 

  9. 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, 1091 (2015)

    Article  Google Scholar 

  10. Gupta, A.K., Sharma, S., Redhu, P.: Analyses of lattice traffic flow model on a gradient highway. Commun. Theor. Phys. 62, 393 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  11. Li, Y.F., Sun, D.H., Liu, W.N., Zhang, M., Zhao, M., Liao, X.Y., Tang, L.: Modeling and simulation for microscopic traffic flow based on multiple headway, velocity and acceleration difference. Nonlinear Dyn. 66, 15–28 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Peng, G.H., Cai, X.H., Liu, C.Q., Tuo, M.X.: A new lattice model of traffic flow with the anticipation effect of potential lane changing. Phys. Lett. A 376, 447–451 (2012)

    Article  MATH  Google Scholar 

  13. Zhou, T., Sun, D.H., Kang, Y.R., Li, H.M., Tian, C.: A new car-following model with consideration of the prevision driving behavior. Commun. Nonlinear Sci. Numer. Simul. 19, 3820–3826 (2014)

    Article  MathSciNet  Google Scholar 

  14. Moussa, N., Daoudia, A.K.: Numerical study of two classes of cellular automaton models for traffic flow on a two-lane roadway. Eur. Phys. B 31, 413–420 (2003)

    Article  Google Scholar 

  15. 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, 1205–1211 (2012)

    Article  MathSciNet  Google Scholar 

  16. 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 

  17. Pipes, L.A.: An operational analysis of traffic dynamic. J. Appl. Phys. 24, 274–281 (1953)

    Article  MathSciNet  Google Scholar 

  18. Bagdadi, O., Varhelyi, A.: Development of a method for detecting jerks in safety critical events. Accid. Anal. Prev. 50, 83–91 (2013)

    Article  Google Scholar 

  19. Yu, S.W., Shi, Z.K.: An extended car-following model considering vehicular gap fluctuation. Measurement 70, 137–147 (2015)

  20. Newell, G.F.: Nonlinear effects in the dynamics of car following. Oper. Res. 9, 209–229 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  21. Tang, T.Q., Huang, H.J., Shang, H.Y.: A new macro model for traffic flow with the onsideration of the driver’s forecast effect. Phys. Lett. A 374, 1668–1672 (2010)

    Article  MATH  Google Scholar 

  22. Jiang, R., Wu, Q.S., Jia, B.: Intermittent unstable structures induced by incessant constant disturbances in the full velocity difference car-following model. Phys. D 237, 467–474 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  23. Bando, M., Haseba, 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 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  26. Ge, H.X., Cheng, R.J., Li, Z.P.: Two velocity difference model for a car following theory. Phys. A 387, 5239–5245 (2008)

    Article  Google Scholar 

  27. Ge, J.L., Orosz, G.: Dynamics of connected vehicle systems with delayed acceleration feedback. Transp. Res. C 46, 46–64 (2014)

  28. Yu, S.W., Shi, Z.K.: Dynamics of connected cruise control systems considering velocity changes with memory feedback. Measurement 64, 34–48 (2015)

    Article  Google Scholar 

  29. Yu, S.W., Shi, Z.K.: An extended car-following model at signalized intersections. Phys. A 407, 152–159 (2014)

    Article  MathSciNet  Google Scholar 

  30. Yu, S.W., Shi, Z.K.: An improved car-following model with two preceding cars’ average speed. Int. J. Mod. Phys. C 26, 1550094 (2015)

    Article  MathSciNet  Google Scholar 

  31. Peng, G.H., Sun, D.H.: A dynamical model of car-following with the consideration of the multiple information of preceding cars. Phys. Lett. A 374, 1694–1698 (2010)

    Article  MATH  Google Scholar 

  32. Tang, T.Q., Li, C.Y., Huang, H.J., Shang, H.Y.: A new fundamental diagram theory with the individual difference of the drivers’ perception ability. Nonlinear Dyn. 67, 2255–2265 (2012)

    Article  Google Scholar 

  33. Li, Z.P., Li, W.Z., Xu, S.Z., Qian, Y.Q.: Analysis of vehicles’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)

  34. Zhu, W.X., Yu, R.L.: Nonlinear analysis of traffic flow on a gradient highway. Phys. A 391, 954 (2012)

    Article  Google Scholar 

  35. Yu, S.W., Shi, Z.K.: An improved car-following model considering headway changes with memory. Phys. A 421, 1–14 (2015)

    Article  Google Scholar 

  36. Lv, F., Zhu, H.B., Ge, H.X.: TDGL and mKdv equations for car-following model considering driver’s anticipation. Nonlinear Dyn. 77, 1245–1250 (2014)

    Article  MathSciNet  Google Scholar 

  37. Nagatani, T.: Jamming transition in the lattice models of traffic. Phys. Rev. E 59, 4857–4864 (1999)

    Article  Google Scholar 

  38. Nagatani, T.: Thermodynamic theory for the jamming transition in traffic flow. Phys. Rev. E 58, 4271–4276 (1998)

    Article  Google Scholar 

  39. Nagatani, T.: TDGL and mKdV equation for jamming transition in the lattice models of traffic. Phys. A 264, 581–592 (1999)

    Article  Google Scholar 

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

    Article  Google Scholar 

Download references

Acknowledgments

Supported by the National Natural Science Foundation of China under Grant No. 71571107, the Scientific Research Fund of Zhejiang Provincial, China (Grant Nos. LY15A020007, LY15E080013, LY16G010003). The Natural Science Foundation of Ningbo under Grant Nos. 2015A610167, 2015A610168 and the K.C. Wong Magna Fund in Ningbo University, China.

Author information

Authors and Affiliations

  1. Faculty of Maritime and Transportation, Ningbo University, Ningbo, 315211, China

    Liu Fangxun, Cheng Rongjun & Ge Hongxia

  2. Jiangsu Province Collaborative Innovation Center for Modern Urban Traffic Technologies, Nanjing, 210096, China

    Liu Fangxun, Cheng Rongjun & Ge Hongxia

  3. National Traffic Management Engineering and Technology Research Centre Ningbo University Sub-centre, Ningbo, 315211, China

    Liu Fangxun, Cheng Rongjun & Ge Hongxia

  4. Department of Civil and Architectural Engineering, City University of Hong Kong, Kowloon, 999077, Hong Kong, China

    Lo Siuming

Authors
  1. Liu Fangxun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cheng Rongjun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ge Hongxia
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lo Siuming
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cheng Rongjun.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fangxun, L., Rongjun, C., Hongxia, G. et al. An improved car-following model considering the influence of optimal velocity for leading vehicle. Nonlinear Dyn 85, 1469–1478 (2016). https://doi.org/10.1007/s11071-016-2772-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-016-2772-7

Keywords

Search

Navigation