Skip to main content
SpringerLink
Log in

A new lattice hydrodynamic model considering the effects of bilateral gaps on vehicular traffic flow

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

Abstract

This study proposes a new lattice hydrodynamic model considering the effects of bilateral gaps on a road without lane discipline. In particular, a lattice hydrodynamic model is proposed to capture the impacts from the lateral gaps of the right-side and left-side sites of the considered lattice sites. Linear stability analysis of the proposed model is performed using the perturbation method to obtain the stability condition. Nonlinear analysis of the proposed model is performed using the reductive perturbation method to derive the modified Korteweg–de Vries (mKdV) equation to characterize the density wave propagation. Results from numerical experiments illustrate that the smoothness and stability of the proposed model are improved compared with the model that considers the effect of unilateral gap. Also, the proposed model is able to more quickly dissipate the effect of perturbation occurring in the vehicular 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.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Brackstone, M., McDonald, M.: Car-following: a historical review. Transp. Res. Part F 2(4), 181–196 (1999)

    Article  Google Scholar 

  2. Wilson, R.E., Ward, J.A.: Car-following models: fifty years of linear stability analysis—a mathematical perspective. Transp. Plan. Technol. 34(1), 3–18 (2010)

    Article  Google Scholar 

  3. Li, Y., Sun, D.: Microscopic car-following model for the traffic flow: the state of the art. J. Control Theory Appl. 10(2), 133–143 (2012)

    Article  MathSciNet  Google Scholar 

  4. Saifuzzaman, M., Zheng, Z.: Incorporating human-factors in car-following models: a review of recent developments and research needs. Transp. Res. Part C 48, 379–403 (2014)

    Article  Google Scholar 

  5. Li, Y., Zhang, L., Zheng, T., Li, Y.: Lattice hydrodynamic model based delay feedback control of vehicular traffic flow considering the effects of density change rate difference. Commun. Nonlinear Sci. Numer. Simul. 29(1–3), 224–232 (2015)

    Article  MathSciNet  Google Scholar 

  6. Bando, M., Hasebe, K., Nakayama, A., Shibata, A., Sugiyama, Y.: Dynamics model of traffic congestion and numerical simulation. Phys. Rev. E 1(51), 1035–1042 (1995)

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

    Article  Google Scholar 

  8. Jiang, R., Wu, Q.S., Zhu, Z.J.: Full velocity difference model for a car-following theory. Phys. Rev. E 64, 017101–017105 (2001)

    Article  Google Scholar 

  9. Li, Y., Sun, D., Liu, W., Zhang, M., Zhao, M., Liao, X., Tang, L.: Modeling and simulation for microscopic traffic flow based on multiple headway, velocity and acceleration difference. Nonlinear Dyn. 66(1–2), 15–28 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Tian, J., Jia, B., Li, X., Gao, Z.: A new car-following model considering velocity anticipation. Chin. Phys. B 19(1), 010511–010519 (2010)

    Article  Google Scholar 

  11. Tang, T., Wang, Y., Yang, X., Wu, Y.: A new car-following model accounting for varying road condition. Nonlinear Dyn. 70(2), 1397–1405 (2012)

    Article  MathSciNet  Google Scholar 

  12. Li, Y., Zhu, H., Cen, M., Li, Y., Li, R., Sun, D.: On the stability analysis of microscopic traffic car-following model: a case study. Nonlinear Dyn. 74(1–2), 335–343 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  13. Tang, T., Shi, W., Shang, H., Wang, Y.: A new car-following model with consideration of inter-vehicle communication. Nonlinear Dyn. 76(4), 2017–2023 (2014)

    Article  Google Scholar 

  14. Chandra, S., Kumar, U.: Effect of lane width on capacity under mixed traffic conditions in India. J. Transp. Eng. 129(2), 155–160 (2003)

    Article  Google Scholar 

  15. Gunay, B.: Car following theory with lateral discomfort. Transp. Res. Part B 41(7), 722–735 (2007)

    Article  Google Scholar 

  16. Jin, S., Wang, D., Tao, P., Li, P.: Non-lane-based full velocity difference car following model. Phys. A 389(21), 4654–4662 (2010)

    Article  Google Scholar 

  17. Li, Y., Zhang, L., Peeta, S., Pan, H., Zheng, T., Li, Y., He, X.: Non-lane-discipline-based car-following model considering the effects of two-sided lateral gaps. Nonlinear Dyn. 80(1–2), 227–238 (2015)

    Article  MATH  Google Scholar 

  18. Li, Y., Zhang, L., Zheng, H., He, X., Peeta, S., Zheng, T., Li, Y.: Evaluating the energy consumption of electric vehicles based on car-following model under non-lane discipline. Nonlinear Dyn. 82(1), 1–13 (2015)

    MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  20. Nagatani, T.: TDGL and MKdV equations for jamming transition in the lattice models of traffic. Phys. A 264(3), 581–592 (1999)

    Article  MathSciNet  Google Scholar 

  21. Li, Z., Li, X., Liu, F.: Stabilization analysis and modified KdV equation of lattice models with consideration of relative current. Int. J. Mod. Phys. C 19(08), 1163–1173 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  22. Zhu, W.X., Chi, E.X.: Analysis of generalized optimal current lattice model for traffic flow. Int. J. Mod. Phys. C 19(05), 727–739 (2008)

    Article  MATH  Google Scholar 

  23. Peng, G., Cai, X., Liu, C., Cao, B.: A new lattice model of traffic flow with the consideration of the honk effect. Int. J. Mod. Phys. C 22(09), 967–976 (2011)

    Article  MATH  Google Scholar 

  24. Peng, G.: A new lattice model of traffic flow with the consideration of individual difference of anticipation driving behavior. Commun. Nonlinear Sci. Numer. Simul. 18(10), 2801–2806 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  25. Ge, H.X., Cheng, R.J., Lei, L.: The theoretical analysis of the lattice hydrodynamic models for traffic flow theory. Phys. A 389(14), 2825–2834 (2010)

    Article  Google Scholar 

  26. Wang, T., Gao, Z., Zhao, X., Tian, J., Zhang, W.: Flow difference effect in the two-lane lattice hydrodynamic model. Chin. Phys. B 21, 070507–070516 (2012)

  27. Ge, H., Cui, Y., Zhu, K., Cheng, R.: The control method for the lattice hydrodynamic model. Commun. Nonlinear Sci. Numer. Simul. 22(1), 903–908 (2015)

    Article  Google Scholar 

  28. Li, Z., Zhang, R., Xu, S., Qian, Y.: 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(1), 52–63 (2015)

    Article  MathSciNet  Google Scholar 

  29. Peng, G., Cai, X., Cao, B., Liu, C.: Non-lane-based lattice hydrodynamic model of traffic flow considering the lateral effects of the lane width. Phys. Lett. A 375(30), 2823–2827 (2011)

    Article  MATH  Google Scholar 

  30. Peng, G., Nie, F., Cao, B.: A driver’s memory lattice model of traffic flow and its numerical simulation. Nonlinear Dyn. 67(3), 1811–1815 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  31. Ge, H., Zheng, P., Lo, S., Cheng, R.: TDGL equation in lattice hydrodynamic model considering driver’s physical delay. Nonlinear Dyn. 76(1), 441–445 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  32. Wang, T., Gao, Z., Zhang, J.: Stabilization effect of multiple density difference in the lattice hydrodynamic model. Nonlinear Dyn. 73(4), 2197–2205 (2013)

    Article  MathSciNet  Google Scholar 

  33. 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), 27–34 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  34. 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)

    Article  Google Scholar 

Download references

Acknowledgments

Thanks to the support from the project by the National Natural Science Foundation of China (Grant No. 61304197), the Scientific and Technological Talents of Chongqing (Grant No. cstc2014kjrc-qnrc30002), the Key Project of Application and Development of Chongqing (Grant No. cstc2014yykfB40001), Wenfeng Talents of Chongqing University of Posts and Telecommunications, “151” Science and Technology Major Project of Chongqing-General Design and Innovative Capability of Full Information Based Traffic Guidance and Control System (Grant No. cstc2013jcsf-zdzxqqX0003), National Key Research and Development Program (2016YFB0100900), and the Doctoral Start-up Funds of Chongqing University of Posts and Telecommunication (Grant No. A2012-26).

Author information

Authors and Affiliations

  1. Chongqing Collaborative Innovation Center for Information Communication Technology, College of Automation, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Yongfu Li, Yu Song, Huizong Feng & Yinguo Li

  2. College of Advanced Manufacturing, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Bin Yang & Taixiong Zheng

Authors
  1. Yongfu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bin Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Taixiong Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Huizong Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Yinguo Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yongfu Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Y., Song, Y., Yang, B. et al. A new lattice hydrodynamic model considering the effects of bilateral gaps on vehicular traffic flow. Nonlinear Dyn 87, 1–11 (2017). https://doi.org/10.1007/s11071-016-2940-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-016-2940-9

Keywords

Search

Navigation