Skip to main content
SpringerLink
Log in

An extended continuum model incorporating the electronic throttle dynamics for traffic flow

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

Abstract

This study develops a novel continuum model with consideration of the effect of electronic throttle (ET) dynamics to capture the behaviour of vehicles in traffic flow. In particular, the continuum model is proposed by incorporating the opening angle of ET based on the throttle-based full velocity difference model. Theoretical analyses including stability, negative velocity and shock wave are performed systematically. Numerical experiments and comparisons are conducted to verify the performance of the proposed continuum model. Results show that the steady-state performance of the proposed model is improved with respect to the stability. In addition, the proposed model is effective to rapidly dissipate the effect of external perturbation. Also, the phenomenon of negative velocity can be avoided by the proposed model.

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
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Davoodi, N., Soheili, A.R., Hashemi, S.M.: A macro-model for traffic flow with consideration of driver’s reaction time and distance. Nonlinear Dyn. 83(3), 1621–1628 (2016)

    Article  MathSciNet  Google Scholar 

  2. Li, Y.F., Zhang, L., Zheng, H., et al.: Nonlane-discipline-based car-following model for electric vehicles in transportation-cyber-physical systems. IEEE Trans. Intell. Transp. Syst. 19(1), 38–47 (2018)

    Article  Google Scholar 

  3. Gupta, A.K., Katiyar, V.K.: A new multi-class continuum model for traffic flow. Transportmetrica 3(1), 73–85 (2007)

    Article  Google Scholar 

  4. Tang, T.Q., Zhang, J., Liu, K.: A speed guidance model accounting for the driver’s bounded rationality at a signalized intersection. Physica A 473, 45–52 (2017)

    Article  Google Scholar 

  5. 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(15–16), 1694–1698 (2010)

    Article  MATH  Google Scholar 

  6. Li, Y.F., Zhang, L., Peeta, S., et al.: 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 

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

    Article  Google Scholar 

  8. Tang, T.Q., Wang, Y.P., Yang, X.B., et al.: A new car-following model accounting for varying road condition. Nonlinear Dyn. 70(2), 1397–1405 (2012)

    Article  MathSciNet  Google Scholar 

  9. Li, Y.F., Zhang, L., Zhang, B., et al.: Non-lane-discipline-based car-following model considering the effect of visual angle. Nonlinear Dyn. 85(3), 1901–1912 (2016)

    Article  Google Scholar 

  10. Ou, H., Tang, T.Q.: An extended two-lane car-following model accounting for inter-vehicle communication. Physica A 495, 260–268 (2018)

    Article  Google Scholar 

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

    Article  Google Scholar 

  12. Tang, T.Q., Yi, Z.Y., Zhang, J., Zheng, N.: Modeling the driving behavior at a signalized intersection with the information of remaining green time. IET Intelligent Transport Systems 11, 596–603 (2017)

    Article  Google Scholar 

  13. Lighthill, M.J., Whitham, G.B.: On kinematic waves II. A theory of traffic flow on long crowded roads. Proc. R. Soc. Lond. Ser. A 229(1178), 317–345 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  14. Richards, P.I.: Shock waves on the highway. Oper. Res. 4(1), 42–51 (1956)

    Article  MathSciNet  Google Scholar 

  15. Payne, H.J.: Models of freeway traffic and control. In: Bekey, G.A. (ed.) Mathematical Models of Public System. Simulation Councils Proceedings Series, vol. 1, pp. 51-61 (1971)

  16. Daganzo, C.F.: Requiem for second-order fluid approximation of traffic flow. Transp. Res. B 29(4), 277–286 (1995)

    Article  Google Scholar 

  17. Li, Y.F., 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), 1–11 (2017)

    Article  MATH  Google Scholar 

  18. 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 

  19. Ge, H.X., Zheng, P.J., Lo, S.M., et al.: TDGL equation in lattice hydrodynamic model considering driver’s physical delay. Nonlinear Dyn. 76(1), 441–445 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  20. Gupta, A.K., Dhiman, I.: Phase diagram of a continuum traffic flow model with a static bottleneck. Nonlinear Dyn. 79, 663–671 (2015)

    Article  MathSciNet  Google Scholar 

  21. Li, Y.F., Zhang, L., Peeta, S., et al.: A car-following model considering the effect of electronic throttle opening angle under connected environment. Nonlinear Dyn. 85(4), 2115–2125 (2016)

    Article  Google Scholar 

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

    Article  Google Scholar 

  23. Jiang, R., Wu, Q.S., Zhu, Z.J.: Full velocity difference model for a car-following theory. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 64(1), 017101–017105 (2001)

    Article  Google Scholar 

  24. 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 

  25. Ou, H., Tang, T.Q.: Impacts of moving bottlenecks on traffic flow. Physica A 500, 131–138 (2018)

    Article  MathSciNet  Google Scholar 

  26. Ioannou, P., Xu, Z.: Throttle and brake control system for automatic vehicle following. Intel. Veh. Highw. Syst. J. 1(4), 345–377 (1994)

    Google Scholar 

  27. Pipes, L.A.: Vehicle accelerations in the hydrodynamic theory of traffic flow. Transp. Res. 3(2), 229–234 (1969)

    Article  Google Scholar 

  28. Castillo, J.M.D., Benítez, F.G.: On the functional form of the speed-density relationship—I: general theory. Transp. Res. B 29(5), 373–389 (1995)

    Article  Google Scholar 

  29. Herrmann, M., Kerner, B.S.: Local cluster effect in different traffic flow models. Physica A 255(1–2), 163–188 (1998)

    Article  Google Scholar 

  30. Kerner, B.S., Konhäuser, P.: Cluster effect in initially homogeneous traffic flow. Phys. Rev. E 48(4), R2335–R2338 (1993)

    Article  Google Scholar 

Download references

Acknowledgements

This work is jointly supported by the National Natural Science Foundation of China under Grants 61773082 and 71301095, by the Key Project of Basic Science and Emerging Technology of Chongqing under Grant cstc2017jcyjBX0018, by the Key Project of Crossing and Emerging Area of CQUPT under Grant A2018-02, by the Venture & Innovation Support Program for Chongqing Overseas Returnees under Grant CX2017044, and by the National Key Research and Development Program under Grant 2016YFB0100906. The authors make equal contribution to this paper.

Author information

Authors and Affiliations

  1. Key Laboratory of Industrial Internet of Things & Networked Control, Ministry of Education, College of Automation, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Yongfu Li & Huan Yang

  2. Industrial IoT Collaborative Innovation Center, College of Automation, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Yongfu Li & Huan Yang

  3. College of Automation and Center for Automotive Electronics and Embedded System, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Bin Yang & Taixiong Zheng

  4. Shanghai Key Laboratory of Financial Information Technology, Shanghai University of Finance and Economics, Shanghai, 200433, China

    Chao Zhang

Authors
  1. Yongfu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huan Yang
    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. Chao Zhang
    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., Yang, H., Yang, B. et al. An extended continuum model incorporating the electronic throttle dynamics for traffic flow. Nonlinear Dyn 93, 1923–1931 (2018). https://doi.org/10.1007/s11071-018-4298-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-018-4298-7

Keywords

Search

Navigation